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7  GROUP C1—MATERIALS

C.100 - May 17


Object:


These directives enable the user to specify the materials.


Syntax:
    "MATE" . . .

Comments:


These directives are described in detail on the following pages.


Do not forget the corresponding dimensioning (GBA_0070).

7.1  GENERALITIES ABOUT MATERIALS

C.100 - Aug 13


Object:


This instruction enables the user to enter the properties of various materials.


Syntax:

    "MATE"   (  < "LOI" numldc >  . . .  )
LOI

This keyword announces that a number will be assigned to the constitutive law whose definition follows.
numldc

Number of the constitutive law.

Comments:


The word "MATE" is compulsory and may only be used once, at the beginning of the data sequence relative to the instruction MATERIALS.


The numbers introduced by the "LOI" directive may be in arbitrary order, and some numbers may be missing. This is very useful in the case of multiple materials: one can add or move material data in the input file without changing the number of the corresponding material law (see "MULT", page C.380).


If the "LOI" directive is absent, the number automatically attributed to the law by EUROPLEXUS is the index of the material in the order its constitutive law is listed in the input data.

The material models are (in alphabetical order):


numbernamereflaw of behaviour
74ABSE  
53ADCJ7.7.25hypothetical core disruptive accident with law of type JWL for the bubble
34ADCR7.7.19containment accident (fast neutrons)
47ADFM7.7.32advection-diffusion fluid
71APPU7.4Material for elements of type PPUI
32ASSE motor asservissement (meca)
11BETO7.6.12concrete (NAHAS model)
57BILL7.7.26LIBRE (user’s free particle material), or FLUIDE (isothermal fluid particle: c = cte)
29BL3S7.6.61reinforced concrete for discrete elements
20BLMT7.6.13DYNAR LMT Concrete
75BOIS7.6.27wood for shock adsorbing (only compression)
121BPEL7.6.13model for prestressing cable-concrete friction
114BREC7.7.12data for pipeline break
59BUBB7.7.38Balloon model for air blast simulations
89CAMC7.6.44Modified Cam-clay material
8CAVI isothermal fluid with cavitation
68CDEM7.7.39Discrete Equation Method for Combustion
64CHAN7.6.22Multi-layer with the CHANG-CHANG criterion
51CHOC7.7.22Shock waves, Rankine-Hugoniot equation
21CLVF7.8.33Boundary conditions for finite volumes
90CLAY7.6.45Modified Cam-clay material (backward fully implicit algorithm, viscoplastic regularization)
88COMM7.6.43Composite material (linear orthotropic), Ispra implementation
113CREB  
58CRIT7.6.18damage criteria calculation : PY (damage of type P/Y), DUCTile (ductile damage)
100CRTM7.6.57Composite manufactured by RTM process
109DADC7.6.16Dynamic Anisotropic Damage Concrete
110DEMS7.7.40Discrete Equation Method for Two Phase Stiffened Gases
38DONE7.6.40viscoplastic material
111DPDC7.6.17dynamic plastic damage concrete
87DPSF7.6.42Drucker Prager with softening and viscoplastic regularization
83DRPR7.6.51Drucker Prager Ispra model
12DRUC7.6.6Drucker-Prager
19DYNA7.6.7dynamic Von Mises isotropic rate-dependent
22EAU7.7.9two-phase water (liquid + vapour)
115ENGR7.6.20elastic gradient damage material
105EOBT7.6.19anisotropic damage of concrete
49EXVL7.7.20hydrogen explosion Van Leer
17FANT7.6.30phantom: ignore the associated elements
27FLFA7.7.15rigid tube bundles
86FLMP7.7.35Fluid multi-phase
7FLUI7.7.2isothermal fluid ( c = cte )
36FLUT7.7.30fluid, to be specified by the user
93FOAM7.6.52Aluminium foam (for crash simulations)
80FUNE7.6.46specialized cable material (no compression resistance)
9GAZP7.7.4perfect gas
118GGAS7.7.1generic ideal gas material
44GLAS7.6.60glass with strain-rate effect
116GLIN7.6.3generic linear material
92GLRC7.6.53Plasticity with kinematic softening for orthotropic shells. Global plastic criterion.
52GPDI7.7.23diffusive perfect gas Van Leer
117GPLA7.6.4generic plastic material
48GVDW7.7.28Van Der Waals gas
40GZPV7.7.24perfect gas for Van Leer
28HELI7.7.10helium
3HILL7.6.59Isotropic plasticity associated with a HILL criterion and with a orthotropic elastic behaviour
95HYPE7.6.54hyperelastic material (Model of Mooney-Rivlin, Hart-Smith and Ogden)
16IMPE7.8impedance
43IMPV7.8.21impedance Van Leer
4ISOT7.6.7isotropic Von Mises
108JCLM7.6.65Johnson-Cook with Damage Lemaitre-Chaboche for SPHC
91JPRP7.11for bushing elements
50JWL7.7.21explosion (Jones-Wilkins-Lee model)
66JWLS7.7.29Explosion (Jones-Wilkins-Lee for solids)
72LEM17.6.9Von Mises isotropic coupled with damage (type Lemaitre)
13LIBR7.6.31free (material defined by the user)
1LINE7.6.1linear elasticity
23LIQU7.7.14incompressible (or quasi-) fluid
70LMC27.6.11Von Mises isotropic coupled with damage (Lemaitre) with strain-rate sensitivity
63LSGL7.6.62laminated security glass material
26MASS7.6.29mass of a material point
85MAZA7.6.15Mazars-linear elastic law with damage
82MCFF7.7.34multicomponent fluid material (far-field)
81MCGP7.7.33multicomponent fluid material (perfect gas)
60MCOU7.6.21Linear multi-layer homogenised through the thickness
45MECA7.9mechanism associated to articulated systems
33MHOM7.7.16homogenization
97MINT7.6.55Material for interface element
31MOTE motor force or couple (meca)
25MULT7.7.13multiple materials (coupled monodim.)
10NAH27.7.7sodium-water reaction
18ODMS7.6.26nonlinear damage with orthotropy (ODM)
42ORTE7.6.25linear damage with orthotropy
41ORTH7.6.23linear orthotropic in user system
46ORTS7.6.24linear elastic orthotropic with local reference frame
2PARF7.6.7perfectly plastic Von Mises
56PARO7.7.11friction and heat exchange for pipeline walls
96PBED particle bed
6POST post-rupture (beton)
69PRGL7.7.27Porous jelly for the particles
39PUFF7.7.17equation of state of type "PUFF"
123RESG7.6.4Material for RL3D spring element in the global reference frame
61RESL7.6.1Material for RL3D spring element in the local reference frame
125RIGI7.6.67Rigid material (for rigid bodies)
54RSEA7.8.13reaction sodium-water with three constituents
103SG2P  
112SGBN  
104SGMP  
107SLIN7.6.64Linear Damage for SPHC
99SLZA7.6.56Steinberg-Lund-Zerilli-Armstrong
106SMAZ7.6.63Mazars Damage for SPHC
24SOUR7.7.6imposed pressure in a continuum element
30STGN7.6.8Steinberg - Guinan
102STIF  
94SUPP7.5support
101TAIT  
5TETA7.6.7Von Mises dependent upon temperature
98TVMC7.6.58elastoplastic short fibres with damage
37VM1D7.6.39material for elements of type "ED1D"
35VM237.6.38Von Mises elasto-plastic radial return
2/4/5/19VMIS7.6.7Von Mises materials
76VMJC7.6.47Johnson-Cook
78VMLP7.6.48Ludwig-Prandtl
79VMLU7.6.49Ludwik
84VMSF7.6.41Von Mises with softening and viscoplastic regularization
77VMZA7.6.50Zerilli-Armstrong
120VPJC7.6.66visco-plastic Johnson-Cook
67ZALM7.6.10Zerilli-Armstrong with damage Lemaitre-Chaboche
 


The "FANT" material may be allocated to any element, with the effect of ’eliminating’ it from the mesh, as far as mechanical resistance is concerned.


The different elements may use the following materials (defined by their numbers):

 AVAILABLE MATERIALS FOR EACH ELEMENT
 ====================================

 NO. | ELEMENT | AVAILABLE MATERIALS
 ----|---------|----------------------------
   1 |  COQU   | LINE PARF ISOT TETA DYNA ORTH
   2 |  TRIA   | LINE PARF ISOT TETA POST FLUI CAVI GAZP NAH2 BETO
     |         | DRUC DYNA EAU  LIQU SOUR MULT FLFA STGN ADCR VM23
     |         | PUFF ORTH JWL  CHOC ADCJ RSEA CRIT BUBB JWLS ZALM
     |         | LMC2 LEM1 BOIS VMJC VMZA VMLP VMLU DRPR VMSF DPSF
     |         | CAMC CLAY SGMP ENGR VPJC
   3 |  BARR   | LINE PARF ISOT DYNA
   4 |  PONC   | LINE PARF ISOT
   5 |  MEMB   | LINE
   6 |  CUBB   | LINE PARF ISOT DPDC
   7 |  CL2D   | IMPE CLVF IMPV
   8 |  CAR1   | LINE PARF ISOT TETA POST FLUI CAVI GAZP NAH2 BETO
     |         | DRUC DYNA EAU  LIQU SOUR MULT FLFA STGN ADCR VM23
     |         | DONE PUFF ORTH JWL  CHOC ADCJ RSEA CRIT BUBB JWLS
     |         | ZALM LMC2 LEM1 BOIS VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY SGMP VPJC
   9 |  CAR4   | LINE PARF ISOT TETA POST FLUI CAVI GAZP BETO DRUC
     |         | DYNA EAU  MULT FLFA STGN VM23 DONE PUFF ORTH GLAS
     |         | CHOC ADCJ CRIT BUBB LSGL ZALM LMC2 LEM1 BOIS VMJC
     |         | VMZA VMLP VMLU DRPR VMSF DPSF CAMC CLAY HYPE ENGR
     |         | VPJC
  10 |  COQC   | LINE PARF ISOT ORTH
  11 |  CUBE   | LINE ISOT TETA FLUI GAZP NAH2 DRUC DESM DYNA BLMT
     |         | EAU  LIQU SOUR MULT FLFA STGN ADCR VM23 PUFF ORTH
     |         | ORTE GLAS ORTS JWL  CHOC ADCJ RSEA ORPE CRIT BUBB
     |         | LSGL JWLS ZALM LMC2 LEM1 BOIS VMJC VMZA VMLP VMLU
     |         | DRPR VMSF MAZA DPSF CAMC CLAY FOAM HYPE PBED TVMC
     |         | SLZA CRTM SGMP EOBT DADC DPDC BDBM VPJC ORTP
  12 |  COQ3   | LINE ISOT TETA DYNA MCOU CHAN
  13 |  CUB6   | LINE ISOT TETA FLUI GAZP DRUC DYNA BLMT MULT STGN
     |         | VM23 PUFF ORTH ORTE GLAS ORTS CHOC ORPE CRIT LSGL
     |         | BOIS VMJC DRPR VMSF DPSF CAMC CLAY FOAM HYPE SLZA
     |         | CRTM VPJC
  14 |  COQ4   | LINE ISOT TETA DYNA MCOU CHAN
  15 |  FS2D   |
  16 |  FS3D   |
  17 |  POUT   | LINE ISOT DYNA
  18 |  CL3D   | IMPE CLVF
  19 |  BR3D   | LINE PARF ISOT DYNA
  20 |  PR6    | LINE HILL ISOT TETA FLUI GAZP BETO DRUC DESM DYNA
     |         | BLMT MULT VM23 PUFF ORTH ORTE ORTS ORPE CRIT ZALM
     |         | LMC2 LEM1 BOIS VMJC DRPR VMSF MAZA DPSF CAMC CLAY
     |         | FOAM HYPE SLZA CRTM EOBT DADC VPJC DPDC
  21 |  TETR   | LINE HILL ISOT TETA FLUI GAZP NAH2 DRUC DESM DYNA
     |         | BLMT EAU  LIQU SOUR MULT FLFA ADCR VM23 PUFF ORTH
     |         | ORTE ORTS JWL  CHOC ADCJ RSEA ORPE CRIT BUBB JWLS
     |         | ZALM BOIS VMJC DRPR VMSF MAZA DPSF CAMC CLAY FOAM
     |         | HYPE SLZA CRTM SGMP EOBT DADC ENGR VPJC DPDC
  22 |  TUBE   | FLUI GAZP NAH2 EAU  LIQU SOUR MULT HELI ADCR GVDW
     |         | JWL  RSEA PARO JWLS
  23 |  TUYA   | LINE ISOT FLUI GAZP NAH2 EAU  LIQU SOUR MULT HELI
     |         | ADCR GVDW RSEA PARO
  24 |  CL1D   | IMPE CLVF
  25 |  BIFU   | FLUI GAZP NAH2 EAU  LIQU SOUR ADCR GVDW RSEA
  26 |  CAVI   | FLUI GAZP NAH2 EAU  LIQU SOUR MULT ADCR GVDW RSEA
     |         | PARO
  27 |  PRIS   | LINE HILL ISOT TETA FLUI GAZP NAH2 DRUC DESM DYNA
     |         | BLMT EAU  SOUR MULT FLFA ADCR VM23 PUFF ORTH ORTE
     |         | ORTS JWL  CHOC ADCJ RSEA ORPE CRIT BUBB JWLS ZALM
     |         | LMC2 LEM1 BOIS VMJC DRPR VMSF DPSF CAMC CLAY FOAM
     |         | HYPE CRTM SGMP EOBT VPJC DPDC
  28 |  PMAT   | LINE MASS
  29 |  CL3T   | IMPE CLVF
  30 |  CUB8   | LINE HILL ISOT TETA FLUI GAZP DRUC DESM ODMS DYNA
     |         | BLMT MULT STGN VM23 PUFF ORTH ORTE GLAS ORTS CHOC
     |         | ORPE CRIT LSGL ZALM LMC2 LEM1 BOIS VMJC VMZA VMLP
     |         | VMLU DRPR VMSF MAZA DPSF CAMC CLAY FOAM HYPE SLZA
     |         | CRTM EOBT DADC DPDC ENGR BDBM VPJC ORTP
  31 |  CLTU   | IMPE CLVF
  32 |  APPU   | APPU SUPP
  33 |  MECA   | MOTE ASSE MECA ABSE
  34 |  QAX1   | FLUI GAZP BUBB
  35 |  QPPS   | LINE ISOT DYNA VM23 DONE GLAS MCOU LSGL CHAN LEM1
     |         | VMJC VMZA VMLP VMLU VMSF DPSF GLRC SLZA VPJC
  36 |  FHQ2   | MHOM
  37 |  FHT2   | MHOM
  38 |  Q92    | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  39 |  Q93    | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  40 |  COQI   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | COMM VPJC
  41 |  TUBM   | FLUI GAZP NAH2 EAU  LIQU ADCR GVDW RSEA GAZD TAIT
     |         | STIF SG2P SGMP SGBN
  42 |  CL23   | IMPE
  43 |  ED01   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | VPJC
  44 |  ED1D   | VM1D
  45 |  TVL1   | GZPV GVDW EXVL GPDI
  46 |  CVL1   | GZPV GVDW EXVL GPDI
  47 |  CMC3   | LINE ISOT BETO ORTH
  48 |  FS3T   |
  49 |  Q92A   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  50 |  CL3L   |
  51 |  T3GS   | LINE ISOT TETA DYNA VM23 DONE GLAS LSGL LEM1 VMJC
     |         | VMZA VMLP VMLU VMSF DPSF GLRC VPJC
  52 |  FLU1   | FLUT BUBB
  53 |  FLU3   | FLUT BUBB
  54 |  PFEM   | FLUI
  55 |  FL2S   | FLUT BUBB FLMP
  56 |  ED41   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | VPJC
  57 |  ADC8   | ADFM
  58 |  ADQ4   | ADFM
  59 |  FL3S   | FLUT BUBB FLMP
  60 |  CL2S   | IMPE FLUT
  61 |  CL3S   | IMPE FLUT
  62 |  CL32   | IMPE
  63 |  CL33   | IMPE
  64 |  FL23   | FLUT BUBB FLMP
  65 |  FL24   | FLUT BUBB FLMP
  66 |  FL34   | FLUT BUBB FLMP
  67 |  FL35   | FLUT BUBB FLMP
  68 |  FL36   | FLUT BUBB FLMP
  69 |  FL38   | FLUT BUBB FLMP
  70 |  CL22   | IMPE FLUT IMPV MCFF
  71 |  Q41    | VM23 DONE LSGL VMSF DPSF
  72 |  Q42    | VM23 DONE LSGL VMSF DPSF
  73 |  Q41N   | VM23 DONE LSGL VMSF DPSF
  74 |  Q42N   | VM23 DONE LSGL VMSF DPSF
  75 |  Q41L   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  76 |  Q42L   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  77 |  Q95    | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
  78 |  CL3I   | IMPE FLUT MCFF
  79 |  BILL   | LINE ISOT PUFF BILL PRGL MAZA
  80 |  ELDI   | BL3S
  81 |  CUVL   | GZPV GVDW EXVL GPDI
  82 |  PRVL   | GZPV GVDW EXVL GPDI
  83 |  DST3   | LINE HILL ISOT TETA DYNA VM23 DONE GLAS ORTS MCOU
     |         | LSGL CHAN LEM1 VMJC VMZA VMLP VMLU VMSF DPSF HYPE
     |         | SLZA VPJC
  84 |  DKT3   | LINE ISOT DYNA VM23 DONE GLAS MCOU LSGL CHAN LEM1
     |         | VMJC VMZA VMLP VMLU VMSF DPSF GLRC SLZA VPJC
  85 |  SHB8   | LINE ISOT DYNA ZALM LMC2 LEM1 SLZA
  86 |  XCUB   | LINE PARF ISOT ODMS ORTE VMJC VMSF
  87 |  XCAR   | LINE PARF ISOT VMJC VMSF
  88 |  PROT   | LINE ISOT
  89 |  SPHC   | LINE ISOT LEM1 SMAZ SLIN JCLM
  90 |  Q4G4   | LINE ISOT
  91 |  CQD4   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | COMM VPJC
  92 |  CQD9   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | COMM VPJC
  93 |  CQD3   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | COMM VPJC
  94 |  CQD6   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU VMSF DPSF
     |         | COMM VPJC
  95 |  CLD3   | IMPE
  96 |  CLD6   | IMPE
  97 |  MC23   | MCGP
  98 |  MC24   | MCGP
  99 |  CL3Q   | IMPE FLUT MCFF
 100 |  Q42G   | VM23 DONE
 101 |  MC34   | MCGP
 102 |  MC35   | MCGP
 103 |  MC36   | MCGP
 104 |  MC38   | MCGP
 105 |  MS24   | LINE
 106 |  S24    | LINE
 107 |  MS38   | LINE
 108 |  S38    | LINE
 109 |  FUN2   | VM23 DONE VMJC VMZA VMLP VMLU FUNE VPJC
 110 |  FUN3   | VM23 DONE VMJC VMZA VMLP VMLU FUNE VPJC
 111 |  Q4GR   | LINE HILL ISOT TETA DYNA VM23 DONE GLAS MCOU LSGL
     |         | CHAN LEM1 VMJC VMZA VMLP VMLU VMSF DPSF GLRC SLZA
     |         | VPJC
 112 |  Q4GS   | LINE HILL ISOT TETA DYNA VM23 DONE GLAS ORTS MCOU
     |         | LSGL CHAN LEM1 VMJC VMZA VMLP VMLU VMSF DPSF GLRC
     |         | HYPE SLZA VPJC
 113 |  RL3D   | RESL RESG
 114 |  BSHT   | JPRP
 115 |  BSHR   | JPRP
 116 |  TUYM   | FLUI GAZP NAH2 EAU  LIQU ADCR GVDW RSEA GAZD TAIT
     |         | STIF SG2P SGMP SGBN
 117 |  SH3D   | JPRP
 118 |  MAP2   |
 119 |  MAP3   |
 120 |  MAP4   |
 121 |  MAP5   |
 122 |  MAP6   |
 123 |  MAP7   |
 124 |  INT4   | LINE MINT
 125 |  INT6   | LINE MINT
 126 |  INT8   | LINE MINT
 127 |  SH3V   |
 128 |  MOY4   |
 129 |  MOY5   |
 130 |  ASHB   | LINE ISOT DYNA ZALM LMC2 LEM1 SLZA
 131 |  T3VF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 132 |  Q4VF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 133 |  CUVF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 134 |  PRVF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 135 |  TEVF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 136 |  PYVF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ BUBB JWLS CDEM
     |         | GAZD TAIT STIF SG2P SGMP DEMS SGBN CREB
 137 |  COQ2   | LINE ISOT TETA
 138 |  Q4MC   | LINE HILL ISOT DYNA ORTS ORPE
 139 |  T3MC   | LINE HILL ISOT DYNA VM23 ORTS ORPE LSGL VPJC
 140 |  DEBR   |
 141 |  INS6   |
 142 |  INS8   |
 143 |  P3ZT   | LINE HILL ISOT DYNA ORTS ORPE PIEZ
 144 |  C272   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
 145 |  C273   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
 146 |  BREC   | EAU  MULT BREC
 147 |  TUVF   | FLUI GAZP EAU  MULT ADCR GVDW JWL  ADCJ PARO JWLS
     |         | GAZD TAIT STIF SG2P SGMP SGBN
 148 |  TYVF   | LINE ISOT FLUI GAZP EAU  MULT ADCR GVDW JWL  ADCJ
     |         | PARO JWLS GAZD TAIT STIF SG2P SGMP SGBN
 149 |  BIVF   | FLUI GAZP EAU  ADCR GVDW JWL  ADCJ JWLS GAZD TAIT
     |         | STIF SG2P SGMP SGBN
 150 |  CAVF   | FLUI GAZP EAU  MULT ADCR GVDW JWL  ADCJ JWLS GAZD
     |         | TAIT STIF SG2P SGMP SGBN
 151 |  CL92   | IMPE
 152 |  CL93   | IMPE
 153 |  LIGR   | MECA
 154 |  RNFR   | BPEL
 155 |  C81L   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC
 156 |  C82L   | VM23 DONE GLAS LSGL VMJC VMZA VMLP VMLU DRPR VMSF
     |         | DPSF CAMC CLAY VPJC

  AVAILABLE ELEMENTS FOR EACH MATERIAL
  ====================================

  E AFTER MATERIAL INDICATES ERODIBLE.

 NO. | MATERIAL| AVAILABLE ELEMENTS
 ----|---------|----------------------------
   1 |  LINE E | COQU TRIA BARR PONC MEMB CUBB CAR1 CAR4 COQC CUBE
     |         | COQ3 CUB6 COQ4 POUT BR3D PR6  TETR TUYA PRIS PMAT
     |         | CUB8 QPPS CMC3 T3GS BILL DST3 DKT3 SHB8 XCUB XCAR
     |         | PROT SPHC Q4G4 MS24 S24  MS38 S38  Q4GR Q4GS INT4
     |         | INT6 INT8 ASHB COQ2 Q4MC T3MC P3ZT TYVF
   2 |  PARF E | COQU TRIA BARR PONC CUBB CAR1 CAR4 COQC BR3D XCUB
     |         | XCAR
   3 |  HILL   | PR6  TETR PRIS CUB8 DST3 Q4GR Q4GS Q4MC T3MC P3ZT
   4 |  ISOT E | COQU TRIA BARR PONC CUBB CAR1 CAR4 COQC CUBE COQ3
     |         | CUB6 COQ4 POUT BR3D PR6  TETR TUYA PRIS CUB8 QPPS
     |         | CMC3 T3GS BILL DST3 DKT3 SHB8 XCUB XCAR PROT SPHC
     |         | Q4G4 Q4GR Q4GS ASHB COQ2 Q4MC T3MC P3ZT TYVF
   5 |  TETA E | COQU TRIA CAR1 CAR4 CUBE COQ3 CUB6 COQ4 PR6  TETR
     |         | PRIS CUB8 T3GS DST3 Q4GR Q4GS COQ2
   6 |  POST   | TRIA CAR1 CAR4
   7 |  FLUI   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR TUBE TUYA BIFU
     |         | CAVI PRIS CUB8 QAX1 TUBM PFEM TUYM T3VF Q4VF CUVF
     |         | PRVF TEVF PYVF TUVF TYVF BIVF CAVF
   8 |  CAVI   | TRIA CAR1 CAR4
   9 |  GAZP   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR TUBE TUYA BIFU
     |         | CAVI PRIS CUB8 QAX1 TUBM TUYM T3VF Q4VF CUVF PRVF
     |         | TEVF PYVF TUVF TYVF BIVF CAVF
  10 |  NAH2   | TRIA CAR1 CUBE TETR TUBE TUYA BIFU CAVI PRIS TUBM
     |         | TUYM
  11 |  BETO E | TRIA CAR1 CAR4 PR6  CMC3
  12 |  DRUC E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8
  14 |  IFS    |
  15 |  DESM   | CUBE PR6  TETR PRIS CUB8
  16 |  IMPE   | CL2D CL3D CL1D CL3T CLTU CL23 CL2S CL3S CL32 CL33
     |         | CL22 CL3I CLD3 CLD6 CL3Q CL92 CL93
  18 |  ODMS   | CUB8 XCUB
  19 |  DYNA E | COQU TRIA BARR CAR1 CAR4 CUBE COQ3 CUB6 COQ4 POUT
     |         | BR3D PR6  TETR PRIS CUB8 QPPS T3GS DST3 DKT3 SHB8
     |         | Q4GR Q4GS ASHB Q4MC T3MC P3ZT
  20 |  BLMT   | CUBE CUB6 PR6  TETR PRIS CUB8
  21 |  CLVF   | CL2D CL3D CL1D CL3T CLTU
  22 |  EAU    | TRIA CAR1 CAR4 CUBE TETR TUBE TUYA BIFU CAVI PRIS
     |         | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF BREC TUVF
     |         | TYVF BIVF CAVF
  23 |  LIQU   | TRIA CAR1 CUBE TETR TUBE TUYA BIFU CAVI TUBM TUYM
  24 |  SOUR   | TRIA CAR1 CUBE TETR TUBE TUYA BIFU CAVI PRIS
  25 |  MULT   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR TUBE TUYA CAVI
     |         | PRIS CUB8 BREC TUVF TYVF CAVF
  26 |  MASS   | PMAT
  27 |  FLFA   | TRIA CAR1 CAR4 CUBE TETR PRIS
  28 |  HELI   | TUBE TUYA
  29 |  BL3S   | ELDI
  30 |  STGN   | TRIA CAR1 CAR4 CUBE CUB6 CUB8
  31 |  MOTE   | MECA
  32 |  ASSE   | MECA
  33 |  MHOM   | FHQ2 FHT2
  34 |  ADCR   | TRIA CAR1 CUBE TETR TUBE TUYA BIFU CAVI PRIS TUBM
     |         | TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF BIVF
     |         | CAVF
  35 |  VM23 E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 QPPS
     |         | Q92  Q93  COQI ED01 Q92A T3GS ED41 Q41  Q42  Q41N
     |         | Q42N Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9 CQD3 CQD6
     |         | Q42G FUN2 FUN3 Q4GR Q4GS T3MC C272 C273 C81L C82L
  36 |  FLUT   | FLU1 FLU3 FL2S FL3S CL2S CL3S FL23 FL24 FL34 FL35
     |         | FL36 FL38 CL22 CL3I CL3Q
  37 |  VM1D   | ED1D
  38 |  DONE   | CAR1 CAR4 QPPS Q92  Q93  COQI ED01 Q92A T3GS ED41
     |         | Q41  Q42  Q41N Q42N Q41L Q42L Q95  DST3 DKT3 CQD4
     |         | CQD9 CQD3 CQD6 Q42G FUN2 FUN3 Q4GR Q4GS C272 C273
     |         | C81L C82L
  39 |  PUFF   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 BILL
  40 |  GZPV   | TVL1 CVL1 CUVL PRVL
  41 |  ORTH   | COQU TRIA CAR1 CAR4 COQC CUBE CUB6 PR6  TETR PRIS
     |         | CUB8 CMC3
  42 |  ORTE   | CUBE CUB6 PR6  TETR PRIS CUB8 XCUB
  43 |  IMPV   | CL2D CL22
  44 |  GLAS E | CAR4 CUBE CUB6 CUB8 QPPS Q92  Q93  COQI ED01 Q92A
     |         | T3GS ED41 Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9 CQD3
     |         | CQD6 Q4GR Q4GS C272 C273 C81L C82L
  45 |  MECA   | MECA LIGR
  46 |  ORTS   | CUBE CUB6 PR6  TETR PRIS CUB8 DST3 Q4GS Q4MC T3MC
     |         | P3ZT
  47 |  ADFM   | ADC8 ADQ4
  48 |  GVDW   | TUBE TUYA BIFU CAVI TUBM TVL1 CVL1 CUVL PRVL TUYM
     |         | T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF BIVF CAVF
  49 |  EXVL   | TVL1 CVL1 CUVL PRVL
  50 |  JWL    | TRIA CAR1 CUBE TETR TUBE PRIS T3VF Q4VF CUVF PRVF
     |         | TEVF PYVF TUVF TYVF BIVF CAVF
  51 |  CHOC   | TRIA CAR1 CAR4 CUBE CUB6 TETR PRIS CUB8
  52 |  GPDI   | TVL1 CVL1 CUVL PRVL
  53 |  ADCJ   | TRIA CAR1 CAR4 CUBE TETR PRIS T3VF Q4VF CUVF PRVF
     |         | TEVF PYVF TUVF TYVF BIVF CAVF
  54 |  RSEA   | TRIA CAR1 CUBE TETR TUBE TUYA BIFU CAVI PRIS TUBM
     |         | TUYM
  55 |  ORPE   | CUBE CUB6 PR6  TETR PRIS CUB8 Q4MC T3MC P3ZT
  56 |  PARO   | TUBE TUYA CAVI TUVF TYVF
  57 |  BILL   | BILL
  58 |  CRIT   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8
  59 |  BUBB   | TRIA CAR1 CAR4 CUBE TETR PRIS QAX1 FLU1 FLU3 FL2S
     |         | FL3S FL23 FL24 FL34 FL35 FL36 FL38 T3VF Q4VF CUVF
     |         | PRVF TEVF PYVF
  60 |  MCOU   | COQ3 COQ4 QPPS DST3 DKT3 Q4GR Q4GS
  61 |  RESL   | RL3D
  62 |  PIEZ   | P3ZT
  63 |  LSGL   | CAR4 CUBE CUB6 CUB8 QPPS Q92  Q93  COQI ED01 Q92A
     |         | T3GS ED41 Q41  Q42  Q41N Q42N Q41L Q42L Q95  DST3
     |         | DKT3 CQD4 CQD9 CQD3 CQD6 Q4GR Q4GS T3MC C272 C273
     |         | C81L C82L
  64 |  CHAN   | COQ3 COQ4 QPPS DST3 DKT3 Q4GR Q4GS
  65 |  MORI   |
  66 |  JWLS   | TRIA CAR1 CUBE TETR TUBE PRIS T3VF Q4VF CUVF PRVF
     |         | TEVF PYVF TUVF TYVF BIVF CAVF
  67 |  ZALM E | TRIA CAR1 CAR4 CUBE PR6  TETR PRIS CUB8 SHB8 ASHB
  68 |  CDEM   | T3VF Q4VF CUVF PRVF TEVF PYVF
  69 |  PRGL   | BILL
  70 |  LMC2   | TRIA CAR1 CAR4 CUBE PR6  PRIS CUB8 SHB8 ASHB
  71 |  APPU   | APPU
  72 |  LEM1 E | TRIA CAR1 CAR4 CUBE PR6  PRIS CUB8 QPPS T3GS DST3
     |         | DKT3 SHB8 SPHC Q4GR Q4GS ASHB
  73 |  GAZD   | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF
     |         | BIVF CAVF
  74 |  ABSE   | MECA
  75 |  BOIS E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8
  76 |  VMJC E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 QPPS
     |         | Q92  Q93  COQI ED01 Q92A T3GS ED41 Q41L Q42L Q95
     |         | DST3 DKT3 XCUB XCAR CQD4 CQD9 CQD3 CQD6 FUN2 FUN3
     |         | Q4GR Q4GS C272 C273 C81L C82L
  77 |  VMZA E | TRIA CAR1 CAR4 CUBE CUB8 QPPS Q92  Q93  COQI ED01
     |         | Q92A T3GS ED41 Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9
     |         | CQD3 CQD6 FUN2 FUN3 Q4GR Q4GS C272 C273 C81L C82L
  78 |  VMLP E | TRIA CAR1 CAR4 CUBE CUB8 QPPS Q92  Q93  COQI ED01
     |         | Q92A T3GS ED41 Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9
     |         | CQD3 CQD6 FUN2 FUN3 Q4GR Q4GS C272 C273 C81L C82L
  79 |  VMLU E | TRIA CAR1 CAR4 CUBE CUB8 QPPS Q92  Q93  COQI ED01
     |         | Q92A T3GS ED41 Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9
     |         | CQD3 CQD6 FUN2 FUN3 Q4GR Q4GS C272 C273 C81L C82L
  80 |  FUNE   | FUN2 FUN3
  81 |  MCGP   | MC23 MC24 MC34 MC35 MC36 MC38
  82 |  MCFF E | CL22 CL3I CL3Q
  83 |  DRPR E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 Q92
     |         | Q93  Q92A Q41L Q42L Q95  C272 C273 C81L C82L
  84 |  VMSF E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 QPPS
     |         | Q92  Q93  COQI ED01 Q92A T3GS ED41 Q41  Q42  Q41N
     |         | Q42N Q41L Q42L Q95  DST3 DKT3 XCUB XCAR CQD4 CQD9
     |         | CQD3 CQD6 Q4GR Q4GS C272 C273 C81L C82L
  85 |  MAZA   | CUBE PR6  TETR CUB8 BILL
  86 |  FLMP   | FL2S FL3S FL23 FL24 FL34 FL35 FL36 FL38
  87 |  DPSF E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 QPPS
     |         | Q92  Q93  COQI ED01 Q92A T3GS ED41 Q41  Q42  Q41N
     |         | Q42N Q41L Q42L Q95  DST3 DKT3 CQD4 CQD9 CQD3 CQD6
     |         | Q4GR Q4GS C272 C273 C81L C82L
  88 |  COMM   | COQI CQD4 CQD9 CQD3 CQD6
  89 |  CAMC   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 Q92
     |         | Q93  Q92A Q41L Q42L Q95  C272 C273 C81L C82L
  90 |  CLAY   | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 Q92
     |         | Q93  Q92A Q41L Q42L Q95  C272 C273 C81L C82L
  91 |  JPRP   | BSHT BSHR SH3D
  92 |  GLRC   | QPPS T3GS DKT3 Q4GR Q4GS
  93 |  FOAM E | CUBE CUB6 PR6  TETR PRIS CUB8
  94 |  SUPP   | APPU
  95 |  HYPE   | CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 DST3 Q4GS
  96 |  PBED   | CUBE
  97 |  MINT   | INT4 INT6 INT8
  98 |  TVMC   | CUBE
  99 |  SLZA   | CUBE CUB6 PR6  TETR CUB8 QPPS DST3 DKT3 SHB8 Q4GR
     |         | Q4GS ASHB
 100 |  CRTM   | CUBE CUB6 PR6  TETR PRIS CUB8
 101 |  TAIT   | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF
     |         | BIVF CAVF
 102 |  STIF   | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF
     |         | BIVF CAVF
 103 |  SG2P   | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF
     |         | BIVF CAVF
 104 |  SGMP   | TRIA CAR1 CUBE TETR PRIS TUBM TUYM T3VF Q4VF CUVF
     |         | PRVF TEVF PYVF TUVF TYVF BIVF CAVF
 105 |  EOBT   | CUBE PR6  TETR PRIS CUB8
 106 |  SMAZ   | SPHC
 107 |  SLIN   | SPHC
 108 |  JCLM   | SPHC
 109 |  DADC   | CUBE PR6  TETR CUB8
 110 |  DEMS   | T3VF Q4VF CUVF PRVF TEVF PYVF
 111 |  DPDC   | CUBB CUBE CUB8 PRIS PR6  TETR
 112 |  SGBN   | TUBM TUYM T3VF Q4VF CUVF PRVF TEVF PYVF TUVF TYVF
     |         | BIVF CAVF
 113 |  CREB   | T3VF Q4VF CUVF PRVF TEVF PYVF
 114 |  BREC   | BREC
 115 |  ENGR   | TRIA CAR4 TETR CUB8
 116 |  GLIN E |
 117 |  GPLA   |
 118 |  GGAS   |
 119 |  BDBM   | CUBE CUB8
 120 |  VPJC E | TRIA CAR1 CAR4 CUBE CUB6 PR6  TETR PRIS CUB8 QPPS
     |         | Q92  Q93  COQI ED01 Q92A T3GS ED41 Q41L Q42L Q95
     |         | DST3 DKT3 CQD4 CQD9 CQD3 CQD6 FUN2 FUN3 Q4GR Q4GS
     |         | T3MC C272 C273 C81L C82L
 121 |  BPEL   | RNFR
 122 |  ORTP   | CUBE CUB8
 123 |  RESG   | RL3D


To print out (on the log file!) an up-to-date version of the above element and material tables, just run EUROPLEXUS with any input data file by adding the option OPTI DPEM (see also page GBH_0090).

7.2  AUXILIARY FILE

C.105


Object:


This directive allows to read the material data from an auxiliary file.


Syntax:

    "MATE"     < "FICHIER"   'nom.fic'  >


In certain cases the data may be bulky. It is then advised to store the data on an auxiliary file in order to shorten the main input data file. The auxiliary file is activated by means of the keyword "FICHIER", followed by the full name (under Unix) of the file. Therefore, only the words "MATE" "FICHIER" ’nom.fic’ remain in the main input file.


The auxiliary file (in free format) will contain the whole set of material data, with the exception of the "MATE" keyword. To return to the main input data file, the auxiliary file must be terminated by the keyword "RETOUR".

7.3  LOCALISED DAMPING

C.106


Object:


This directive allows to add a localised damping on some d.o.f.s of some particular nodes. It works for the serial runs only.


Syntax:

    "AMORTISSEMENT" ( /LECDDL/  "BETA" beta   "FREQ" freq   /LECTURE/ )
/LECDDL/

Concerned degrees of freedom.
beta

Reduced damping β.
freq

Frequency f of the global mode to be damped out.
/LECTURE/

List of the concerned nodes.

Comments:


The value β=1 corresponds to the critical damping for the frequency f. All frequencies are damped. The components with a frequency lower than the cut-off frequency: fcf will be damped in a pseudo-periodic manner while those having higher frequencies will be damped in an aperiodic manner.


This damping is proportional to the mass M and to the particles velocity v, and may be used in order to damp out preferably the structures without influence on the internal fluid, for example.


One adds an external force Famort of the form:

    Famort = − 2  β ω M v

where ω=2π f.


It is evident that the work of external forces will be modified by the damping forces.


This directive differs from the global damping directive (OPTI AMOR ..., see page H.30) mainly by the fact that here the region to which damping is applied may be specified by the user, while in the other case the damping applies to the whole model (but limitedly to some element types, see page H.30).

7.4  NON-LINEAR SUPPORTS : "APPU"

C.108


Object :

This directive allows to model non-linear supports of type spring or damper. It may be used only for the elements of type "APPUI" (material points with 6 d.o.f.s). The user gives the evolution curve of the force applied by the support as a function of its displacement (for the springs) or of its velocity (for the dampers). These supports work in translation or in rotation.


Syntax :

    "APPUI" |[ "RESS" ; "AMOR" ]|  |[ "TRAN" ; "ROTA" ]|
            "CMPX" cmpx     "CMPY" cmpy     "CMPZ" cmpz
            "COEF" coef     "NUFO" nufo    <"MASS" mass>
           <"INCR" incr>   <"DECX" decx>   <"DECY" decy>  /LECTURE/
"RESS"

The support is of type spring.
"AMOR"

The support is of type damper.
"TRAN"

The support works in translation.
"ROTA"

The support works in rotation.
cmpx

Component in X of the translation or rotation axis of the support.
cmpy

Component in Y of the translation or rotation axis of the support.
cmpz

Component in Z of the translation or rotation axis of the support.
coef

Multiplicative coefficient of the function.
nufo

Number of the function.
mass

Inertia of the support along its working direction.
incr

Increment of the velocity or displacement for the calculation of the local stiffness.
decx

Offset of the abscissas of the force/displacement or force/velocity curve.
decy

Offset of the ordinates of the force/displacement or force/velocity curve.
/LECTURE/

List of the concerned nodes.

Comments :

The user must define a vector corresponding to the rotation axis or translation axis of the support. This vector does not need to be normalised, just its direction matters. This direction defines the local reference frame of the support: it is the projection of the displacement (or of the velocity) of the concerned node onto this axis that allows to determine the reaction force.


An APPUI element may not work simultaneously as a spring AND as a damper, nor in translation AND in rotation. Therefore it will be sometimes necessary to define several APPUI elements, geometrically coincident, in order to correctly define the local stiffness.


The function defining the force generated by the support in response to displacement or velocity of its application point on the supported structure is of the form:

F = coef   f(D)     or     F = coef   f(V)

with f(D) or f(V) given by the user. Warning: these values have a sign. Do not forget to give the force with the opposite sign as the displacement (this is a reminder).


For the estimation of the stability step, it is necessary to know the local slope of the behaviour curve. To this end, the user must specify the keyword "INCR". The computation of the local stiffness will then be (by default, incr=1.E-4):

K = (F(D+incr)−F(D))/incr       or     C = (F(V+incr)−F(V))/incr 


In the case that the structure is not in equilibrium for a zero displacement at the beginning of the calculation, the user may impose a translation of vector (decx, decy) of the behaviour curve. The computed force will then be (by default, decx and decy are zero):

F = ( coef   f(D+decx) ) − decy 

( in fact : decy = coef   f(decx) )


Outputs :

The components of the ECR vector are:

ECR(1): Force (resp. moment) along X.

ECR(2): Force (resp. moment) along Y.

ECR(3): Force (resp. moment) along Z.

ECR(4): Current stiffness.

ECR(5): Current velocity (or angular velocity).

ECR(6): Total displacement (or rotation).

ECR(7): Applied force (or moment) to the node (reaction force).

7.5  NON-LINEAR SUPPORTS : "SUPP"

C.109


Object :

This directive allows to model a complex non-linear support, having arbitrary stiffness and damping values along the 6 dofs of the concerned node. It may only be used in conjunction with elements of type "APPUI" (material point with 6 dofs). The user gives the evolution curve of the reaction force generated by the support as a function of the displacement or of the velocity of the associated node.


Syntax :

  "SUPP"  "MASS" m
           < |[ "KX" kx ; "KY" ky ; "KZ" kz ]|
               |[
                  "NFKT" nufo1 ;
                  "NFKX" nufokx "NFKY" nufoky "NFKZ" nufokz
               ]| >
           < |[ "AX" ax ; "AY" ay ; "AZ" az ]| "NFAT" nufo2 >
           <"IRX" irx>  <"IRY" iry>  <"IRZ" irz>
           < |[ "KRX" krx ; "KRY" kry ; "KRZ" krz ]| "NFKR" nufo3 >
           < |[ "ARX" arx ; "ARY" ary ; "ARZ" arz ]| "NFAR" nufo4 >
           /LECTURE/
m

Additional translational mass (optional).
kx, ky, kz

Translationl stiffnesses along the global axes.
nufo1

Index of the function associated with translational stiffnesses.
nufokx, nufoky, nufokz

Indexes of the functions associated with 3 translational stiffnesses.
ax, ay, az

Translationl dampings along the global axes.
nufo2

Index of the function associated with translational dampings.
irx, iry, irz

Additional rotational inertias along the global axes (optional).
krx, kry, krz

Rotational stiffnesses along the global axes.
nufo3

Index of the function associated with rotational stiffnesses.
arx, ary, arz

Rotational dampings along the global axes.
nufo4

Index of the function associated with rotational dampings.
/LECTURE/

List of the concerned nodes.

Comments :

The stiffnesses and the dampings are given along the global (fixed) axes of the problem. Each of the 4 associated functions applies to the 3 corresponding stiffnesses (or dampings). For translational stiffnesses one can prescribe three different functions.


If a key-word is missing, the corresponding value is zero, and the order in which the parameters are specified is irrelevant.


The reaction force generated by the support has the form (e.g., assuming translation along Ox):

Fx = kx f1(Dx) + ax f2(Vx)  


If the displacement (or the velocity) is positive, the function f1 (or f2) must be negative in order to obtain a correct reaction.


Outputs :

The components of the ECR vector are:

ECR(1): Reaction of the support along X.

ECR(2): Reaction of the support along Y.

ECR(3): Reaction of the support along Z.

ECR(4): Reaction of the support along RX.

ECR(5): Reaction of the support along RY.

ECR(6): Reaction of the support along RZ.

7.6  SOLID MATERIALS

7.6.1  LINEAR ELASTICITY

C.110


Object:


This option enables materials with a linear elastic behaviour to be used.


Syntax:

    "LINE"   "RO" rho  "YOUN" young  "NU" nu
              <"VISC" visc "KRAY" kray "MRAY" mray>   /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
visc

Viscosity coefficient (decay factor), used only by spectral elements (MS24, MS38) and finite elements of the following types: TRIA, CAR1, CAR4, CUBE, CUB6, CUB8, TETR, PR6, PRIS.
kray, mray

Rayleigh’s stiffness and mass proportional damping coefficients, used only by finite elements of the following types: POUT, TUYA, DKT3, T3GS, Q4GS. Default values: kray=0, mray=0. For information about Rayleigh’s damping see reference [862].
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


Outputs:


The components of the ECR table are as follows:


Solid elements:
ECR(1): pressure

ECR(2): Von Mises criterion


Shells:
ECR(1): Von Mises criterion (membrane)

ECR(2): Von Mises criterion (membrane + bending)


Beams (3D):
ECR(1): Von Mises criterion (bending)

ECR(2): Von Mises criterion (membrane + bending + torsion)


Bars (BARR, PONC, BR3D):
ECR(1): elastic strain

ECR(2): Von Mises criterion

7.6.2  RESL: NONLINEAR SPRING IN THE LOCAL REFERENCE FRAME

C.111


Object:

This directive allows to model a complex non-linear two-node spring, having arbitrary stiffness and damping values along the 3 dofs of the two concerned nodes. It may only be used in conjunction with RL3D elements (two-node spring). Stiffness and damping are given along local axes. The first local axe (xloc) is defined by the direction of the element that why the element must have a non-zero length. Second (yloc) and third (zloc) axes are defined by the user. The user gives the evolution curve of the reaction force generated by the spring as a function of the displacement or of the velocity.


Syntax:

  "RESL"
           <|[ "KL" kl ; "KT1" kt1 ; "KT2" kt2 ]|
               |[
                  "NFKT" nufo1 ;
                  "NFKL" nufokl "NFKS" nufoks
               ]| >
           <|[ "AL" al ; "AT1" at1 ; "AT2" at2 ]|
               |[
                  "NFAT" nufo2 ;
                  "NFAL" nufoal "NFAS" nufoas
               ]| >
           <|[ "VX" vx ; "VY" vy ; "VZ" vz ]|>
           /LECTURE/
kl, kt1, kt2

Translational stiffnesses along the local axes: xloc, yloc, zloc.
nufo1

Index of the function associated with translational stiffnesses.
nufokl, nufoks

Indexes of the functions associated with longitudinal and transverse stiffnesses.
al, at1, at2

Translational dampings along the local axes.
nufo2

Index of the function associated with translational dampings.
nufoal, nufoas

Indexes of the functions associated with longitudinal and transverse dampings.
vx, vy, vz

Coordinates of the vector v. Projection of v on the "orthogonal to xloc" plane gives yloc.
/LECTURE/

List of the concerned elements.

Comments:

The stiffnesses and the dampings are given along the local axes of the problem in the initial configuration. If a single function is specified for stifnesses (dampings), it applies to the 3 corresponding stiffnesses (dampings).


If a key-word is missing, the corresponding value is put to zero. The order in which the parameters are specified is irrelevant.


The reaction force generated by the spring has the form (e.g., assuming translation along the xloc axis):

Fx = kx f1(Dx) + ax f2(Vx)  


If the displacement (or the velocity) is positive, the function f1 (or f2) must be negative in order to obtain a correct reaction.


Outputs:

The components of the ECR vector are:

ECR(1): Force in the spring along xloc.

ECR(2): Force in the spring along yloc.

ECR(3): Force in the spring along zloc.

7.6.3  GENERIC LINEAR ELASTICITY

C.112


Object:


This option enables materials with a linear elastic behaviour to be used. It is an interface to convert the input to the appropriate material (LINE 7.6.1, VM23 7.6.38) for the elements used.


Syntax:

    "GLIN"   "RO" rho  "YOUN" young  "NU" nu   /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
LECTURE

List of the elements concerned.

Outputs:

The output variables are according to the material in which the generic material is converted.

7.6.4  GENERIC PLASTICITY

C.113


Object:


This option enables materials with a linear elastic behaviour to be used. It is an interface to convert the input to the appropriate material (VMIS ISOT 7.6.7, VM23 7.6.38) for the elements used.


Syntax:

    "GPLA"   "RO" rho  "YOUN" young  "NU" nu   "ELAS" sige ...
        ...        "TRAC"  npts*( sig  eps )    /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
"TRAC"

This key-word introduces the yield curve.
npts

Number of points (except the origin) defining the yield curve.
sig

Stress.
eps

Total strain (elastic + plastic)
LECTURE

List of the elements concerned.

Outputs:

The output variables are according to the material in which the generic material is converted.

7.6.5  RESG: NONLINEAR SPRING IN THE GLOBAL REFERENCE FRAME

C.114


Object:

This directive allows to model a complex non-linear two-node spring having arbitrary stiffness and damping values along the 3 dofs of the two concerned nodes. It may only be used in conjunction with RL3D elements (two-node spring). The user gives the evolution curve of the reaction force generated by the spring as a function of the displacement or of the velocity.


Syntax:

  "RESG"
           <|[ "KX" kx ; "KY" ky ; "KZ" kz ]| "NFKT" nufo1>
           <|[ "AX" ax ; "AY" ay ; "AZ" az ]| "NFAT" nufo2>
           /LECTURE/
kx, ky, kz

Translational stiffnesses along the global axes.
nufo1

Index of the function associated with translational stiffnesses.
ax, ay, az

Translational dampings along the global axes.
nufo2

Index of the function associated with translational dampings.
/LECTURE/

List of the concerned elements.

Comments:

The stiffnesses and the dampings are given along the global (fixed) axes of the problem. Each of the 2 associated functions applies to the 3 corresponding stiffnesses (or dampings).


If a key-word is missing, the corresponding value is put to zero. The order in which the parameters are specified is irrelevant.


The reaction force generated by the spring has the form (e.g., assuming translation along Ox):

Fx = kx f1(Dx) + ax f2(Vx)  


If the displacement (or the velocity) is positive, the function f1 (or f2) must be negative in order to obtain a correct reaction.


Outputs:

The components of the ECR vector are:

ECR(1): Force in the support along X.

ECR(2): Force in the support along Y.

ECR(3): Force in the support along Z.

7.6.6  DRUCKER-PRAGER

C.115


Object:


This option enables to specify materials with a perfect elasto-plastic behaviour (Drucker-Prager criterion).


Syntax:

    "DRUC"  "RO"  rho  "YOUNG"  young  "POISSON"  nu  ...
      ...  "TRACTION"  sigt  "COMPRESSION"  sigc  ...
      ...  < "FRACTURE"   pf  >   /LECTURE/


rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
sigt

Maximum stress under tension (without confinement).
sigc

Maximum stress under compression (without confinement).
FRACTURE pf

The material is fractured (does no longer resist tension) as soon as the criterion is reached for the first time. Then, the domain changes and the new D.P. criterion corresponds to vanishing cohesion whereas the slope is equivalent to the one in the previous case. The parameter ’pf’ is compulsory and represents the maximum pressure of fracturing under compression. If the criterion is reached for the first time when the pressure is superior to pf, the domain does not change and the criterion is the same as initially.
/LECTURE/

Numbers of the elements concerned.

Comments:


The values of sigt, sigc and pf are absolute values.


If P defines the pressure (positive under tension) and SIG* the Von Mises criterion, the Drucker-Prager criterion is defined by:

    Criterion = SIG* - cohe + P * pente   ( always <= 0 )


The 2 parameters : cohe and pente (slope), are calculated from sigt and sigc values, they are printed after the reading of the data. The parameter cohe (cohesion) corresponds to a maximum Von Mises under non-existant pressure. The slope is the straight line limiting the domain, in the coordinate system (P,SIG*).


In the space of the principal stresses the criterion determines a cone the axis of which is the straight line of equation: sig(1)= sig(2) = sig(3).


The maximum stresses: sigt and sigc correspond to the values observed during uniaxial tests without confinement. These two points enable the Drucker-Prager domain to be defined.


The value of the parameter "FRACTURE" enables the behaviour of concrete to be represented in a very simplified way. Two domains may be distinguished:

- Brittle rupture

- Ductile rupture (strong compressions)


Most often one may take pf = sigc/3. A great value for pf delay the fracturation.


Outputs:


The different components of the ECR table are as follows:

ECR(1): pressure

ECR(2): Von Mises

ECR(3): equivalent plastic strain

ECR(4): D.P. criterion ( always <= 0 )

ECR(5): cohesion (becomes non-existant in the case of brittle rupture)

7.6.7  VON MISES MATERIAL

C.120


Object:


This sub-directive enables materials with an elasto-plastic behaviour to be used. There are four options:


- "VMIS" "PARF" : perfectly plastic Von Mises material;


- "VMIS" "ISOT" : isotropic Von Mises material;


- "VMIS" "DYNA" : isotropic Von Mises material depending on strain rate;


- "VMIS" "TETA" : isotropic Von Mises material depending on temperature.


Syntax:

    "VMIS"
           $[
               "PARF" . . . ;
               "ISOT" . . .
               "DYNA" . . .
               "TETA" . . .
           ]$

Comments:


This sub-instruction may be repeated as many times as necessary with different options each time (if need be). The word "VMIS" cannot be separated from the option which follows.

PERFECTLY PLASTIC VON MISES

C.125


Object:

Perfectly plastic Von Mises material.


Syntax:

    "VMIS"  "PARF"  "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige   ...
               ...  /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
ncrit
LECTURE

List of the elements concerned.

Comments:

The law of behaviour is described by the following diagram of stresses and strains:


Figure 4: VMIS - stress-strain relation


Outputs:

The components of the ECR table are as follows:


Solid elements:
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain

Shells integrated through the thickness:
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain

Global model shells:
ECR(1): Von Mises criterion (membrane)
ECR(2): Von Mises criterion (membrane + bending)
ECR(3): plastic strain

Bars (BARR, PONC, BR3D):
ECR(1): elastic strain
ECR(2): Von Mises criterion
ECR(3): plastic strain

ISOTROPIC VON MISES

C.130


Object:

Isotropic Von Mises material.


Syntax:
    "VMIS" "ISOT" "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige ...
                   <FAIL fail LIMI limi>
        ...        "TRAC"  npts*( sig  eps )    /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
FAIL

Optional keyword: introduces an element failure model represented by a failure criterion and a by failure limit value. Two failure criteria only available for POUT and bar (BR3D, BARR, PONC) elements are:

fail = 1 for a criterion based upon Von Mises stress (membrane + bending + torsion),

fail = 2 for a criterion based upon plastic strain.

limi

Optional parameter, indicates the failure limit for the chosen criterion.
"TRAC"

This key-word introduces the yield curve.
npts

Number of points (except the origin) defining the yield curve.
sig

Stress.
eps

Total strain (elastic + plastic).
/LECTURE/

List of the elements concerned.

Comments:

1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


Outputs:

The components of the ECR table are as follows:


Solid elements
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit

Shells integrated through the thickness:
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit

Global model shells:
ECR(1): Von Mises criterion (membrane)
ECR(2): Von Mises criterion (membrane + bending)
ECR(3): plastic strain
ECR(7): new elastic limit

Beams (3D):
ECR(1): Von Mises criterion (bending)
ECR(2): Von Mises criterion (membrane + bending + torsion)
ECR(3): plastic strain
ECR(7): new elastic limit
ECR(10): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)

Bars (BARR, PONC, BR3D):
ECR(1): elastic strain
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit ECR(10): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)

DYNAMIC VON MISES

C.135


Object:

Isotropic Von Mises material depending on strain rate.


Syntax:
    "VMIS"  "DYNA"  "RO" rho  "YOUN" young  "NU" nu  ...
       ...  "TRAC"  npts*( sig  eps )  ...

       ...   $[ "SYMO"  "D" d   "P" p              ;
                "ISPR" "VITE"  a  b  c  d  e  f    ;
                "LIBR"  num  "PARA"  /LECPARA/     :
                "ARMA" "ALFAY" alfay "ALFAU" alfau
                <"FAIL" nfail "LIMI" limi >         ]$   /LECTURE/


rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
"TRAC"

This key-word introduces the yield curve.
npts

Number of points (except the origin) defining the yield curve (in the case of the ARMA model only 3 points should be used : the yield point, the onset of hardening and the ultimate point before softening. Yield curve is defined analytically thanks to the assumption that it is a portion of parabola begining at the onset of hardening and reaching a maximum at the ultimate point).
sig

Stress
eps

Total strain (elastic + plastic).
"SYMO"

Constitutive relation of Symonds and Cowper.
d

First coefficient of the Symonds and Cowper law.
p

Second coefficient of the Symonds and Cowper law.
"VITE"

This key-word introduces the parameters of the dynamic yield curve.
a,b,c,d,e,f

The 6 parameters of the dynamic yield curve.
"LIBRE"

Introduces the utilisation of a user’s subroutine to compute the dynamic amplification coefficient.
num

Identification number of the free material.
"PARA"

Keyword that can be used to introduce a series of parameters for the free material. The number of parameters is arbitrary, because the /LECTURE/ procedure signals the termination of the list.
"ARMA"

This key-word introduces the parameters of the dynamic yield curve for steel reinforcing bars.
alfay

Coefficient to obtain the DIF for the yield stress.
alfau

Coefficient to obtain the DIF for the ultimate stress.
FAIL

Optional keyword: introduces an element failure model represented by a failure criterion and a by failure limit value. Two failure criteria only available for POUT and bar (BR3D, BARR) elements are:

fail = 1 for a criterion based upon Von Mises stress (membrane + bending + torsion),

fail = 2 for a criterion based upon plastic strain.

limi

Optional parameter, indicates the failure limit for the chosen criterion.
/LECTURE/

List of the elements concerned.

Comments:


For the Symonds and Cowper law, the dynamic traction curve is derived from the static one through a multiplicative coefficient which depends upon the strain rate (EPSP):

    SIG(dyna) = SIG(stat) * ( 1 + ( EPSP / D ) ** (1/P) )


Indicatively, for the stainless steel 304 L, experimental results suggest: D = 100 s-1 and P = 10 (Forrestal and Sagartz 1978). For ordinary steel, it is usually assumed: D = 40 s-1 and P = 5 (Symonds 1965).


For titanium TI-50A, the values suggested are: D = 120 s-1 and P = 9 (Symonds et Chon 1974).


For aluminum alloys, some authors use D = 6500 s-1 and P = 4 (Symonds 1965).


In the case of the ISPRA law, the formulation is similar, but the multiplying coefficient depends upon the strain (EPS) as well as on the strain rate (EPSP):

    SIG(dyna) = SIG(stat) * ( 1 + ( EPSP / K ) **M )


with the K and M coefficients of the form:

    K = EXP( ( A + B * EPS ) / ( 1 + C * EPS ) )
    M =      ( D + E * EPS ) / ( 1 + F * EPS )


Examples of data (source ISPRA-CADARACHE):

 Material        a       b         c        d        e       f
 -------------------------------------------------------------
 Steel 304    5.82   168.76     9.62    0.242    2.263   12.77
 Steel 316   6.388   86.215    6.457    0.233      0.0     0.0
 -------------------------------------------------------------


For the ARMA model, the dynamic yield curve is obtained as follows:

The dynamic increase factor for the yield stress is given by:

    SIG_Y(dyna) = SIG_Y(stat) * DIF_Y
    DIF_Y = ( EPSP/ 10-4 ) ** ALFAY

The dynamic increase factor for the ultimate stress is given by:

    SIG_U(dyna) = SIG_U(stat) * DIF_U
    DIF_U = ( EPSP / 10-4 ) ** ALFAU

Then, the yield curve is defined analytically thanks to the assumption that it is a portion of parabola begining at the onset of hardening and reaching a maximum at the ultimate point.


This model is suited for steel reinforcing bars, so it can be used only with bar and beam elements.


It is suggested in "Dynamic Increase Factors for Steel Reinforcing Bars, L. J. Malvar and J. E. Crawford, Twenty-Eighth DDESB Seminar, Orlando, Florida, USA, August 1998" that ALFAY and ALFAU can be estimated by the expressions:

    ALFAY = 0.074 - ( 0.040 * fy / 414. )
    ALFAU = 0.019 - ( 0.009 * fy / 414. )

where fy is the bar yield strengh in MPa.


This formulation is valid for bars with yield stress between 290 and 710 MPa and for strain rates between 10-4 and 225 s-1.


IMPORTANT POINT:

For all formulations, the strain rate EPSP is filtered with a first order low-pass filter:

    dEPSP/dt=(EPSPC - EPSP)/tau

with EPSPC the current value of the strain rate and TAU the filter time constant:

    TAU = 1 / ( 2 * pi * fc)

with fc the cutoff frequency of the filter.
By time integration, we obtains:

    EPSP(n+1) = ( EPSP(n) + (DELTAT / TAU)*EPSPC(n+1) ) / ( 1 + (DELTAT / TAU) )
    DELTAT = t(n+1) - t(n)

Furthermore, we supposed that:

  BETA = DELTAT / TAU = Cte

and introduced FEPSP1:

  FEPSP1 = BETA / (1 + BETA) = DELTAT / (DELTAT + TAU)

FEPSP1 is defined in OPTI FVIT.
Default value is 1, meaning TAU = 0, no filter is applied.
Advised value for FEPSP1 is 0.01.


Outputs:


The components of the ECR table are as follows:


Solid elements:
ECR (1): pressure
ECR (2): Von Mises criterion in dynamics
ECR (3): equivalent plastic strain
ECR (7): new elastic limit in statics
ECR (8): equivalent strain rate
ECR (9): total equivalent deformation
ECR(11): elastic limit in dynamics

Shells integrated through the thickness:
ECR (1): pressure
ECR (2): Von Mises criterion in dynamics
ECR (3): equivalent plastic strain
ECR (7): new elastic limit in statics
ECR (8): equivalent strain rate
ECR (9): total equivalent deformation
ECR(11): elastic limit in dynamics

Global model Shells:
ECR (1): Von Mises criterion (membrane)
ECR (2): global Von Mises criterion (membrane + bending)
ECR (3): equivalent plastic strain
ECR (7): new elastic limit
ECR (8): equivalent strain rate
ECR (9): total equivalent deformation
ECR(11): elastic limit in dynamics

Beams (3D) for ARMA only:
ECR(1): Von Mises criterion (bending)
ECR(2): Von Mises criterion (membrane + bending + torsion)
ECR(3): plastic strain
ECR(7): new elastic limit
ECR(10): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)
ECR(11): elastic limit in dynamics

Bars (BARR, BR3D) for ARMA only:
ECR(1): elastic strain
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit
ECR(10): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)
ECR(11): elastic limit in dynamics

TEMPERATURE-DEPENDENT VON MISES

C.140


Object:

Von Mises isotropic material dependent upon the temperature.


Syntax:
    "VMIS"  "TETA"  "RO" rho < "NU" nu >...
       ...  "NBCOURBE"  nc*( "TETA" ti "YOUNG" yg  <"NUT"> nut ...
       ...              "TRAC" npts*( sig eps ) ) /LECTURE/


rho

Density.
nu

Poisson coefficient. Only if NU does not depend on the temperature.
nc

Number of traction curves thet allow the interpolation as a function of temperature.
ti

Temperature associated with the following traction curve.
yg

Young’s modulus.
nut

Poisson Poisson. If NU depend on temperature.
"TRAC"

Introduces the traction curve.
npts

Number of points (excluding the origin) which define the traction curve.
sig

Stress.
eps

Total strain (elastic + plastic).
/LECTURE/

List of the elements concerned.

Comments:


Each element is isothermal, i.e. its temperature remains constant during the whole calculation.


Depending upon temperature, the Young’s modulus, the poisson coefficient and the traction curve are interpolated starting from the values associated to the known temperatures.


Note that it is possible to define either a temperature-dependant Poisson coefficient or not which can be sufficient in case of steels for example.


Outputs:


The components of the ECR table are as follows:


Continuum elements:
ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : equivalent plastic strain

Shells integrated through the thickness:
ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : equivalent plastic strain

Global model hells:
ECR(1) : Von Mises criterion (membrane)
ECR(2) : global Von Mises criterion (membrane + bending)
ECR(3) : equivalent plastic strain

7.6.8  STEINBERG-GUINAN

C.145


Object:


This is a Von Mises isotropic material whose Young’s modulus and elastic limit are a function of hydrostatic pressure, temperature increase and strain rate.


Syntax:

    "STGN"  "RO"  rhoz   "YOUN"  youngz  "NU"    nu      ...
       ...  "SIGE" sigez "SIGD"  sigd    "CHSP"  cv      ...
       ...  "TF"  tfus   "TINI"  tini    "B"      b      ...
       ...  "H" h        "BETA"  beta    "N"      n    /LECTURE/


rhoz

Density at the initial temperature.
youngz

Young’s modulus at the initial temperature.
nu

Poisson coefficient (constant).
sigez

Static elastic limit at the initial temperature.
sigd

Dynamic elastic limit at the initial temperature.
cv

Specific heat capacity of the solid.
tfus

Melting temperature of the material.
tini

Initial temperature of the material.
b,h,beta,n

Coefficients of the STEINBERG and GUINAN law.
/LECTURE/

List of the elements concerned.

Comments:


The STEINBERG and GUINAN law uses the Young’s modulus E, and an elastic limit Y, which vary according to the following expressions:

        E = youngz * P1

        Y = yield * P1


with:

        P1 = 1 + b*P / K**(1/3) + h*dteta

        yield  = MIN ( sigd , sigez*P2 )

        P2 = ( 1+beta*EPSP )**n


where:

P is the hydrostatic pressure;

K is the compression ratio (ratio between the current density and the initial density);

EPSP is the total equivalent strain rate;

dteta is the temperature increase with respect to the initial temperature.


On the other hand, when the current temperature (teta = tini + dteta) exceeds the melting temperature of the material (tfus), it is assumed that the material is liquefied: the Young’s modulus and the elastic limit are then taken as zero.


Outputs:


The various components of the ECR table are as follows:

ECR(1) : hydrostatic pressure

ECR(2) : Von Mises

ECR(3) : equivalent plastic strain

ECR(4) : temperature increase (dteta)

ECR(5) : current elastic limit

ECR(6) : current Young’s modulus

ECR(7) : eauivalent plastic strain rate

7.6.9  LEM1

C.147


Object :

This directive allows to describe the behaviour of an elasto-plastic material that may undergo some damage, according to the Lemaitre model. There is coupling between damage and plasticity, represented by the Von Mises criterion. The damage evolution rate is a function of the triaxiality ratio of stresses and of the equivalent plastic strain rate. A failure criterion is implicitly contained within the model: rupture occurs when the damage exceeds a critical value. Two optional parameters allow to introduce a limitation of the damage rate (thanks to the delayed damage model) in order to avoid the mesh dependency.


Syntax:
    "LEM1"  "RO" rho "YOUN" young "NU" nu  "ELAS" sige ...
            "EPSD" epsd  "S0" s0  "DC" dc ...
            <"CSTA" csta "TAUC" tauc "NOCO" noco> ...
            "TRAC"  npts*( sig  eps )   /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s coefficient.
sige

Elastic limit.
epsd

Damage threshold (i.e. equivalent plastic strain, weighted by a function of stress triaxiality, within which damage vanishes).
s0

Parameter driving the damage evolution rate.
dc

Critical damage defining the failure criterion.
csta

Parameter of the delayed damage model
tauc

Characteristic time of the delayed damage model. (1/tauc) represents the maximum damage rate.
noco

Optional parameter indicating what to do when no convergence is reached in the material routine. The value 0 is the default and means that an error message is issued and the calculation is stopped. The value 1 indicates that the element (or more precisely, the element’s current Gauss point) is made to fail (eroded). The value -1 indicates that subcycling is activated in an attempt to reach convergence, by subdividing the load step into smaller sub-cycles.
"TRAC"

Introduces the traction curve.
npts

Number of points (except the origin) defining the traction curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of concerned elements.

Comments:

A detailed description of the model can be found in the report DMT/98-026A, available on request.


Outputs:

The components of the ECR table are as follows for Continuum elements:

ECR(1) : pressure

ECR(2) : Von Mises criterion

ECR(3) : equivalent plastic strain

ECR(4) : plasticity multiplier

ECR(5) : damage

ECR(7) : new elastic limit

When the “erosion” algorithm is activated (see page A.30, Section 4.4, keyword EROS), an integration point is considered as failed if damage >= dc. It will be eroded concerning the rules for EROS.

7.6.10  ZALM

C.148


Object :

This directive allows to describe the behaviour of an Zirelli-Armstrong material that may undego some damage, according to the Lemaitre model. There is coupling between damage and plasticity, represented by the Von Mises criterion. The damage evolution rate is a function of the triaxiality ratio of stresses and of the equivalent plastic strain rate. A failure criterion is impicitly contained within the model: rupture occurs when the damage exceeds a critical value. Two optional parameters allow to introduce a limitation of the damage rate (thanks to the delayed damage model) in order to avoid the mesh dependency.


Syntax:
    "ZALM"  "RO" rho "YOUN" young "NU" nu  "ELAS" sige ...
            "EPSD" epsd  "S0" s0  "DC" dc ...
            "ZAC0" zac0 "ZAC1" zac1 "ZAC2" zac2 "ZAC3" zac3 ...
            "ZAC4" zac4 "ZAC5" zac5 "ZAN" zan ...
            <"CSTA" csta "TAUC" tauc> ...
            "TRAC"  npts*( sig  eps )   /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s coefficient.
sige

Elastic limit.
epsd

Damage threshold (i.e. equivalent plastic strain, weighted by a function of stress triaxiality, within which damage vanishes).
s0

Parameter driving the damage evolution rate.
dc

Critical damage defining the rupture criterion.
csta

Parameter of the delayed damage model
zac0

Parameter of zerilli-armstrong model c0
zac1

Parameter of zerilli-armstrong model c1
zac2

Parameter of zerilli-armstrong model c2
zac3

Parameter of zerilli-armstrong model c3
zac4

Parameter of zerilli-armstrong model c4
zac5

Parameter of zerilli-armstrong model c5
zan

Parameter of zerilli-armstrong model n
tauc

Characteristic time of the delayed damage model. (1/tauc) represents the maximum damage rate.
"TRAC"

Introduces the traction curve.
npts

Number of points (except the origin) defining the traction curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of concerned elements.

Outputs:

The components ov the ECR table are as follows for Continuum elements:

ECR(1) : pressure

ECR(2) : Von Mises criterion

ECR(3) : equivalent plastic strain

ECR(4) : plasticity multiplier

ECR(5) : damage

ECR(7) : new elastic limit

When the “erosion” algorithm is activated (see page A.30, Section 4.4, keyword FAIL), an element is considered as failed if damage >= dc.

7.6.11  LMC2

C.149


Object:

This directive allows to describe the behaviour of an elasto-plastic material that may undego some damage, according to the Lemaitre-Chaboche model. There is coupling between damage and plasticity, represented by the Von Mises criterion. The damage evolution rate is a function of the triaxiality ratio of stresses and of the equivalent plastic strain rate. A failure criterion is impicitly contained within the model: rupture occurs when the damage exceeds a critical value. Unlike model LEM1, the material properties may depend upon the strain rate. Two optional parameters allow to introduce a limitation of the damage rate (thanks to the delayed damage model) in order to avoid the mesh dependency


Syntax:

   "LMC2"  "RO" rho ...
           "YOUN" young < "FONC" nfyou ...
                 $[ "TABL" nptyou*( para vyou ) ; "ROUT" ; "DONE" ]$ > ...
           "NU" nu      < "FONC" nfnu  ...
                 $[ "TABL"  nptnu*( para vnu  ) ; "ROUT" ; "DONE" ]$ > ...
           "ELAS" sige  < "FONC" nfela ...
                 $[ "TABL" nptela*( para vela ) ; "ROUT" ; "DONE" ]$ > ...
           "EPSD" epsd  < "FONC" nfepd ...
                 $[ "TABL" nptepd*( para vepd ) ; "ROUT" ; "DONE" ]$ > ...
           "S0" s0      < "FONC" nfs0  ...
                 $[ "TABL"  npts0*( para vs0  ) ; "ROUT" ; "DONE" ]$ > ...
           "DC" dc      < "FONC" nfdc  ...
                 $[ "TABL"  nptdc*( para vdc  ) ; "ROUT" ; "DONE" ]$ > ...
           <"CSTA" csta "TAUC" tauc> ...

If the traction curve is given by a table:
           "TRAC" ctra "FTRA" nftra ...
                 $ "TABL" npt*( sig eps ) ; "ROUT" ; "DONE" $ ...

If the traction curve is given by an abaque:
           "TRAC" ctra "ATRA" natra $ "SET" npara ...
                  "NPTM" nptm*( "PARA" para "TABL" npt*( sig eps )); ...
                  "DONE" $ ...

          /LECTURE/
rho

Density.
young

Young’s modulus if it is constant or multiplicative coefficient of Young’s modulus if it is defined by a function.
nfyou

Number of the function defining the variation of the Young’s modulus with the strain rate.
nptyou

Number of point defining the variation of the Young’s modulus with the strain rate.
para

Parameter (here the strain rate).
vyou

Value of the Young’s modulus corresponding to the parameter.
nu

Poisson’s coefficient if it is constant or multiplicative coefficient of Poisson’s coefficient if it is defined by a function.
nfnu

Number of the function defining the variation of the Poisson’s coefficient with the strain rate.
nptnu

Number of point defining the variation of the Poisson’s coefficient with the strain rate.
vnu

Value of the Poisson’s coefficient corresponding to the parameter.
sige

Elastic limit if it is constant or multiplicative coefficient of the elastic limit if it is defined by a function.
nfela

Number of the function defining the variation of the elastic limit with the strain rate.
nptela

Number of point defining the variation of the elastic limit with the strain rate.
vela

Value of the elastic limit corresponding to the parameter.
epsd

Damage threshold (i.e. equivalent plastic strain, weighted by a function of traixiality rate of stresses, below which the damage is zero) if it is constant or multiplicative coefficient of the damage threshold if it is defined by a function.
nfepd

Number of the function defining the variation of the damage threshold with the strain rate.
nptepd

Number of point defining the variation of the damage threshold with the strain rate.
vepd

Value of the damage threshold corresponding to the parameter.
s0

Parameter driving the evolution rate of damage if it is constant or multiplicative coefficient of the parameter driving the evolution rate of damage if it is defined by a function.
nfs0

Number of the function defining the variation of the parameter driving the evolution rate of damage with the strain rate.
npts0

Number of point defining the variation of the parameter driving the evolution rate of damage with the strain rate.
vs0

Value of the dparameter driving the evolution rate of damage corresponding to the parameter.
dc

Critical damage defining the rupture criterion if it is constant or multiplicative coefficient of critical damage if it is defined by a function.
nfdc

Number of the function defining the variation of the critical damage with the strain rate.
nptdc

Number of point defining the variation of the critical damage with the strain rate.
vdc

Value of the critical damage corresponding to the parameter.
csta

Parameter of the delayed damage model
tauc

Characteristic time of the delayed damage model. (1/tauc) represents the maximum damage rate.
"TRAC"

Introduces the traction curve.
ctra

Multiplicative coefficient of the stress in the traction curve or curves.
"FTRA"

Introduces the single traction curve for all strain rates.
nftra

Number of the function defining the traction curve.
npt

Number of point (except the origin) defining the traction curve.
item[sig]

Stress. item[eps]

Strain (elastic+plastic).
"ATRA"

Introduces an abaque giving the traction curve for different strain rates.
natra

Number of the abaque defining the traction curves.
npara

Number of the set of parametrised functions that associate to each strain rate the corresponding traction curve.
nptm

Maximum number of point (except the origin) definig the traction curve amongst the set of parametrised functions.
LECTURE

List of the concerned elements.

Comments:

In the case of traction curve, parametrised or not, the origin is always omitted.


If both the Young’s modulus and the traction curve are parametrised, the strain rate parameter should be identical.


Dans le cas de la courbe de traction parametree, il faudra fournir les vitesses de deformation de maniere croissante.


In the case of a component dependent upon strain rate, it is mandatory to give its value for a zero velocity (static case) and for a very large velocity.


A detailed description of the model may be found in the report DMT/98-036A, available on request.


Outputs:

The components of the ECR table are as follows for Continuum elements :

ECR(1) : pressure

ECR(2) : Von Mises criterion

ECR(3) : equivalent plastic strain

ECR(4) : plasticity multiplier

ECR(5) : damage

ECR(7) : new elastic limit

ECR(8) : strain rate

ECR(11): = 1 critical damage reached, otherwise < 1

When the “erosion” algorithm is activated (see page A.30, Section 4.4, keyword FAIL), an element is considered as failed if ECR(11) > 0.99.

7.6.12  CONCRETE: Old version

C.150


Object:


This option is used to define materials such as concrete, soil, rock, etc.


Comments:


The law of behaviour used in this model is based on plasticity; it takes into account three modes of damaging the material:

1) Damage due to traction;
2) Damage due to shear;
3) Damage due to hydrostatic pressure.


A material of this type possesses 38 input parameters; however, only some of them are compulsory. Each parameter is entered into the input file by means of a key-word, these words can be entered in any order. Just remember that the data placed between angle brackets are not compulsory, for example: <"PREC" prec>.


The numerical values of the different parameter are entered in absolute value. Moreover the following conventions have been adopted for the outputs:

positive values: tension stresses;
negative values: compression stresses.


The option "BETON" can be repeated as many times as necessary.


Syntax:


The data can be classified in 4 groups.


- 1) Generic data

    "BETON"  "RO" rho  "YOUN" young  "NU" nu
                 < "ALPH" alph >  < "PREC" prec >


rho

Density of the material.
young

Elasticity modulus.
nu

Poisson’s ratio.
alpha

Coefficient of thermal expansion.
prec

Precision of the computation on the internal iterations.

- 2) Data concerning the damage due to traction:


This kind of damage occurs in 3 phases:

- a) elastic behaviour;

- b) cracked elastic behaviour;

- c) perfectly plastic behaviour.



            A           .           .
       sig  |<--- a --->.<--- b --->.<----- c -----
            |           .           .
        ltr |...........*           .
            |          * *          .
            |         *   *         .
            |        *     *        .
            |       *       *       .
            |      *         *      .
            |     *         * *     .
            |    *         *   *    .
            |   *         *     *   .
            |  *         *       *  .
            | *         *         * .
            |*         *           *.
          O .------------------------------------------>  eps
                                   eptr

    < "BETA"  cisail >

  * initially isotropic material:

      "LTR"  ltr
      "EPTR" eptr

  * initially anisotropic material:

    < "IFIS" ifis >

    < "LT1"  lt1  >  < "LT2"  lt2  >  < "LT3"  lt3   >
    < "EPT1" ept1 >  < "EPT2" ept2 >  < "EPT3" ept3  >

    < "OUV1" ouv1 >  < "OUV2" ouv2 >  < "OUV3" ouv3  >

    < "ANGL" angle >  or  < "V1X" v1x    "V1Y" v1y    "V1Z" v1z >
                          < "V2X" v2x    "V2Y" v2y    "V2Z" v2z >
                          < "V3X" v3x    "V3Y" v3y    "V3Z" v3z >


cisail

Value of residual shear after cracking, in comparison with the initial status (value between 0 and 1).
ltr

Limit in traction in the case of an initially isotropic material.
eptr

Rupture strain in the case of an initially isotropic material.
ifis

Cracking index (0: no cracking, 1: one crack only, 2: two cracks, 3: three cracks).
lt1, lt2, lt3

Traction limits along the directions 1, 2 and 3 in the case of an initially anisotropic material.
ept1, ept2, ept3

Rupture strains along the directions 1, 2 and 3 in the case of an initially anisotropic material.
ouv1, ouv2, ouv3

Opening of the cracks along the directions 1, 2 and 3 in the case of an initially cracked material (deformations).
angle

Crack angle in the (X-Y) plane, in degrees, in the case of a plane stress analysis.
v1x,v1y,v1z

Components of the vector defining direction 1.
v2x,v2y,v2z

Components of the vector defining direction 2.
v3x,v3y,v3z

Components of the vector defining direction 3.


The model takes into account the anisotropy induced by the cracking.


The opening and closing of cracks is managed by the model.


For an axisymmetric or three-dimensional analysis, the user can enter different characteristics for the three directions.


In the case of an initially cracked material, one can input the opening of cracks by means of initial deformations along the cracked direction.


- 3) Data relative to shear damage:


Triaxial tests, carried out at different confinement levels, are necessary to determine the various parameters of the model. The results are then linearized and entered onto the diagram (sig1-sig3, eps1). The user may distinguish two different domains:

- a) brittle behaviour corresponding to the confinement levels, i.e. low sig3. This behaviour can be schematized by a decreasing branch and a negative work-hardening.

- b) ductile behaviour corresponding to the high confinement levels, i.e. high sig3. They can be schematized by a decrease in the elastic modulus and the appearance of irreversible strains and work-hardening.


Hence, the existence of a threshold stress of confinement, sig3, has been assumed. It corresponds to the border between the two domains: sig3 = PCT.


            A
  sig1-sig3 |
            |
    lcd-pcd |. . . . . . . . *-------------------
            |             *  .
            |          *     .
    lct-pct |. . . .*----------------------------
            |      *         .
            |     *          .
            |    *           .
        lcs | . *            .
            |  * *           .
            | *   *          .
            |*     *         .
          O .--------------------------------------->  eps1
                   epcs      epcd

      "LCS" lcs   "EPCS" epcs

    < "LBIC" lbic >  or  < "LCT" lct   "PCT" pct >
                         < "LCD" lcd   "PCD"  pcd   "EPCD" epcd  >


lcs

Uniaxial compression limit.
epcs

Strain at rupture in uniaxial compression.
lbic

Limit in biaxial compression in the case of a plane stress analysis.
lct

Compression limit under a confinement pressure equal to the threshold confinement value (sig3).
pct

Threshold confinement pressure.
lcd

Compression limit under the pressure of ductile confinement.
pcd

Pressure of ductile confinement.
epcd

Strain corresponding to the beginning of the perfectly plastic behaviour in the ductile domain.

- 4) Data relative to damage due to hydrostatic pressure:


A test is carried out where the sample is submitted to a hydrostatic pressure. The results are then linearized and entered onto the diagram: (P, Dv/v)

            A
         P  |
            |                     *
            |                 *
            |             *
            |         *   pente
       lph  |. . .*. . . . . . . . . . .
            |    *
            |   *
            |  *
            | *
            |*
          O .-------------------------------------->   Dv/v

    "LPH" lph   "PENT" pente


lph

Limit under hydrostatic pressure.
pente

Slope of the plastic branch on the diagram.

Outputs:


The different components of the ECR table are as follows:

ECR(1): hydrostatic pressure

ECR(2): Von Mises criterion

ECR(3): equivalent plastic strain

ECR(4): crack angle in the (X-Y) plane (in degrees)

ECR(5): yield limit in traction along direction 1

ECR(6): yield limit in traction along direction 2

ECR(7): yield limit in traction along direction 3

ECR(8): crack opening in direction 1

ECR(9): crack opening in direction 2

ECR(10): crack opening in direction 3

ECR(11): X component of the vector defining direction 1

ECR(12): Y component of the vector defining direction 1

ECR(13): Z component of the vector defining direction 1

ECR(14): lambda(1) damage due to hydrostatic pressure

ECR(15): lambda(2) damage due to the steady ductile Drucker criterion

ECR(16): lambda(3) damage due to Von Mises criterion with hardening

ECR(17): lambda(4) damage due to the steady brittle Drucker criterion

ECR(18): lambda(5) damage due to the brittle Drucker criterion with hardening

ECR(19): index of the damage criterion (0: no shear, 1: ductile shear, 2: brittle shear, 3: both).

ECR(19): crack index (0: no crack, 1: one crack only, 2: two cracks, 3: three cracks).


Default values for an ordinary concrete:


All values are given in S.I. units.


- 1) Generic data:
        RO      =     2.400E+03    Kg / m3
        YOUN    =     37000E+06    Pa
        NU      =     0.2100000
        ALPH    =     1.200E-05
        PREC    =     1.000E-03

- 2) Data for the traction damage:
        BETA    =     0.1000000
        LTR     =     4.440E+06    Pa
        EPTR    =     3.600E-04

- 3) Data for shear damage:
        LCS     =    44.400E+06    Pa
        EPCS    =     1.200E-02
        LBIC    =   111.000E+06    Pa
        LCT     =   243.312E+06    Pa
        PCT     =    71.040E+06    Pa
        LCD     =   255.406E+06    Pa
        PCD     =    79.920E+06    Pa
        EPCD    =     6.000E-02

- 4) Data for the hydrostatic pressure damage:
        LPH     =   134.887E+06    Pa
        PENT    =  7088.120E+06    Pa

7.6.13  CONCRETE: DYNAR LMT (BLMT)

C.151


Object:

Isotropic visco-damage and viscoplastic concrete material.


References:


Syntax:
   "BLMT"  "RO" rho  "YOUN" young  "NU" nu  "F0" f0
           "Q1" q1 "Q2" q2 "Q3" q3 "SGM0" sigM0 "XN" n
           "NVP" nvp "MVP" mvp "K" k "MDT" mDt "NDT" nDt
           "MDC" mDc "NDC" nDc "ED0" epsD0
           "AC" ac "BC" bc "AT" at "BT" bt   /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
f0

Initial porosity of the concrete (0.3)
q1

Parameter of the modified Gurson plasticity criterion (0.5 to 2.)
q2

Parameter of the modified Gurson plasticity criterion (0.5 to 2.)
q3

Parameter of the modified Gurson plasticity criterion (0.5 to 2.)
sigM0

Resistance of the cement paste without pores (70 Mpa)
n

Exponent of the viscoplasticity threshold (15.)
nvp

Parameter of the Perzyna type viscoplasticity (1.5)
mvp

Parameter of the Perzyna type viscoplasticity (1.D-2)
k

Influence the porosity evolution (15 to 60)
mDt

Tension damage viscosity parameter (0.5D-4)
nDt

Tension damage viscosity parameter (5.)
mDc

Compression damage viscosity parameter (0.5D-3)
nDc

Compression damage viscosity parameter (20.)
epsD0

Strain tension threshold (1.D-04)
ac

Parameter for the compression (3000)
bc

Parameter for the compression (4.)
at

Parameter for the tension (20000)
bt

Parameter for the tension (1.6)

Comments:

1/ - BE CAREFUL the initial porosity influence the real young modulus

Km=YOUNG/(3*(1-2*NU))

Gm=YOUNG/(2*(1+NU))


2/ - Compressibily and shear moduli with porosity f (Mori-Tanaka)

Kporo=4*XKm*XGm*(1-f)/(4*XGm+3*XKm*f)

Gporo=XGm*(1-f)/(1+f*(6*XKm+12*XGm)/(9*XKm+8*XGm))


3/ - Plasticity criterion FNT:

F = 3*J2(SIG) / SGM**2 + 2Q1f cosh(Q2 I1 / 2SGM) - (1+(Q3 f)**2)


4/ - Plastic strain evolution:

EPSP = 1/(1-D)*(FNT/MVP)**NVP * dFNT/dSIG


5/ - Porosity evolution:

Df = K * f/(1-f) * (FNT/MVP)**NVP

f(t+dt) = f(t) + df


6/ - Damage threshold function in tension and compression:

FDi = (EPSE - ED0 - 1/Ai*(Di/(1-Di))**(1/Bi))


7/ - Damage evolution in tension and compression:

Di= (FDi/MDi)**NDi


Outputs:

The components of the ECR table are as follows:

ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : Isotropic damage variable
ECR(4) : Material porosity
ECR(5) : xx plastic strain
ECR(6) : yy plastic strain
ECR(7) : zz plastic strain
ECR(8) : xy plastic strain
ECR(9) : yz plastic strain
ECR(10): zx plastic strain
ECR(11): Stress in the matrix without pores
ECR(12): Tension damage variable
ECR(13): Compression damage variable
ECR(14): Mazars threshold

7.6.14  BPEL: MODEL FOR PRESTRESSING CABLE-CONCRETE FRICTION

C.152


Object:


This material allows modelling friction between a prestressing cable and concrete according to BPEL rools (Prestressed Concrete with Borderlines). In French, BPEL stands for Beton Precontraint aux Etats Limites. This is a particular Coulomb-type friction law where the friction force threshold depends on tension in the cable. At each time step, the tension in a cable node is calculated first (mean tension between those in two cables elements using the considered node), then the friction force is calculated ans compared with a threshold.


Syntax:

    "BPEL"  "FRLI" phil "FRCO" phic   /LECTURE/


phil

Friction coefficient for rectilinear motion,by unit length (1/m)
phic

Friction coefficient for curvilinear motion,by unit angle (1/rad)
LECTURE

List of the elements concerned.

Comments:


This material can be used with RNFR element (nonlinear frictional spring) only.


Outputs:


The components of the ECR table are as follows:

ECR(1): Tangential friction force.

ECR(2): Total relative tangential displacement between cable and concrete.

ECR(3): State indicator: 0 if sliding, 1 if adherence.

7.6.15  CONCRETE: MAZARS-LINEAR ELASTIC LAW WITH DAMAGE

C.153


Object:

Isotropic linear elastic with a modified Mazars damage for concrete and brittle rupture materials.


References:

1- Jacky MAZARS, "Application de la mécanique de l’endommagement au comportement non linéaire et à la rupture du béton de structure", Thèse de doctorat, Université Pierre et Marie Curie - Paris 6, 1984.


2- Yann CHUZEL-MARMOT, "Caractérisation expérimentale et simulation numérique d’impacts de glace à haute vitesse", Thèse de doctorat, Université MEGA de Lyon - INSA Lyon, 2009.


Syntax:
   "MAZA" "RO"   rho  "YOUN" young  "NU"   nu   "EPSD" epsd
          "DCRI" dcri "AT"   at     "AC"   ac   "BT"   bt
        "BC"   bc   "LCAR" lcar   "CSTA" csta "DCOE" dcoe
        "VCRI" vcri "VIMP" vimp                           /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
epsd

Initial strain threshold.
dcri

Critical value of damage (=1 per default).
at

Parameter of the tension law (asymptote of the curve stress-strain)
ac

Parameter of the compression law (asymptote of the curve stress-strain)
bt

Parameter of the tension law (shape of the curve stress-strain)
bc

Parameter of the compression law (shape of the curve stress-strain)
lcar

Length parameter of the delay-damage
csta

Parameter of the delay-damage (=1 per default)
dcoe

Exponent of the sensitivity to the strain rate in tension (=1/3 per default)
vcri

Critical velocity in tension (=1 per default)
vimp

Velocity impact of the body (or strain rate if it’s not an impact)

Comments:

You can deactivate the delay effect with a negative value for the parameter lcar.


You can also deactivate the damage (so you obtain a linear material) with a negative value for the parameter epsd.


Outputs:

The components of the ECR table are as follows:

ECR(1) : Pressure
ECR(2) : Von Mises criterion
ECR(3) : Equivalent deformation
ECR(4) : Global Damage
ECR(5) : Level "traction/compression"
ECR(6) : Strain rate
ECR(7) : Threshold damage
ECR(8) : Damage in traction
ECR(9) : Damage in compression
ECR(10): Factor of dynamic amplification in traction
ECR(11): Bc parameter eventually corrected

7.6.16  DADC: Dynamic Anisotropic Damage Concrete

C.154 - Feb 13


Object:

Concrete material with induced anisotropic damage represented by one damage variable and modelling biaxial behaviour.


Reference:

Armand Leroux, Modèle multiaxial d’endommagement anisotrope: Gestion numerique de la rupture et application à la ruine des structures en bèton armè sous impacts. Thèse LaMSID-UMR EDF/CNRS/CEA (2012)[804]


Syntax:
   "DADC"  "RO" rho      "YOUN" young    "NU" nu     "SIGT" sigyt
           "SIGC" sigyc <"SGBC" sigybc>  "ALPH" alpha
           "BETA" beta  "BT" bt    "DC" dc
           <"XINF" xinf>     <"BV" bv>     <"DTFI" dtfi>
           <"TCS" tcs>       /LECTURE/
rho

Density
young

Young’s modulus
nu

Poisson’s ratio
sigyt

Elastic limit for the tension
sigyc

Elastic limit for the compression in absolute value
sigybc

Elastic limit for the bi-compression in absolute value. Default value is taken from Kupfer diagram as 1.1· SIGC.
alpha

Damage parameter ALPH. This parameter allows to modify peak values in tension and compression strengths.
beta

Damage parameter BETA. This parameter allows to modify the post-peak behaviour in compression and bi-compression
bt

Parameter of the function b(Tx). It is used for Hillerborg regularization.
dc

Critical value of the damage for the numerical control of rupture. (0.9 to 1)
Optional parameters
dinf

Delay damage parameter (suggested value: 50000. s-1)
bv

Delay damage parameter (suggested value: 1.)
dtfi

Activating calculation of time step in the behaviour law with a value of first time step (recommended value, 1E-8 s.). The parameter is considered when the option "PAS AUTO" is used.
tcs

Formulation of the selected function b(Tx) (1: Formulation TCS1(default), 2: Formulation TCS2 )

Outputs:

The components of the ECR table are as follows:

ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : Damage Dxx
ECR(4) : Damage Dyy
ECR(5) : Damage Dzz
ECR(6) : Damage Dxy
ECR(7) : Damage Dyz
ECR(8) : Damage Dzx
ECR(9) : Rotation matrix for the eigenvector basis damage matrix (xx)
ECR(10): Rotation matrix for the eigenvector basis damage matrix (xy)
ECR(11): Rotation matrix for the eigenvector basis damage matrix (xz)
ECR(12): Rotation matrix for the eigenvector basis damage matrix (yx)
ECR(13): Rotation matrix for the eigenvector basis damage matrix (yy)
ECR(14): Rotation matrix for the eigenvector basis damage matrix (yz)
ECR(15): Rotation matrix for the eigenvector basis damage matrix (zx)
ECR(16): Rotation matrix for the eigenvector basis damage matrix (zy)
ECR(17): Rotation matrix for the eigenvector basis damage matrix (zz)
ECR(18): Critical state damage flag
ECR(19): Damage rate
ECR(20): Equivalent effective stress
ECR(21): 1st eigen value basis damage matrix
ECR(22): 2nd eigen value basis damage matrix
ECR(23): 3rd eigen value basis damage matrix
ECR(24): The biggest three eigen values basis damage matrix
ECR(25): Proposed time step
ECR(26): Filtered stress tensor after five time steps
ECR(27): Time step first flag
ECR(28): Estimation error flag (0=ok,1=error)
ECR(29): stress triaxiality
ECR(30): Component of filtered stress tensor (xx)
ECR(31): Component of filtered stress tensor (yy)
ECR(32): Component of filtered stress tensor (zz)
ECR(33): Component of filtered stress tensor (xy)
ECR(34): Component of filtered stress tensor (yz)
ECR(35): Component of filtered stress tensor (zx)
ECR(36): Number of times that the damage criterion (for the calculation of the time step in the behaviour law) is not respected
ECR(37): Largest components (absolute values) of the strain rate tensor

7.6.17  DPDC: Dynamic Plastic Damage Concrete

C.155


Object:

DPDC A three-invariant cap model with isotropic damage for concrete material. Perfect plasticity with isotropic hardening cap model, brittle and ductile damage, crack closing and strain rate effect.


Reference:

Damage Plastic Model for Concrete Failure Under Impulsive Loadings, Daniel Guilbaud,
XIII International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS XIII (2015), E. Oñate, D.R.J. Owen, D. Peric and M. Chiumenti (Eds)


Comments:

All values must be given in SI units.


Syntax:
   "DPDC"  "RO" rho     "YOUN" young   "NU" nu     "FC" fc
           "DAGG" dagg
            <"GFT" gft       "GFC" gfc       "GFS" gfs>
            <"PWRC" pwrc>   <"PWRT" pwrt>
            <"B" b>         <"D" d>
            <"OVEC" overc>   <"OVET" overt>   <"SRAT" srate>
            <"R" r>         <"XO" xo>       <"W" w>
            <"D1" d1>       <"D2" d2>       <"PMOD" pmod>
            <"TXCA" txca "TXCT" txct "TXCL" txcl "TXCB" txcb>
            <"TXEA" txea "TXET" txet "TXEL" txel "TXEB" txeb>
            <"FTR"  ftr  "FBCR" fbcr "I1CR" i1cr "RJCR" rjcr>
            <"NC" nc "NOC" noc>     <"NT" nt "NOT" not>
            <"REPW" repow>   <"RECO" recov>
            <"PRED" pred>   <"COPP" copp>  <"EXCT" excent>
            <"LC" lc "DINF" dpinf>
            <"VERS" vers>
            <"EFVI">
            <"EFVN">
            <"EROD" <"ENDT" endt> <"ENDC" endc> <"DVOL" dvol>>
             /LECTURE/
rho

Density
youn

Young’s modulus
nu

Poisson’s ratio
fc

Uniaxial compressive strength (Pa)
dagg

Maximum aggregate size (m)
vers

Version number (8 = old version intended to be replaced by version 9) (9 = new version). Version 9 is used by default.
Optional parameters
gft

Tensile fracture energy at fc = 10MPa (interpolated as a function of the maximum aggregate size) (J/m2)
gfc

Compressive fracture energy at fc = 10MPa (default value: 200 gft) (J/m2)
gfs

Shear fracture energy at fc = 10MPa (default value: gft) (J/m2)
pwrc

Shear-to-compression transition parameter (default value: 1.) (advised value: 3.3) (without unit)
pwrt

Shear-to-tension transition parameter (default value: 1.) (without unit)
b

Ductile shape softening parameter (default value: 100) (without unit)
d

Brittle shape softening parameter (default value: 0.1) (without unit)
overc

Maximum overstress allowed in compression (interpolated as a function of the material strength in compression) (Pa)
overt

Maximum overstress allowed in tension (interpolated as a function of the material strength in compression) (Pa)
srate

Ratio of effective shear stress to tensile stress fluidity parameter (default value: 1.) (without unit)
r

Cap aspect ratio (default value: 5.) (advised value: 1.) (without unit)
xo

Cap initial location (interpolated as a function of the material strength in compression) (advised value: -10.E6) (Pa)
w

Maximum plastic volume compaction (default value: 0.05) (without unit)
d1

Linear shape parameter of the cap (default value: 2.5E-10 Pa-1)
d2

Quadratic shape parameter of the cap (default value: 3.49E-19 Pa-2)
parameters for meridians (for all versions untill 7)
txca

TXC surface constant term (TXC: triaxial compression) (interpolated as a function of the material strength in compression) (Pa)
txct

TXC surface linear term (interpolated as a function of the material strength in compression) (without unit)
txcl

TXC surface nonlinear term (interpolated as a function of the material strength in compression) (Pa)
txcb

TXC surface exponent (interpolated as a function of the material strength in compression) (Pa-1)
txea

TXE surface constant term (TXE: triaxial extension) (interpolated as a function of the material strength in compression) (without un
txet

TXE surface linear term (interpolated as a function of the material strength in compression) (Pa-1)
txel

TXE surface nonlinear term (interpolated as a function of the material strength in compression) (without unit)
txeb

TXE surface exponent (interpolated as a function of the material strength in compression) (Pa-1)
parameters for meridians (for versions 8 and 9)
ftr

ratio ft/fc with ft uniaxial tensile strength (default value: 0.1)
    Beware! ftr should be such that: 0.06 < ftr < 0.11
fbcr

ratio fbc/fc with fbc biaxial compressive strength (default value: 1.16)
i1cr

ratio i1/fc : horizontal coordinate of a point belonging to the compressive meridian (default value: -8.806)
rjcr

ratio √J2/fc : vertical coordinate of the same point (default value: 2.4985)
pmod

Modify moderate pressure softening parameter (default value: 0.) (without unit)
nc

Rate effects power for uniaxial compressive strength (default value: 0.78) (without unit)
noc

Rate effects parameter for uniaxial compressive strength (interpolated as a function of the material strength in compression). Default unit: s-0.22. The unit depends on the value of nc
nt

Rate effects power for uniaxial tensile strength (default value: 0.48) (without unit)
not

Rate effects parameter for uniaxial tensile strength (interpolated as a function of the material strength in compression). Default unit: s-0.52. The unit depends on the value of nt
repow

Power which increases fracture energy with rate effects (default value: 1.) (without unit)
recov

Option to recover stiffness in compression from tensile damage (default value: 0.) (without unit)
pred

Damage level for predamaged concrete (default value: 0.) (without unit)
copp

Coefficient for potential surface (default value: 1. associated plasticity)
excent

Constant excentricity (default value: excentricity function of J1)
lc

Caracteristic length for damage (m) (first parameter for EFVN option)
dpinf

Maximum rate of damage (1/s) (second parameter for EFVN option)
EFVI

Strain rate effect option (default value : strain rate effect excluded)
EFVN

Bounded damage rate effect option available with verion 9 only
EROD

Mandatory keyword to introduce different failure criteria (damage, plastic strain). The keyword "EROS" must be added in the problem description of the data file to activate the "erosion" algorithm of the code.
endt

Brittle damage threshold
endc

Ductile damage threshold
dvol

Volumetric strain threshold

Outputs:

The components of the ECR table are as follows:

ECR(1) : Pressure
ECR(2) : Von Mises criterion
ECR(3) : Equivalent plastic strain
ECR(4) : Cube root of initial element volume (if version8)
ECR(5) : Lode angle
ECR(6) : Total variation of the isotropic hardening parameter
ECR(7) : Volumetric strain
ECR(8) : Plastic volumetric strain
ECR(9) : Ductile damage parameter
ECR(10): Brittle damage parameter
ECR(11): Ductile damage threshold
ECR(12): Brittle damage threshold
ECR(13): Current damage (not used in version 9)
ECR(14): Initial damage threshold in compression
ECR(15): Initial damage threshold in tension
ECR(16): filtered effective strain rate
ECR(17-22): Components of elastoplastic stress tensor
ECR(23-28): Components of viscoplastic stress tensor
ECR(29-34): Back stress if version 2
else:

ECR(29): Effective strain rate
ECR(30): Triaxiality
ECR(31): Static ductile damage threshold
ECR(32): Static brittle damage threshold

7.6.18  DAMAGE

C.160


Object:

This option allows to associate to the materials VON MISES ISOTROPE and VON MISES PARFAIT different damage laws, and to request the calculation of several fracture criteria. Now, only one criterion (Tuler-Butcher) is available.


Syntax:

    "CRIT"  $[ "TULE" <"SIGL" sigl >  <"EPSL" epsl >  <"TAUL" taul >
                       "SIGS" sigs     "LAMB" lamb    <"KER"  ker  >  ]$
                       /LECTURE/
"CRIT"

Indicates that the calculation of different damage criteria is required.
"TULE"

The TULER-BUTCHER’s criterion is selected.
sigl

Maximum principal stress criterion.
epsl

Maximum volumetric deformation criterion.
taul

Octahedral shear stress criterion.
sigs

First parameter of the Tuler-Butcher law.
lamb

Second parameter of the Tuler-Butcher law.
ker

Third parameter of the Tuler-Butcher law.
LECTURE

List of the concerned elements.

Comments:

The element types accepting these materials are: in 2D elements TRIA, CAR1 and CAR4 and in 3D elements CUBE, CUBE6, CUBE8, PRIS, TETR and PRI6.


Currently the damage model is only available in association with the materials Isotropic Von Mises, Steinberg-Guinan and dynamic Von Mises.


The isotropic Von Mises material must appear first in the input file, before the calculation of the damage criteria, if any, and one of the two damage laws, if necessary.


The Tuler-Butcher is given by the following expression where σ123 representing the principal stresses:

t


0
 (Max123)−σs) λ  dt    <    ker 


The results stored in the ECR table (5 values) are, according to the material type:


Tuler-Butcher :

ECR(1) = Maximum principal stress
ECR(2) = Maximum principal deformation
ECR(3) = Octahedral shear stress
ECR(4) = Volume deformation
ECR(5) = Tuler-Butcher criterion

Exemple:

A criterion "LOI 3", is associated with the principal material "LOI 1".


The corresponding data will be for example:

  LOI  1    VMIS ISOT RO 7800.  YOUN 74020E6  NU .3  ELAS 350E6
                      ENDO 3
                 TRAC 4
                       350.E6         .472845E-2
                       476.26E6      7.2835E-2
                       518.51E6      15.700E-2
                       538.03E6      21.607E-2
                       550.24E6      26.083E-2
                 LECT TOUS

  LOI 3    CRIT TULE  SIGS 1E7 LAMB 1.0
                 LECT TOUS

7.6.19  EOBT: ANISOTROPIC DAMAGE OF CONCRETE (EDF)

C.161


Object:

Concrete material with induced anisotropic damage.


Reference:

V. Godard, Modélisation de l’endommagement anisotrope du béton avec prise en compte de l’effet unilatéral : Application à la simulation numérique des enceintes de confinement, Thèse de l’Université Paris VI, 2005. M. Bottoni, Loi de comportement ENDO_ORTH_BETON, Manuel de référence de Code_Aster, R7.01.09.


Syntax:
   "EOBT"  "RO" rho   "YOUN" young   "NU" nu   "K0" k0
           "K1" k1   "K2" k2   "ECRB" ecrb    "ECRD" ecrd
           < "DC" dc >  < "DM" dm >   /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
k0

Threshold in stress for the tension.
k1

Parameter for the threshold in stress in compression.
k2

Parameter for the threshold in stress in compression.
ecrb

Parameter driving the evolution of the loading surface while the damage tensor B is growing.
ecrd

Parameter driving the evolution of the loading surface while the damage scalar d is growing.

Optional parameters:
dc

Limit value for the eigenvalues of the damage tensor B and for the damage scalar d. When this limit is reached, the material is cons
dm

Imposed value for damage when it reaches its limit value. By default, dm is set to 0.999

Outputs:

The components of the ECR table are as follows:

ECR(1) : pressure
ECR(2) : Damage in compression D
ECR(3) : Damage Dxx
ECR(4) : Damage Dyy
ECR(5) : Damage Dzz
ECR(6) : Damage Dxy
ECR(7) : Damage Dyz
ECR(8) : Damage Dzx
ECR(9) : Rotation matrix for the eigenvector basis damage matrix (xx)
ECR(10): Rotation matrix for the eigenvector basis damage matrix (xy)
ECR(11): Rotation matrix for the eigenvector basis damage matrix (xz)
ECR(12): Rotation matrix for the eigenvector basis damage matrix (yx)
ECR(13): Rotation matrix for the eigenvector basis damage matrix (yy)
ECR(14): Rotation matrix for the eigenvector basis damage matrix (yz)
ECR(15): Rotation matrix for the eigenvector basis damage matrix (zx)
ECR(16): Rotation matrix for the eigenvector basis damage matrix (zy)
ECR(17): Rotation matrix for the eigenvector basis damage matrix (zz)
ECR(21): 1st eigen value of the damage tensor B
ECR(22): 2nd eigen value of the damage tensor B
ECR(23): 3rd eigen value of the damage tensor B

7.6.20  ENGR: ELASTIC GRADIENT DAMAGE MATERIAL

C.162


Object:

This section describes an elastic-damage material with gradient regularization. The development is still in progress and a more detailed presentation can be found in [889], [890].

This model can be used to predict crack initiation and propagation in a quasi-brittle medium (such as glass or concrete) under dynamic loading conditions. In particular, no plasticity is currently accounted for in this model. It can be seen as a variational approach to fracture in the sense of [Francfort and Marigo 1998, Revisiting brittle fracture as an energy minimization problem]. Crack nucleation, kinking, branching, coalescence or arrest can be automatically predicted through energy minimization. It is known that traditional approaches (with or without X-FEM numerical schemes) in fracture mechanics may fail in the case of crack initiation from a perfectly regular domain or complex crack topological changes. The variational approach can thus be considered as a unified and complete framework of fracture.

An additional scalar nodal field 0≤α≤ 1, called damage, is introduced to the model. This field depicts a continuous transition between the undamaged part α=0 and the crack α=1. Spurious mesh dependency observed in traditional damage mechanics is suppressed by gradient regularization ∇α. As a consequence, a material characteristic internal length ℓ naturally appears, which determines the size of the damage process zone. This parameter is linked to the maximal tensile stress σm that can be supported by the material.

Only two mandatory fracture-type material parameters need to be entered. One is the fracture toughness Gc defined as the energy needed to create a crack of unit area. Through Irwin’s formula this quantity Gc can be related to the criterion in stress intensity factors KIC. Another parameter is the internal length ℓ or equivalently the maximal tensile stress σm.

From a computational point of view, we need to solve at every time step a bound-constrained (quadratic or convex) minimization problem for damage. For that reason, the parallel linear algebra library PETSc is used to manipulate the Hessian matrix and various vectors. For various options of PETSc used for this material ENGR, it is advised to refer to 12.23.


Syntax:
   "ENGR"     "RO"   rho   "YOUN" young   "NU"   nu   "GC"   gc
           |[ "ELL"  ell ; "SIGM" sigm ]|
            < "LAW"  law   "TC"   tc      "AC"   ac   >  /LECTURE/

Mandatory parameters:
rho

Density ρ.
young

Young’s modulus E.
nu

Poisson’s ratio ν.
gc

Fracture toughness Gc.

ONE additional mandatory fracture parameter from two possibilities:
ell

Material characteristic (internal) length ℓ.
sigm

Maximal tensile stress σm.

Optional parameters:
law

Damage constitutive law describing local stiffness degradation due to damage a(α) and local damage dissipation evolution function w(α). 3 choices are currently implemented.
tc

This parameter determines the tension-compression asymmetry formulation. For brittle materials such as glass or concrete, the material can be easily damaged or cracked under tension. It is no longer the case under compression. Currently 6 formulations are available.
ac

This parameter can be used with the erosion mechanism to define a critical stiffness degradation. Its default value is 10−3. If this value is reaches, the Gauss point will be considered as eroded.

Outputs:

No public ECR components are available for output.

7.6.21  LINEAR MULTI-LAYER

C.165


Object


This directive allows to define materials obtained by homogenisation through the thickness of different layers (or plies) each having a linear orthotropic behaviour.


Syntax:

    "MCOU"      |[    "BACON"     ibacon                     ;
                     "NBCOUCHE"  ...          /LECTURE/      ]|

   For the user data option (NBCOUCHE) :

     ... "NBCOUCHE"  nbcouche  "ZMIN"  zmin

        nbcouche times   :

        |  "ZMAX"  zmax   "TETA"  teta   "ROCO"  roco   "YG1"   yg1 |
        |  "YG2"   yg2    "NU12"  nu12   "G12"   g12                |
        | < "G13"  g13 >  < "G23"  g23 >  "TERM"                    |


ibacon

Logical unit number of the BACON file from which the characteristics of this material will be read. Using this option implies the necessity to introduce the keyword "MBACON" in part A of the input file (see page A.30) in order to dimension the arrays used by this model.
NBCOUCHE

The characteristics will be listed below.
nbcouche

Numbers of layers of the composite.
zmin

Minimum side of the first layer.
zmax

Maximum side of the current layer.
teta

Angle (in degrees) of the first vector of the orthotropy frame of the current layer with respect to the first side of the element.
roco

Density of the current layer.
yg1

Young’s modulus along direction 1 of the current layer.
yg2

Young’s modulus along direction 2 of the current layer.
nu12

Poisson’s coefficient among directions 1-2.
g12

Shear modulus among directions 1-2.
g13

Shear modulus among directions 1-3.
g23

Shear modulus among directions 2-3.
TERM

Indicates that the data for layer i are terminated.
LECTURE

List of the concerned elements.

Comments:


When the BACON option is used, EUROPLEXUS reads the numbers of the elements associated with this material directly from the BACOn file: the /LECTURE/ procedure is redundant. Currently, one may read only one type of laminated material per calculation. On the other hand, EUROPLEXUS will write on the logical unit (ibacon+1):

   1) the element number (1 value)
   2) the angle (in degrees) between the first side and the
           first direction of the laminated (1 value)
   3) the components of the symmetric matrices A, B and D
           ( A(1,1), A(2,1),A(2,2), A(3,1),A(3,2),A(3,3)...)
           (3x6= 18 values).


For the NBCOUCHE option, the various layers must be described in growing order of z. In particular, zmax(couche_i) = zmin(couche_i+1).


The value z=0 corresponds to the neutral fiber of the element. This material allows to take excentricity into account.


For the shells that consider transverse shears, i.e. DST3, Q4G4, Q4GR, Q4GS, it is necessary to give the values of G23 and G13.


Outputs:


The various components of the ECR table (values computed in the local reference of the shell element) are as follows:


Element COQ3:

ECR(1) : Von Mises on the lower face of the shell

ECR(2) : Von Mises on the upper face of the shell

ECR(3) : -d3w/dx3 at the integration point

ECR(4) : -d3w/dy3 at the integration point

ECR(5) : -d3w/dx2dy at the integration point

ECR(6) : -d3w/dxdy2 at the integration point


Elements DKT3 and DST3:

ECR(1) : Von Mises on the lower face of the shell

ECR(2) : Von Mises on the upper face of the shell

ECR(3) : d2beta_x/dx2 at the first integration point

ECR(4) : d2beta_x/dy2 at the first integration point

ECR(5) : d2beta_x/dxdy at the first integration point

ECR(6) : d2beta_y/dx2 at the first integration point

ECR(7) : d2beta_y/dy2 at the first integration point

ECR(8) : d2beta_y/dxdy at the first integration point



Recall that the table of deformations EPST is composed by the following parameters (computed at the integration point):

EPST(1) : du/dx (membrane deformation e_xx)

EPST(2) : dv/dy (membrane deformation e_yy)

EPST(3) : du/dy+dv/dx (membrane deformation 2*e_xy)

EPST(4) : dbeta_x/dx (=-d2w/dx2 if thin shell)

EPST(5) : dbeta_y/dy (=-d2w/dy2 if thin shell)

EPST(6) : dbeta_y/dx + dbeta_x/dy

EPST(7) : 2*epsi_xz (eventually)

EPST(8) : 2*epsi_yz (eventually)


Example:


We assume a composite formed by 6 layers regularly spaced on a thickness of 0.12 m. The corresponding data will be:

   MCOUCH    NBCOUCHE  6       ZMIN -0.06
       ZMAX -0.04  TETA  5. ROCO 2.5E3  YG1 40E9 YG2 20E9
                   NU12 0.2 G12 16.6666667E9 TERM
       ZMAX -0.02  TETA 36. ROCO 2.5E3  YG1 40E9 YG2 25E9
                   NU12 0.2 G12 16.6666667E9 TERM
       ZMAX -0.00  TETA 48. ROCO 2.5E3  YG1 40E9 YG2 20E9
                   NU12 0.2 G12 16.6666667E9 TERM
       ZMAX  0.02  TETA 135 ROCO 2.5E3  YG1 40E9 YG2 20E9
                   NU12 0.2 G12 16.6666667E9 TERM
       ZMAX  0.04  TETA 33. ROCO 2.5E3  YG1 40E9 YG2 20E9
                   NU12 0.2 G12 16.6666667E9 TERM
       ZMAX  0.06  TETA 15. ROCO 2.5E3  YG1 40E9 YG2 40E9
                   NU12 0.2 G12 16.6666667E9 TERM
                                                  LECT 3  4 5 TERM

7.6.22  CHANG-CHANG MULTI-LAYER MODEL

C.170


Object:


This directive allows to define composite materials using the CHANG-CHANG criterion, as described in:

  A Progressive Damage Model of Laminated Composites
    Containing Stress Concentrations
  by F.-K. CHANG and K.-Y. CHANG
  in  Journal of Composite Materials, Vol. 21, Sept. 1987.

Syntax:

    "CHANG"     |[    "BACON"     ibacon                     ;
                $    "NBCOUCHE"  ...  PBASE ....  /LECTURE/      $

    For the user data option (NBCOUCHE) :

     ... "NBCOUCHE"  nbcouche  "ZMIN"  zmin

        nbcouche times   :

        |  "ZMAX"  zmax   "TETA"  teta   "ROCO"  roco   "YG1"   yg1 |
        |  "YG2"   yg2    "NU12"  nu12   "G12"   g12                |
        |  "XT"    xt     "XC"    xc     "YT"    yt     "YC"    yc  |
        |  "SC"    sc     "A0"    a0     "BETA"  beta               |
        | "TERM"                                                    |

    Once described the layers, one gives 2 points in order to
    define a reference direction:

         "PBASE"   "LECTURE" nod1 nod2 "TERM"


ibacon

Logical unit number of the BACON file from which the characteristics of this material will be read. Using this option implies the necessity to introduce the keyword "MBACON" in part A of the input file (see page A.30) in order to dimension the arrays used by this model.
NBCOUCHE

The characteristics will be listed below in the main input file.
nbcouche

Number of layers in the composite.
zmin

Minimum side of the first layer.
zmax

Maximum side of the current layer.
teta

Angle (in degrees) of the first vector of the orthotropy frame of the current layer with respect to the reference direction.
roco

Density of the current layer.
yg1

Young’s modulus along direction 1 of the current layer.
yg2

Young’s modulus along direction 2 of the current layer.
nu12

Poisson’s coefficient among directions 1-2.
g12

Shear modulus among directions 1-2.
xt

Traction limit along direction 1 of the orthotropy frame.
xc

Compression limit along direction 1 of the orthotropy frame.
yt

Traction limit along direction 2 of the orthotropy frame.
yc

Compression limit along direction 2 of the orthotropy frame.
sc

Shear limit 1-2 of the orthotropy frame.
a0

Critical area a0 of the CHANG-CHANG criterion.
beta

Weibull coefficient.
TERM

Indicates that the data for layer i are terminated.
nod1,nod2

Numbers of 2 nodes defining the reference direction.
LECTURE

List of the concerned elements.

Comments:


When the BACON option is used, EUROPLEXUS reads the numbers of the associated elements directly from the BACON file: the procedure /LECTURE/ is redundant. For this material, the number of laminas is unlimited. However, one should give the adequate numbers in the dimensioning section of the input file: see the key-words MATE and ECRO in the DIMENSIONS directive.


For the NBCOUCHE option, the various layers must be described along increasing order of z. In particular, zmax(couche_i) = zmin(couche_i+1).


The value z=0 corresponds to the neutral fiber of the element. This material allows to account for excentricity.


Outputs:


This constitutive law computes the damages appearing in each plie of the laminated structure. To this end, it is necessary to define the damage parameters in each layer. In each ply, the ECR table is dimensioned at 10, and the main parameters are:

DIMENSION ECR(10,NPLIS)

ECR(2,ipli) : Von Mises of the ply

ECR(3,ipli) : Rupture criterion of the matrix in traction

ECR(4,ipli) : Rupture criterion of the matrix in compression

ECR(5,ipli) : Rupture criterion of the fiber, or fiber-matrix delamination.

7.6.23  LINEAR ORTHOTROPY

C.181


Object:


The directive is used to enter materials with a linear orthotropic behaviour into a coordinate system defined by the user. The model is described in: Mécanique des Matériaux Solides (J-Lemaitre, L-Chaboche. Ed: Dunod, 1986).


Syntax:

    "ORTH"  "RO"  rho    "YG1"  yg1    "YG2"   yg2  "YG3" yg3
            "NU12" nu12  "NU13" nu13   "NU23" nu23
            "G12"  g12   "G13"  g13    "G23" g23          /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

Young’s modulus along direction 3.
nu12

Poisson’s ratio between directions 1 and 2.
nu13

Poisson’s ratio between directions 1 and 3.
nu23

Poisson’s ratio between directions 2 and 3.
g12

Shear modulus between directions 1 and 2.
g13

Shear modulus between directions 1 and 3.
g23

Shear modulus between directions 2 and 3.
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated coordinate system is defined by the option "CORTHO" (see page C1.95) for the multilayer element CMC3.


The associated coordinate system is defined by the option "MORTHO" (see page C1.96) for the continuum elements in 3D and in plane strain.


The associated coordinate system is defined by the directive "COMPLEMENT" (pages C1.95 and C1.96):


- "COMPLEMENT" "CORTHO" for the shells;


- "COMPLEMENT" "MORTHO" for the continuum elements 3D and 2D plane strain and axisymmetric.


Verify that this material is available for your elements, by means of the tables of page C.100.


Outputs:


The different components of the ECR table are as follows, for the CMC3 element:

ECR(1): Von mises criterion on the lower face of the multilayer element CMC3.

ECR(2): Vom mises criterion on the upper face of the multilayer element CMC3.


The different components of the ECR table are as follows, for the continuum elements:

ECR(1): pressure.

ECR(2): Vom mises criterion.

7.6.24  ORTS : LINEAR ORTHOTROPY (Local basis)

C.182


Object:

Attention: The description of the material is not showing all capabilities of the material. The material allows erosion and has several more input and output variables.


The directive is used to enter materials with a linear orthotropic behaviour into a coordinate system defined by the user. The model is described in: Mécanique des Matériaux Solides (J-Lemaitre, L-Chaboche. Ed: Dunod, 1986).

Stress and strain are expressed in the user coordinate system.


Syntax:

    "ORTS"  "RO"  rho    "YG1"  yg1    "YG2"   yg2  "YG3" yg3
            "NU12" nu12  "NU13" nu13   "NU23" nu23
            "G12"  g12   "G13"  g13    "G23" g23
            <"XT1"  xt1   "XT2"  xt2    "XT3" xt3
            "XC1"  xc1   "XC2"  xc2    "XC3" xc3
            "RST1" rst1  "RST2" rst2   "RST3" rst3
            "CRIT" icrit>        /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

Young’s modulus along direction 3.
nu12

Poisson’s ratio between directions 1 and 2.
nu13

Poisson’s ratio between directions 1 and 3.
nu23

Poisson’s ratio between directions 2 and 3.
g12

Shear modulus between directions 1 and 2.
g13

Shear modulus between directions 1 and 3.
g23

Shear modulus between directions 2 and 3.
xt1

Failure criterion for tension in x-direction.
xt2

Failure criterion for tension in y-direction.
xt3

Failure criterion for tension in z-direction.
xc1

Failure criterion for compression in x-direction.
xc2

Failure criterion for compression in y-direction.
xc3

Failure criterion for compression in z-direction.
rst1

Failure criterion for shear in xy-direction.
rst2

Failure criterion for shear in yz-direction.
rst3

Failure criterion for shear in xz-direction.
icrit

Erosion criteria type (e.g.: tsai-hill)
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated coordinate system is defined by the directive "COMP" (see GBC_0095 and GBC_0096):


Outputs:


The different components of the ECR table are as follows, for the CMC3 element:

ECR(1): Von Mises criterion on the lower face of the multilayer element CMC3.

ECR(2): Von Mises criterion on the upper face of the multilayer element CMC3.


The different components of the ECR table are as follows, for the continuum elements:

ECR(1): pressure.

ECR(2): Von Mises criterion.

7.6.25  ORTE : ELASTIC DAMAGE ORTHOTROPY (only in 3D)

C.183


Object:


The directive is used to enter materials with an orthotropic (local) behaviour into a coordinate system defined by the user, coupling with damage. There is coupling between damage (as material LEM1) and orthotropy (as material ORTS). There are 6 damages : d1,d2,d3,d12,d13,d23. Each damage evolution rate is a function of strain tensor. A failure criterion is implicitly contained within the model: rupture occurs when a damage exceeds a critical value.
Two parameters (for each damage) allow to introduce a limitation of the damage rate (thanks to the delayed damage effect) in order to avoid the mesh dependency.

Dnc = dc < 
є − ep
s0 − ep
 >
ḋ = 
1
to

1−ea<Dncd> 

References:

This material behavior has been studied in [898].


Syntax:

    "ORTE"  "RO"    rho    "YG1"   yg1    "YG2"   yg2    "YG3"  yg3
            "NU12"  nu12   "NU13"  nu13   "NU23"  nu23
            "G12"   g12    "G13"   g13    "G23"   g23
            "EP1"   ep1    "EP2"   ep2    "EP3"   ep3
            "EP12"  ep12   "EP13"  ep13   "EP23"  ep23
            "S01"   s01    "S02"   s02    "S03"   s03
            "S012"  s012   "S013"  s013   "S023"  s023
            "DC1"   dc1    "DC2"   dc2    "DC3"   dc3
            "DC12"  dc12   "DC13"  dc13   "DC23"  dc23
            <"A1"   a1>    <"A2"   a2>    <"A3"   a3>
            <"A12"  a12>   <"A13"  a13>   <"A23"  a23>
            <"TO1"  to1>   <"TO2"  to2>   <"TO3"  to3>
            <"TO12" to12>  <"TO13" to13>  <"TO23" to23>
             /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

Young’s modulus along direction 3.
nu12

Poisson’s ratio between directions 1 and 2.
nu13

Poisson’s ratio between directions 1 and 3.
nu23

Poisson’s ratio between directions 2 and 3.
g12

Shear modulus between directions 1 and 2.
g13

Shear modulus between directions 1 and 3.
g23

Shear modulus between directions 2 and 3.
ep1

Strain threshold for damage in direction 1.
ep2

Strain threshold for damage in direction 2.
ep3

Strain threshold for damage in direction 3.
ep12

Strain threshold for damage in direction 12.
ep13

Strain threshold for damage in direction 13.
ep23

Strain threshold for damage in direction 23.
dc1

Critical damage defining the rupture criterion, in direction 1.
dc2

Critical damage defining the rupture criterion, in direction 2.
dc3

Critical damage defining the rupture criterion, in direction 3.
dc12

Critical damage defining the rupture criterion, in direction 12.
dc13

Critical damage defining the rupture criterion, in direction 13.
dc23

Critical damage defining the rupture criterion, in direction 23.
a1

Parameter of the delayed damage model, for the direction 1.
a2

Parameter of the delayed damage model, for the direction 2.
a3

Parameter of the delayed damage model, for the direction 3.
a12

Parameter of the delayed damage model, for the direction 12.
a13

Parameter of the delayed damage model, for the direction 13.
a23

Parameter of the delayed damage model, for the direction 23.
to1

Characteristic time of the delayed damage model in direction 1. (1/to) represents the maximum damage rate.
to2

Characteristic time of the delayed damage model in direction 2. (1/to) represents the maximum damage rate.
to3

Characteristic time of the delayed damage model in direction 3. (1/to) represents the maximum damage rate.
to12

Characteristic time of the delayed damage model in direction 12. (1/to) represents the maximum damage rate.
to13

Characteristic time of the delayed damage model in direction 13. (1/to) represents the maximum damage rate.
to23

Characteristic time of the delayed damage model in direction 23. (1/to) represents the maximum damage rate.
s01

Critical strain for damage in direction 1.
s02

Critical strain for damage in direction 2.
s03

Critical strain for damage in direction 3.
s012

Critical strain for damage in direction 12.
s013

Critical strain for damage in direction 13.
s023

Critical strain for damage in direction 23.
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated coordinate system is defined by the directive "COMP" (see GBC_0095) and GBC_0096)):


Outputs:


The different components of the ECR table are as follows, for the continuum elements:

ECR(2): Von Mises criterion.

ECR(8) : d1 - damage in direction 1.

ECR(9) : d2 - damage in direction 2.

ECR(10): d3 - damage in direction 3.

ECR(11): d12 - damage in direction 12.

ECR(12): d13 - damage in direction 13.

ECR(13): d23 - damage in direction 23.

ECR(14): d1 - damage not corrected (before delay effect) in direction 1.

ECR(15): d2 - damage not corrected (before delay effect) in direction 2.

ECR(16): d3 - damage not corrected (before delay effect) in direction 3.

ECR(17): d12 - damage not corrected (before delay effect) in direction 12.

ECR(18): d13 - damage not corrected (before delay effect) in direction 13.

ECR(19): d23 - damage not corrected (before delay effect) in direction 23.

ECR(20): T - time.

7.6.26  ODMS : ONERA DAMAGE MODEL (only in 3D)

C.184


Object:


The directive is used to enter materials with an orthotropic (local) behaviour into a coordinate system defined by the user, coupling with damage. There is coupling between damage (as material LEM1) and orthotropy (as material ORTS). There are 3 matrix damages : d1m,d2m,d3m (direction 1, 2 and 3), and 4 fiber damages : d1f,d2f,d3f,d4f (traction direction 1, compression direction 1, traction direction 2, compression direction 2). Each damage evolution rate is a function of strain tensor following the ONERA Damage Mechanics law.
This material behaviour is intended for braided and woven composite materials.


References:

The Onera damage model (ODM) is theorized in [897]. It’s implementation in Europlexus is studied in [898].


Two parameters (for each damage) allow to introduce a limitation of the damage rate (thanks to the delayed damage effect) in order to avoid the mesh dependency.

ḋ = 
1
tau

1−ea<Dncd> 

The constitutive law is :

Ceff−1=Seff=S0 +
3
i=1
 ηi dim H0im+
4
j=1
 djf H0jf = Cmatrix−1 + 
4
j=1
 djf H0jf
[σ] = Cmatrix.[є] − Ceff.[єresidual]

where the matrix 6x6 S0 and H0i are defined as:

Compliance S0: S0(1,1)=1/E10, S0(2,2)=1/E20, S0(3,3)=1/E30 ; S0(1,2)=−ν12/E10, S0(1,3)=−ν13/E10, S0(2,3)=−ν23/E20 ; S0(4,4)=1/G120, S0(5,5)=1/G230, S0(6,6)=1/G130, and 0 otherwise.

Matrix damage effect tensors H0m1, H0m2, H0m3:
H0m1: H0m1(1,1)=h1n/E10 , H0m1(4,4)= h1p/G120, H0m1(6,6)= h 1pn/G130, and 0 otherwise.
H0m2: H0m2(2,2)=h2n/E20 , H0m2(4,4)= h2p/G120, H0m2(5,5)= h2pn/G230, and 0 otherwise.
H0m3: H0m3(3,3)=h3n/E30 , H0m3(5,5)= h3p/G230, H0m3(6,6)= h3pn/G130, and 0 otherwise.

Fiber damage effect tensors H0f1, H0f2, H0f3, H0f4:
H0fi: H0fi(1,1)=hf1i/E10 , H0fi(2,2)=hf2i/E20 , H0fi(3,3)=hf3i/E30 , H0fi(1,2)=H0fi(2,1)=hf4i.S0(1,2) , H0fi(1,3)=H0fi(3,1)=hf5i.S0(1,3) , H0fi(2,3)=H0fi(3,2)=hf6i.S0(2,3) , H0fi(4,4)= hf7i/G120, H0fi(5,5)= hf8i/G230, H0fi(6,6)= hf9i/G130.

Then, the matrix thermodynamic forces yin,yit are computed in function of positive strain as following: yin= 1/2 Cii0i+i+ for i ∈ 1,2,3 and y1t= (b1.C66013+13+ + b2.C44012+12+), y2t= (b3.C55023+23+ + b4.C44012+. є12+), y3t= (b5.C66013+13+ + b6.C55023+23+).
The fiber thermodynamic forces yfi are computed in function of strain as following: yf1= 1/2 C0(1,1).є1+1+, yf2= 1/2 C0(1,1).є11, yf3= 1/2 C0(2,2).є2+2+, yf4= 1/2 C0(2,2).є22.

The damage law is the following :

di=max
gi(yi),di0

where

gi=dci 

1−  e





<
yi
y0i
>
yci





pi





 
 
 

and if : Δ єifєi ,

ηi=1 

if : −Δ єifєi ≤ Δ єif,

ηi=
1
2



1−cos


Π
2
 
єi +Δ єif
Δ єif






if : єi ≤ −Δ єif ,

ηi=0 

where

Δ єif=(1+aifdim)Δ єi0

Syntax:

    "ODMS"  "RO"    rho   "YG1"   yg1   "YG2"   yg2   "YG3"   yg3
            "NU12"  nu12  "NU13"  nu13  "NU23"  nu23  "G12"   g12
            "G13"   g13   "G23"   g23   "DCN1"  dcn1  "DCN2"  dcn2
            "DCN3"  dcn3  "DCT1"  dct1  "DCT2"  dct2  "DCT3"  dct3
            "YON1"  yon1  "YON2"  yon2  "YON3"  yon3  "YCN1"  ycn1
            "YCN2"  ycn2  "YCN3"  ycn3  "YOT1"  yot1  "YOT2"  yot2
            "YOT3"  yot3  "YCT1"  yct1  "YCT2"  yct2  "YCT3"  yct3
            "PN1"   pn1   "PN2"   pn2   "PN3"   pn3   "PT1"   pt1
            "PT2"   pt2   "PT3"   pt3   "HN1"   hn1   "HN2"   hn2
            "HN3"   hn3   "HP1"   hp1   "HP2"   hp2   "HP3"   hp3
            "HHP1"  hhp1  "HHP2"  hhp2  "HHP3"  hhp3  "XSI1"  xsi1
            "XSI2"  xsi2  "XSI3"  xsi3  "AIF1"  aif1  "AIF2"  aif2
            "AIF3"  aif3  "DEO1"  deo1  "DEO2"  deo2  "DEO3"  deo3
            "B1"    b1    "B2"    b2    "B3"    b3    "B4"    b4
            "B5"    b5    "B6"    b6    "TAU1"  tau1  "TAU2"  tau2
            "TAU3"  tau3  "A1"    a1    "A2"    a2    "A3"    a3
            "GHOS"  ghos  "LATE"  late
         <  "DCF1"  dcf1  "DCF2"  dcf2  "DCF3"  dcf3  "DCF4"  dcf4
            "YFO1"  yfo1  "YFO2"  yfo2  "YFO3"  yfo3  "YFO4"  yfo4
            "PF1"   pf1   "PF2"   pf2   "PF3"   pf3   "PF4"   pf4
            "HF11"  hf11  "HF21"  hf21  "HF31"  hf31  "HF41"  hf41
            "HF51"  hf51  "HF61"  hf61  "HF71"  hf71  "HF81"  hf81
            "HF91"  hf91  "HF12"  hf22  "HF32"  hf32  "HF42"  hf42
            "HF52"  hf52  "HF62"  hf62  "HF72"  hf72  "HF82"  hf82
            "HF92"  hf92  "HF13"  hf23  "HF33"  hf33  "HF43"  hf43
            "HF53"  hf53  "HF63"  hf63  "HF73"  hf73  "HF83"  hf83
            "HF93"  hf93  "HF14"  hf14  "HF34"  hf34  "HF44"  hf44
            "HF54"  hf54  "HF64"  hf64  "HF74"  hf74  "HF84"  hf84
            "HF94"  hf94  "HF24"  hf24  "AF1"   af1   "AF2"   af2
            "AF3"   af3   "AF4"   af4   "TOF1"  tof1  "TOF2"  tof2
            "TOF3"  tof3  "TOF4"  tof4  "RDC1"  rdc1  "RDC2"  rdc2
            "RDC3"  rdc3  "RDC4"  rdc4  "EPS1"  eps1  "EPS2"  eps2
            "EPS3"  eps3  "EPS4"  eps4   >
            /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

Young’s modulus along direction 3.
nu12

Poisson’s ratio between directions 1 and 2.
nu13

Poisson’s ratio between directions 1 and 3.
nu23

Poisson’s ratio between directions 2 and 3.
g12

Shear modulus between directions 1 and 2.
g13

Shear modulus between directions 1 and 3.
g23

Shear modulus between directions 2 and 3.
dcn1

Normal critical damage defining the rupture criterion, in direction 1.
dcn2

Normal critical damage defining the rupture criterion, in direction 2.
dcn3

Normal critical damage defining the rupture criterion, in direction 3.
dct1

Tangentiel critical damage defining the rupture criterion, in direction 1.
dct2

Tangentiel critical damage defining the rupture criterion, in direction 2.
dct3

Tangentiel critical damage defining the rupture criterion, in direction 3.
yon1

Normal damage threshold in direction 1.
yon2

Normal damage threshold in direction 2.
yon3

Normal damage threshold in direction 3.
ycn1

Critical normal damage threshold in direction 1.
ycn2

Critical normal damage threshold in direction 2.
ycn3

Critical normal damage threshold in direction 3.
yot1

Tangentiel damage threshold in direction 1.
yot2

Tangentiel damage threshold in direction 2.
yot3

Tangentiel damage threshold in direction 3.
yct1

Critical tangentiel damage threshold in direction 1.
yct2

Critical tangentiel damage threshold in direction 2.
yct3

Critical tangentiel damage threshold in direction 3.
pn1

Parameter in normal damage law for direction 1.
pn2

Parameter in normal damage law for direction 2.
pn3

Parameter in normal damage law for direction 3.
pt1

Parameter in tangentiel damage law for direction 1.
pt2

Parameter in tangentiel damage law for direction 2.
pt3

Parameter in tangentiel damage law for direction 3.
hn1

Parameter in damaged constitutive law for normal direction 1.
hn2

Parameter in damaged constitutive law for normal direction 2.
hn3

Parameter in damaged constitutive law for normal direction 3.
hp1

Parameter in damaged constitutive law for tangentiel direction 1.
hp2

Parameter in damaged constitutive law for tangentiel direction 2.
hp3

Parameter in damaged constitutive law for tangentiel direction 3.
hhp1

Parameter in damaged constitutive law for tangentiel direction 1.
hhp2

Parameter in damaged constitutive law for tangentiel direction 2.
hhp3

Parameter in damaged constitutive law for tangentiel direction 3.
xsi1

Parameter to take into account residual deformation.
xsi2

Parameter to take into account residual deformation.
xsi3

Parameter to take into account residual deformation.
aif1

Parameter to evaluate limit deformation for activation index 1 calculus.
aif2

Parameter to evaluate limit deformation for activation index 2 calculus.
aif3

Parameter to evaluate limit deformation for activation index 3 calculus.
deo1

Parameter to evaluate limit deformation for activation index 1 calculus.
deo2

Parameter to evaluate limit deformation for activation index 2 calculus.
deo3

Parameter to evaluate limit deformation for activation index 3 calculus.
b1

Parameter for thermodynamic forces calculus.
b2

Parameter for thermodynamic forces calculus.
b3

Parameter for thermodynamic forces calculus.
b4

Parameter for thermodynamic forces calculus.
b5

Parameter for thermodynamic forces calculus.
b6

Parameter for thermodynamic forces calculus.
tau1

Characteristic time of the delayed damage model in direction 1. (1/tau) represents the maximum damage rate.
tau2

Characteristic time of the delayed damage model in direction 2. (1/tau) represents the maximum damage rate.
tau3

Characteristic time of the delayed damage model in direction 3. (1/tau) represents the maximum damage rate.
a1

Parameter of the delayed damage model, for the direction 1.
a2

Parameter of the delayed damage model, for the direction 2.
a3

Parameter of the delayed damage model, for the direction 3.
ghos

Parameter driving the post damage evolution: case 0. : nothing special happens (default case is 0.); case 1. : if a fiber damage is almost critical (ratio rdc1, rdc2, rdc3 rdc4) at a Gauss point of the element, then the element becomes Ghost; case 2. : if a strain reaches its given limit value at a Gauss point of the element, then the element becomes Ghost; case 3. : if case 1 or case 2 is reached, then the element becomes Ghost; case 4. : if there is an almost critical damage at each Gauss points of the element, then the element becomes Ghost; case 5. : if there is a critical strain at each Gauss points of the element, then the element becomes Ghost; case 6. : if case 4 or case 5, then the element becomes Ghost.
late

Parameter driving the delay effect : case 0. : delay effect not active (default case is 0.) ; case 1. : delay effect is active in calculus, for the 3 matrix damages (and the 4 fiber damages).
dcf1

Normal critical damage defining the rupture criterion of fiber in tension, in direction 1.
dcf2

Normal critical damage defining the rupture criterion of fiber in compression, in direction 1.
dcf3

Normal critical damage defining the rupture criterion of fiber in tension, in direction 2.
dcf4

Normal critical damage defining the rupture criterion of fiber in compression, in direction 2.
yfo1

Damage threshold in tension, in direction 1.
yfo2

Damage threshold in compression, in direction 1.
yfo3

Damage threshold in tension, in direction 2.
yfo4

Damage threshold in compression, in direction 2.
yfc1

Critical damage threshold in tension, in direction 1.
yfc2

Critical damage threshold in compression, in direction 1.
yfc3

Critical damage threshold in tension, in direction 2.
yfc4

Critical damage threshold in compression, in direction 2.
pf1

Parameter in tangentiel fiber damage law for direction 1, in tension.
pf2

Parameter in tangentiel fiber damage law for direction 1, in compression.
pf3

Parameter in tangentiel fiber damage law for direction 2, in tension.
pf4

Parameter in tangentiel fiber damage law for direction 2, in compression.
hf11

Fiber parameter in damaged constitutive law for tensile direction 1.
hf21

Fiber parameter in damaged constitutive law for tensile direction 1.
hf31

Fiber parameter in damaged constitutive law for tensile direction 1.
hf41

Fiber parameter in damaged constitutive law for tensile direction 1.
hf51

Fiber parameter in damaged constitutive law for tensile direction 1.
hf61

Fiber parameter in damaged constitutive law for tensile direction 1.
hf71

Fiber parameter in damaged constitutive law for tensile direction 1.
hf81

Fiber parameter in damaged constitutive law for tensile direction 1.
hf91

Fiber parameter in damaged constitutive law for tensile direction 1.
hf12

Fiber parameter in damaged constitutive law for compressive direction 1.
hf22

Fiber parameter in damaged constitutive law for compressive direction 1.
hf32

Fiber parameter in damaged constitutive law for compressive direction 1.
hf42

Fiber parameter in damaged constitutive law for compressive direction 1.
hf52

Fiber parameter in damaged constitutive law for compressive direction 1.
hf62

Fiber parameter in damaged constitutive law for compressive direction 1.
hf72

Fiber parameter in damaged constitutive law for compressive direction 1.
hf82

Fiber parameter in damaged constitutive law for compressive direction 1.
hf92

Fiber parameter in damaged constitutive law for compressive direction 1.
hf13

Fiber parameter in damaged constitutive law for tensile direction 2.
hf23

Fiber parameter in damaged constitutive law for tensile direction 2.
hf33

Fiber parameter in damaged constitutive law for tensile direction 2.
hf43

Fiber parameter in damaged constitutive law for tensile direction 2.
hf53

Fiber parameter in damaged constitutive law for tensile direction 2.
hf63

Fiber parameter in damaged constitutive law for tensile direction 2.
hf73

Fiber parameter in damaged constitutive law for tensile direction 2.
hf83

Fiber parameter in damaged constitutive law for tensile direction 2.
hf93

Fiber parameter in damaged constitutive law for tensile direction 2.
hf14

Fiber parameter in damaged constitutive law for compressive direction 2.
hf24

Fiber parameter in damaged constitutive law for compressive direction 2.
hf34

Fiber parameter in damaged constitutive law for compressive direction 2.
hf44

Fiber parameter in damaged constitutive law for compressive direction 2.
hf54

Fiber parameter in damaged constitutive law for compressive direction 2.
hf64

Fiber parameter in damaged constitutive law for compressive direction 2.
hf74

Fiber parameter in damaged constitutive law for compressive direction 2.
hf84

Fiber parameter in damaged constitutive law for compressive direction 2.
hf94

Fiber parameter in damaged constitutive law for compressive direction 2.
tof1

Characteristic time of the delayed damage model in tensile direction 1. (1/tau) represents the maximum damage rate.
tof2

Characteristic time of the delayed damage model in compressive direction 1. (1/tau) represents the maximum damage rate.
tof3

Characteristic time of the delayed damage model in tensile direction 2. (1/tau) represents the maximum damage rate.
tof4

Characteristic time of the delayed damage model in compressive direction 2. (1/tau) represents the maximum damage rate.
af1

Parameter of the delayed damage model, for the tensile direction 1.
af2

Parameter of the delayed damage model, for the compressive direction 1.
af3

Parameter of the delayed damage model, for the tensile direction 2.
af4

Parameter of the delayed damage model, for the compressive direction 2.
rdc1

Fiber damage (tensile direction 1) ratio for which element becomes ghost.
rdc2

Fiber damage (compressive direction 1) ratio for which element becomes ghost.
rdc3

Fiber damage (tensile direction 2) ratio for which element becomes ghost.
rdc4

Fiber damage (compressive direction 2) ratio for which element becomes ghost.
eps1

Strain limit (tensile direction 1) for which element becomes ghost.
eps2

Strain limit (compressive direction 1) for which element becomes ghost.
eps3

Strain limit (tensile direction 2) for which element becomes ghost.
eps4

Strain limit (compressive direction 2) for which element becomes ghost.
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated coordinate system is defined by the directive "COMPLEMENT" (see pages C.95, section 6.29 and C.96, section 6.30):


Verify that this material is available for your elements in the tables of page C.100, section 7.


Outputs:


The different components of the ECR table are as follows, for the continuum elements:

ECR(1): Pression.

ECR(2): Von Mises criterion.

ECR(3): d1 - damage in direction 1.

ECR(4): d2 - damage in direction 2.

ECR(5): d3 - damage in direction 3.

ECR(6): eta1 - activation damage index in direction 1.

ECR(7): eta2 - activation damage index in direction 2.

ECR(8): eta3 - activation damage index in direction 3.

ECR(9): epsilon s 11 - residual deformation 11.

ECR(10): epsilon s 22 - residual deformation 22.

ECR(11): epsilon s 33 - residual deformation 33.

ECR(12): epsilon s 12 - residual deformation 12.

ECR(13): epsilon s 23 - residual deformation 23.

ECR(14): epsilon s 13 - residual deformation 13.

ECR(15): epsilon r 11 - residual deformation 11.

ECR(16): epsilon r 22 - residual deformation 22.

ECR(17): epsilon r 33 - residual deformation 33.

ECR(18): epsilon r 12 - residual deformation 12.

ECR(19): epsilon r 23 - residual deformation 23.

ECR(20): epsilon r 13 - residual deformation 13.

ECR(21) : df1t - fiber tensile damage in direction 1.

ECR(22) : df1c - fiber compressive damage in direction 1.

ECR(23): df2t - fiber tensile damage in direction 2.

ECR(24): df2c - fiber compressive damage in direction 2.

ECR(25): T - time.

7.6.27  WOOD

C.185


Object:


This directive allows to define the BOIS (wood) material, that is used for example for packaging and transportation as a shock absorber. Only the compressive behaviour of the material is considered, while the material response in traction is approximated as perfectly linear (or linear perfecly plastic) because of the lack of experimental data.


Syntax:

    "BOIS"  "RO"  rho    "YG1"  yg1    "YG2"   yg2  "YG3" yg3
            "NU12" nu12  "NU13" nu13   "NU23" nu23
            "G12"  g12   "G13"  g13    "G23" g23
            "SY_1" sy1  "SY_2"  sy2   "SY_3"  sy3
            "ED_1" ed1  "ED_2"  ed2   "ED_3"  ed3
          < "TR_1" tr1  > < "TR_2" tr2  > < "TR_3" tr3  >
          < "COE1" coe1 > < "COE2" coe2 > < "COE3" coe3 >
          < "EDCV" edcv > < "DIRF" idir >
          < "CI23" ci23 > < "CI31" ci31 > < "CI12" ci12 >
          < $[ "RUPT" ; "DECO"]$
            < "CONT" |[ "TR1M" tr1m ; "TR2M" tr2m ; "TR3M" tr3m ;
                        "T23M" t23m ; "T31M" t31m ; "T12M" t12m ;
                        "CO1M" co1m ; "CO2M" co2m ; "CO3M" co3m ]|> ;
            < "DPLA" |[ "EP23" ep23 ; "EP31" ep31 ; "EP12" ep12 ]|> >

                /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

Young’s modulus along direction 3.
nu12

Poisson’s ratio between directions 1 and 2.
nu13

Poisson’s ratio between directions 1 and 3.
nu23

Poisson’s ratio between directions 2 and 3.
g12

Shear modulus between directions 1 and 2.
g13

Shear modulus between directions 1 and 3.
g23

Shear modulus between directions 2 and 3.
sy1

Elastic limit in compression along the first orthotropy direction.
sy2

Elastic limit in compression along the second orthotropy direction.
sy3

Elastic limit in compression along the third orthotropy direction.
ed1

Limit deformation before reconsolidation along the first orthotropy direction.
ed2

Limit deformation before reconsolidation along the second orthotropy direction.
ed3

Limit deformation before reconsolidation along the third orthotropy direction.
tr1

Optional keyword : Limit elastic stress in traction along the first orthotropy direction. If omitted, an elastic behaviour is assumed along this direction.
tr2

Optional keyword : Limit elastic stress in traction along the second orthotropy direction. If omitted, an elastic behaviour is assumed along this direction.
tr3

Optional keyword : Limit elastic stress in traction along the third orthotropy direction. If omitted, an elastic behaviour is assumed along this direction.
coe1

Optional keyword : Scale factor between initial Young’s modulus and Young’s modulus after reconsolidation in direction 1.
coe2

Optional keyword : Scale factor between initial Young’s modulus and Young’s modulus after reconsolidation in direction 2.
coe3

Optional keyword : Scale factor between initial Young’s modulus and Young’s modulus after reconsolidation in direction 3.
edcv

Optional keyword : Threshold deformation in all directions starting convergence of the material towards a consolidated linear elastic material (see comment below).
idir

Optional keyword : Spatial direction of wood fibers, if not the first orthotropy direction (see comment below).
ci23

Optional keyword : Limit elastic shear stress in the (second orthotropy direction,third orthotropy direction) plane. If omitted, an elastic behaviour is assumed. Only available in 3D.
ci31

Optional keyword : Limit elastic shear stress in the (third orthotropy direction,first orthotropy direction) plane. If omitted, an elastic behaviour is assumed. Only available in 3D.
ci12

Optional keyword : Limit elastic shear stress in the (first orthotropy direction,second orthotropy direction) plane. If omitted, an elastic behaviour is assumed. Only available in 3D.
RUPT

Optional keyword : Introduces an element failure model represented by a failure criterion and by a failure limit value. Only available in 3D.
DECO

Optional keyword : Introduces an model of automatic separation of elements defined by a failure criterion and by a failure limit value. Only available in 3D. Only available for CUB8 element. More explanations can be found in [840].
CONT

Failure criterion based upon stress associated to RUPT keyword or DECO keyword (but not the both). Only available in 3D.
DPLA

Failure criterion based upon plastic strain associated to RUPT keyword or DECO keyword (but not the both). Only available in 3D.
tr1m

Optional keyword : Failure limit value for stress in traction along the first orthotropy direction.
tr2m

Optional keyword : Failure limit value for stress in traction along the second orthotropy direction.
tr3m

Optional keyword : Failure limit value for stress in traction along the third orthotropy direction.
t23m

Optional keyword : Failure limit value for shear stress in the (second orthotropy direction,third orthotropy direction) plane.
t31m

Optional keyword : Failure limit value for shear stress in the (third orthotropy direction,first orthotropy direction) plane.
t12m

Optional keyword : Failure limit value for shear stress in the (first orthotropy direction,second orthotropy direction) plane.
co1m

Failure limit value for stress in compression along the first orthotropy direction.
co2m

Optional keyword : Failure limit value for stress in compression along the second orthotropy direction.
co3m

Optional keyword : Failure limit value for stress in compression along the third orthotropy direction.
ep23

Optional keyword : Failure limit value for shear plastic strain in the (second orthotropy direction,third orthotropy direction) plan
ep31

Optional keyword : Failure limit value for shear plastic strain in the (third orthotropy direction,first orthotropy direction) plane
ep12

Optional keyword : Failure limit value for shear plastic strain in the (first orthotropy direction,second orthotropy direction) plan
LECTURE

List of the elements concerned.

Comments:


This material model is taken from the thesis of P. François: “Plasticité du bois en compression multi-axiale : Application à l’absorption d’énergie mécanque”. Doctoral Thesis of the Bordeaux I University (October 1992).


The associated coordinate system is defined by the option MORTHO (see page C.96) for the continuum elements in 2D and 3D.


Verify that this material is available for your elements, by means of the tables of page C.100.


Compression instability may be encountered after reconsolidation, since the material becomes very stiff in the consolidated direction and is still very soft in the other directions. To overcome this problem, it may be considered that the orthotropy of the material is lost when reconsolidation is achieved, since the microstructure has been completely crushed and all the voids filled. This assumption is taken from the observations made in the PhD Thesis of C. Adalian: ”The behaviour of wood under multiaxial dynamic compression - Use for the modelling of crashes of containers”, PhD Thesis of Bordeaux I University (1998)


Such a behaviour is activated using EDCV keyword. The floating value associated to this keyword defines the level of deformation above which the process of convergence towards an elastic isotropic material is started. It should be less than the reconsolidation limit given in each orthotropy direction.


The convergence process is such that material characteristics of the element converge continuously towards the isotropic consolidated values, whatever the first direction is in which reconsolidation is achieved.


Isotropic elastic parameters of the consolidated materials are deduced from elastic parameters given in the wood fibers direction. If this direction is not the first orthotropy direction, it can be specified using "DIRF" keyword. Isotropic consolidated parameters are then obtained by the formulae (assuming the fibers direction is direction 1):

Ec=E1 . coe
νc=
ν1213
2
 
Gc=
Ec
2.(1+ν)
 

Outputs:


The different components of the ECR table are as follows, for the continuum elements:

ECR(1) : Pressure.

ECR(2) : Von mises criterion.

ECR(3) : Plastic strain along the first orthotropy direction.

ECR(4) : Plastic strain along the second orthotropy direction.

ECR(5) : Plastic strain along the third orthotropy direction.

ECR(6) : Principal stress along the first orthotropy direction.

ECR(7) : Principal stress along the second orthotropy direction.

ECR(8) : Principal stress along the third orthotropy direction.

ECR(9) : Total strain along the first orthotropy direction.

ECR(10): Total strain along the second orthotropy direction.

ECR(11): Total strain along the third orthotropy direction.

ECR(12): Flag for isotropic elastic converged material (0: not fully converged, 1: fully converged)

ECR(13): Convergence level in the first orthotropy direction.

ECR(14): Convergence level in the second orthotropy direction.

ECR(15): Convergence level in the third orthotropy direction.

ECR(16): Failure flag (0=virgin Gauss Point, 1=failed Gauss Point) (only in 3D).

ECR(17): Shear stress in the (second orthotropy direction,third orthotropy direction) plane (only in 3D).

ECR(18): Shear stress in the (third orthotropy direction,first orthotropy direction) plane (only in 3D).

ECR(19): Shear stress in the (first orthotropy direction,second orthotropy direction) plane (only in 3D).

ECR(20): Shear Plastic strain in the (second orthotropy direction,third orthotropy direction) plane (only in 3D).

ECR(21): Shear Plastic strain in the (third orthotropy direction,first orthotropy direction) plane (only in 3D).

ECR(22): Shear Plastic strain in the (first orthotropy direction,second orthotropy direction) plane (only in 3D).

ECR(23): Shear total strain in the (second orthotropy direction,third orthotropy direction) plane (only in 3D).

ECR(24): Shear total strain in the (third orthotropy direction,first orthotropy direction) plane (only in 3D).

ECR(25): Shear total strain in the (first orthotropy direction,second orthotropy direction) plane (only in 3D).

7.6.28  ORSR : RATE DEPENDENT LINEAR ORTHOTROPY (Local basis)

C.186


Object:

Attention: The description of the material is not showing all capabilities of the material. The material allows erosion and has several more input and output variables.


The directive is based on ORTS material law, with the possibility to define rate dependent material properties. 9 material properties can be made rate dependent: E11, E22, E33, ν12, ν13, ν23, G12, G13, G23. The rate dependency is based on the following polynomial law:

Xij(ε) = 
5
k=0
 Xijk (log(ε))k     (1)

As for ORTS directive, stress and strain are expressed in the user coordinate system.


Syntax:

    "ORSR"  "RO"  rho    "YG10"  yg10  "YG11"  yg11
              "YG12"  yg12  "YG13"  yg13 "YG14"  yg14
              "YG15"  yg15  "YG20"  yg20 "YG21"  yg21
                  "YG22"  yg22  "YG23"  yg23 "YG24"  yg24
                  "YG25"  yg25  "YG30"  yg30 "YG31"  yg31
                  "YG32"  yg32  "YG33"  yg33 "YG34"  yg34
                  "YG35"  yg35  "N120"  n120 "N121"  n121
                  "N122"  n122 "N123"  n123  "N124"  n124
                  "N125"  n125 "N130"  n130  "N131"  n131
                  "N132"  n132 "N133"  n133  "N134"  n134
                  "N135"  n135 "N230"  n230  "N231"  n231
                  "N232"  n232 "N233"  n233  "N234"  n234
            "N235"  n235 "G120"  g120  "G121"  g121
                  "G122"  g122  "G123"  g123 "G124"  g124
                  "G125"  g125  "G130"  g130 "G131"  g131
                  "G132"  g132  "G133"  g133 "G134"  g134
                  "G135"  g135  "G230"  g230 "G231"  g231
                  "G232"  g232  "G233"  g233 "G234"  g234
                  "G235"  g235  <"XT1"  xt1   "XT2"  xt2
                  "XT3" xt3      "XC1"  xc1   "XC2"  xc2
            "XC3" xc3     "RST1" rst1  "RST2" rst2
            "RST3" rst3   "CRIT" icrit>   /LECTURE/


rho

Density of the material.
yg10

0th order coefficient for the rate dependency of the Young’s modulus along direction 1. Without rate dependency, Young’s modulus along direction 1.
yg11

1st order coefficient for the rate dependency of the Young’s modulus along direction 1.
yg12

2nd order coefficient for the rate dependency of the Young’s modulus along direction 1.
yg13

3rd order coefficient for the rate dependency of the Young’s modulus along direction 1.
yg14

4th order coefficient for the rate dependency of the Young’s modulus along direction 1.
yg15

5th order coefficient for the rate dependency of the Young’s modulus along direction 1.
yg20

0th order coefficient for the rate dependency of the Young’s modulus along direction 2. Without rate dependency, Young’s modulus along direction 2.
yg21

1st order coefficient for the rate dependency of the Young’s modulus along direction 2.
yg22

2nd order coefficient for the rate dependency of the Young’s modulus along direction 2.
yg23

3rd order coefficient for the rate dependency of the Young’s modulus along direction 2.
yg24

4th order coefficient for the rate dependency of the Young’s modulus along direction 2.
yg25

5th order coefficient for the rate dependency of the Young’s modulus along direction 2.
yg30

0th order coefficient for the rate dependency of the Young’s modulus along direction 3. Without rate dependency, Young’s modulus along direction 3.
yg31

1st order coefficient for the rate dependency of the Young’s modulus along direction 3.
yg32

2nd order coefficient for the rate dependency of the Young’s modulus along direction 3.
yg33

3rd order coefficient for the rate dependency of the Young’s modulus along direction 3.
yg34

4th order coefficient for the rate dependency of the Young’s modulus along direction 3.
yg35

5th order coefficient for the rate dependency of the Young’s modulus along direction 3.
n120

0th order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2. Without rate dependency, Poisson’s ratio between directions 1 and 2.
n121

1st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2.
n122

2nd order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2.
n123

3rd order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2.
n124

4st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2.
n125

5st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 2.
n130

0th order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3. Without rate dependency, Poisson’s ratio between directions 1 and 3.
n131

1st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3.
n132

2nd order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3.
n133

3rd order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3.
n134

4st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3.
n135

5st order coefficient for the rate dependency of the Poisson’s ratio between directions 1 and 3.
n230

0th order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3. Without rate dependency, Poisson’s ratio between directions 2 and 3.
n231

1st order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3.
n232

2nd order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3.
n233

3rd order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3.
n234

4st order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3.
n235

5st order coefficient for the rate dependency of the Poisson’s ratio between directions 2 and 3.
g120

0th order coefficient for the rate dependency of the shear modulus between directions 1 and 2. Without rate dependency, shear modulus between directions 1 and 2.
g121

1st order coefficient for the rate dependency of the shear modulus between directions 1 and 2.
g122

2nd order coefficient for the rate dependency of the shear modulus between directions 1 and 2.
g123

3rd order coefficient for the rate dependency of the shear modulus between directions 1 and 2.
g124

4th order coefficient for the rate dependency of the shear modulus between directions 1 and 2.
g125

5th order coefficient for the rate dependency of the shear modulus between directions 1 and 2.
g130

0th order coefficient for the rate dependency of the shear modulus between directions 1 and 3. Without rate dependency, shear modulus between directions 1 and 3.
g131

1st order coefficient for the rate dependency of the shear modulus between directions 1 and 3.
g132

2nd order coefficient for the rate dependency of the shear modulus between directions 1 and 3.
g133

3rd order coefficient for the rate dependency of the shear modulus between directions 1 and 3.
g134

4th order coefficient for the rate dependency of the shear modulus between directions 1 and 3.
g135

5th order coefficient for the rate dependency of the shear modulus between directions 1 and 3.
g230

0th order coefficient for the rate dependency of the shear modulus between directions 2 and 3. Without rate dependency, shear modulus between directions 2 and 3.
g231

1st order coefficient for the rate dependency of the shear modulus between directions 2 and 3.
g232

2nd order coefficient for the rate dependency of the shear modulus between directions 2 and 3.
g233

3rd order coefficient for the rate dependency of the shear modulus between directions 2 and 3.
g234

4th order coefficient for the rate dependency of the shear modulus between directions 2 and 3.
g235

5th order coefficient for the rate dependency of the shear modulus between directions 2 and 3.
xt1

Failure criterion for tension in x-direction.
xt2

Failure criterion for tension in y-direction.
xt3

Failure criterion for tension in z-direction.
xc1

Failure criterion for compression in x-direction.
xc2

Failure criterion for compression in y-direction.
xc3

Failure criterion for compression in z-direction.
rst1

Failure criterion for shear in xy-direction.
rst2

Failure criterion for shear in yz-direction.
rst3

Failure criterion for shear in xz-direction.
icrit

Erosion criteria type (e.g.: tsai-hill)
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated coordinate system is defined by the directive "COMP" (see GBC_0095 and GBC_0096):


Outputs:


The different components of the ECR table are as follows, for the continuum elements:

ECR(1): pressure.

ECR(2): Von Mises criterion.

ECR(16): v1 - Strain rate in direction 1.

ECR(17): v2 - Strain rate in direction 2.

ECR(18): v3 - Strain rate in direction 3.

ECR(19): v4 - Strain rate for shear in 12-direction.

ECR(20): v5 - Strain rate for shear in 23-direction.

ECR(21): v6 - Strain rate for shear in 13-direction.

ECR(22): Apparent modulus in direction 1.

ECR(23): Apparent modulus in direction 2.

ECR(24): Apparent modulus in direction 3.

ECR(25): Apparent Poisson’s ratio between directions 1 and 2.

ECR(26): Apparent Poisson’s ratio between directions 1 and 3.

ECR(27): Apparent Poisson’s ratio between directions 2 and 3.

ECR(28): Apparent shear modulus between directions 1 and 2.

ECR(29): Apparent shear modulus between directions 2 and 3.

ECR(30): Apparent shear modulus between directions 1 and 3.

7.6.29  MASS

C.200


Object:


This directive enables the masses of the material points PMAT to be entered.


Optionally, the Young’s modulus E and the Poisson’s coefficient ν of the material may also be specified. These are used in order to determine the material’s bulk modulus

κ=
E
3(1−2ν)

when the PMAT associated with the MASS material has a (nodal) pinball attached to it. In this case, it is allowed to specify a zero mass (i.e. a 0 value for xm) in order to avoid adding an extra mass to the structure if so desired.


Syntax:

    "MASS" xm
         < "YOUN" youn> < "NU" nu >
           /LECTURE/


xm

Mass.
youn

Young’s modulus. If not specified, it is assumed to be 0.
nu

Poisson’s coefficient. If not specified, it is assumed to be 0.
LECTURE

Numbers of the elements concerned.

Comments:


If the node corresponding to the material point belongs also to another element, the added mass (xm) may be zero. This is very useful in the case of unilateral junctions or of added nodal pinballs for contact.


In this way, added masses may be entered too.


In axisymmetric, the real masses must be divided by 2π.


Outputs:


The different components of the ECR table are as follows:

ECR(1): integrated impulse from the origin

ECR(2): sum of the instantaneous reaction forces.

7.6.30  PHANTOM

C.210


Object:


This directive enables the elimination of elements in a mesh.


Syntax:

    "FANT"  rho  /LECTURE/


rho

Density.
LECTURE

List of the elements concerned.

Comments:


The EUROPLEXUS program considers that all these elements do not exist.


However, the nodes are always present; as their masses may not be zero, it is necessary to give (very low) densities to "FANT" elements.

7.6.31  FREE (USER’S MATERIAL)

C.220


Object:


The directive enables the user to enter his own constitutive laws.


Syntax:

            $  "STRU" ...  $
            $  "FLUI" ...  $
    "LIBR"  $  "PMAT" ...  $    < "PARA"  a b c ... >  /LECTURE/
            $  "MECA" ...  $
            $  "CLIM" ...  $

"STRU" ...

Indicates that the free material is of type “STRUCTURE”.
"FLUI" ...

Indicates that the free material is of type “FLUIDE”.
"PMAT" ...

Indicates that the free material is of type “POINT MATERIEL”.
"MECA" ...

Indicates that the free material is of type “MECANISME”.
"CLIM" ...

Indicates that the free material is of type “CONDITION AUX LIMITES”.
"PARA" ...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The distinction between structure and fluid is due to the processing differences in A.L.E. In fact, there are transport terms for the fluid, whereas the structure is always Lagrangian.


Similarly, the cases of material points, mechanisms and boundary conditions are so peculiar that a dedicated syntax is provided.


These directives are described in detail on the following pages.


Remarks:


In the examples proposed in the following pages, there are some calls to utility routines that are available within EUROPLEXUS:

  1. ERRMSS(STRING1,STRING2) :
    Subroutine named ‘STRING1’ generates the error message ‘STRING2’, increments the error counter and triggers the calculation stop. ‘STRING1’ and ‘STRING2’ are two character strings.
  2. TILT :
    This subroutine without arguments triggers the calculation stop at the end of the current time step, and passes control to the next input directive in the input data set, which is normally either “SUIT” or “FIN”, following the directive “CALCUL”.
  3. QUIDNE(LOOP,NUM,LON,VAL) :
    This subroutine extracts values relative to a node or to an element (of index “NUM”), and places them in the array “VAL”.

    If the quantity to be extracted is a vector (e.g. a velocity), the length of the extracted vector is in “LON”, and the array “VAL” must be dimensioned sufficiently (DIM(VAL) ≥ LON).

    Argument “LOOP” allows to select the values to be extracted.

    For a node :

    LOOP = 0 : Coordinates of node “NUM”,

    LOOP = 1 : Displacements,

    LOOP = 2 : Velocities,

    LOOP = 5 : Nodal masses.

    For an element :

    LOOP = 21 : Stresses in element “NUM”,

    LOOP = 22 : Total deformations,

    LOOP = 23 : Internal variables (ECR),

    LOOP = 24 : Internal energy.

7.6.32  FREE MATERIAL OF TYPE STRUCTURE

C.222


Object:


This directive introduces a user-defined constitutive behaviour of structural type (“STRUCTURE”).


Syntax:

    "LIBR"  "STRU" num   "RO" rho   "YOUN" young   "NU" nu  ...
                ...   < "PARA" /LECPARA/ >  /LECTURE/

"STRU" num

Indicates that the free material of type “STRUCTURE” has the user-specified index num.
"RO" rho

Density. This value is mandatory in order to compute the element mass.
"YOUN" young

Young’s modulus.
"NU" nu

Poisson’s ratio.
"PARA"...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The number num enables several materials chosen by the user to be recognized. The three parameters rho, young and nu are compulsory.


The user specifies his material’s parameters after the keyword “PARAM”. When EUROPLEXUS finds the keyword “LECTURE”, it considers that the list of parameters is terminated, whatever the number of values that have been read.


However, the total number of parameters for this material may not exceed 100, including the three mandatory values (rho, young and nu).


If there are no additional parameters besides the three mandatory ones, the keyword “PARAM” may be omitted.


The parameters are used within the subroutine “MSLIBR” that must be written by the user, compiled and linked with the code libraries to produce a special code executable before launching the run.


The elements that accept the free material of type “STRUCTURE” are the following:

2D : TRIA, CAR1, CAR4.

3D : CUBE, CUB6, CUB8, PRIS, PR6, TETR.


Be careful to respect the conventions chosen to rank the tensor components according to the 2-D plane, 2-D axisymmetric or 3-D cases. See page G.20 for further explanations.


The user can store for each element (and each integration point), the values he wants (up to 10) in the ECR table. For homogeneity with the other materials, the following data will be stored in the first two locations of the ECR table :

ECR(1) = Pressure

ECR(2) = Von Mises


The eight other locations are free.


Examples:


The following example, taken from the standard benchmark "bm_str_2d_libr", concerns the traction of an axisymmetric cylinder.


The material data are as follows:

MATERIAUX  LIBRE  STRUCTURE 901
                  RO 7800. YOUNG 210E9 NU 0.   TOUS


In this particular case there is just one material, identified by the user-supplied index 901. There are no additional parameters besides the three mandatory ones, and the Poisson coefficient is zero. All the elements in the mesh possess this material (keyword “TOUS”).


Programming example relative to MSLIBR:
      SUBROUTINE MSLIBR(NLGEOM,NUM,TT,XMAT,SIG,DEPS,EDOT,RO,PI,
     &                  CSON,ECR,X,IEL,IDIM,NBN)
*
*     ------------------------------------------------------------------
*
*          materiau libre (structure)                  m.lepareux 11.86
*
*     ------------------------------------------------------------------
*
*    entree :
*          num        = numero de reperage du materiau utilisateur
*          tt         = temps du calcul
*          xmat(1)    = masse volumique initiale
*          xmat(2)    = young
*          xmat(3)    = poisson
*          xmat(4: )  = autres parametres du materiau
*          sig        = contraintes au debut du pas
*          deps       = accroissement des deformations
*          edot       = vitesse de deformation
*          ro         = masse volumique courante
*          x          = coordonnees des nbn noeuds
*          iel        = numero de l'element
*          idim       = dimension (2=2d ou axis , 3=3d)
*    sortie :
!          nlgeom     = 0 (dans inico1.ff matal(13)=1)
*          pi         = contraintes a la fin du pas (a calculer)
*          cson       = vitesse du son (a calculer pour la stabilite)
*          ecr(1)     = pression                    (a calculer)
*          ecr(2)     = critere de von mises        (a calculer)
*          ecr(3:7)   = emplacements libres
*
*  attention !  le materiau 901 est utilise par le benchmark
*                               "bm_str_2d_libr.epx"
*
      IMPLICIT NONE
*
*---    variables globales :
      INTEGER, INTENT(IN)  :: NUM,IEL,NBN,IDIM
      INTEGER, INTENT(OUT)  :: NLGEOM
      REAL(8), INTENT(IN)  :: TT,XMAT(*),SIG(*),DEPS(*),EDOT(*),
     &                        RO,X(IDIM,NBN)
      REAL(8), INTENT(OUT) :: CSON,PI(*)
      REAL(8), INTENT(INOUT) :: ECR(*)
*
*---    variables locales :
      REAL(8) :: AMU,ALAMB,AUX,YOUNG,POISS,C1
*
*
*-----    on active les nonlinearites geometriques : nlgeom=0
      NLGEOM = 0
*
      SELECT CASE (NUM)
      CASE(901)
*-----     l'exemple qui suit concerne un mat. elastique (en 2d axis.)
        YOUNG=XMAT(2)
        POISS=XMAT(3)
*-         coefficients de lame :
        C1=YOUNG/(1.+POISS)
        AMU=0.5D0*C1
        ALAMB=C1*POISS/(1-2*POISS)
        AUX=ALAMB*(DEPS(1)+DEPS(2)+DEPS(4))
*-         nouveau tenseur des contraintes :
        PI(1) = SIG(1) + AUX + C1*DEPS(1)
        PI(2) = SIG(2) + AUX + C1*DEPS(2)
        PI(3) = SIG(3)      + AMU*DEPS(3)
        PI(4) = SIG(4) + AUX + C1*DEPS(4)
*-         pression :
        ECR(1)=(PI(1)+PI(2)+PI(4))/3.D0
*-         critere de von mises :
        ECR(2)=SQRT(PI(1)*(PI(1)-PI(2))+PI(2)*(PI(2)-PI(4))
     &             +PI(4)*(PI(4)-PI(1))+3*PI(3)*PI(3))
*-         vitesse du son (stabilite) :
        CSON=DSQRT(YOUNG/RO)
*
      CASE DEFAULT
        CALL ERRMSS('MSLIBR','ROUTINE UTILISATEUR NON PROGRAMMEE')
        STOP ' "MSLIBR" ABSENT'
      END SELECT
*
      END SUBROUTINE MSLIBR

7.6.33  FREE MATERIAL OF TYPE FLUID

C.224


Object:


This directive introduces a user-defined constitutive behaviour of fluid type (“FLUIDE”).


Syntax:

   "LIBR" "FLUI" num  "RO" rho  "PINI" pini  "PREF" pref  "EINT" ei ...
                ...   < "PARA"  /LECPARA/ >  /LECTURE/

"FLUI" num

Indicates that the free material of type “FLUIDE” has the user-specified index num.
"RO" rho

Density. This value is mandatory in order to compute the element mass.
"PINI" pini

Initial pressure.
"PREF" pref

Reference pressure.
"EINT" ei

Initial internal energy per unit mass.
"PARA"...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The number num enables several materials chosen by the user to be recognized. The four parameters rho, pini, pref and ei are compulsory.


The user specifies his material’s parameters after the keyword “PARAM”. When EUROPLEXUS finds the keyword “LECTURE”, it considers that the list of parameters is terminated, whatever the number of values that have been read.


However, the total number of parameters for this material may not exceed 100, including the four mandatory values (rho, pini, pref and ei).


If there are no additional parameters besides the four mandatory ones, the keyword “PARAM” may be omitted.


The parameters are used within the subroutine “MFLIBR” that must be written by the user, compiled and linked with the code libraries to produce a special code executable before launching the run.


The elements that accept the free material of type “FLUIDE” are the following:

1D : TUBE, TUYA, CAVI.

2D : TRIA, CAR1.

3D : CUBE, PRIS, TETR.


Be careful to respect the conventions chosen to rank the tensor components according to the 2-D plane, 2-D axisymmetric or 3-D cases. See page G.20 for further explanations.


The user can store for each element (and each integration point), the values he wants (up to 10) in the ECR table. For homogeneity with the other materials, the following data will be stored in the first two locations of the ECR table :

ECR(1) = Pressure

ECR(2) = Density.


The eight other locations are free.


Examples:


The following example, taken from the standard benchmark "bm_flu_1d_libr", concerns a shock tube with a perfect gas.


The material data are as follows:

MATERIAUX

  LIBRE FLUIDE 903 RO 13. PINI 1e6 PREF 1e5 EINT 192.3077e3
                   PARAM  1.4  640.        LECT tub_1  TERM

  LIBRE FLUIDE 903 RO 1.3 PINI 1e5 PREF 1e5 EINT 192.3077e3
                   PARAM  1.4  640.        LECT tub_2  TERM


In this case there are two materials, whose user index is the same (903), but which have different initial conditions.


Note the value of the initial internal energy, which is mandatory because the behaviour of the perfect gas depends both on the density ρ and on the specific internal energy e:

P = (γ − 1) ρ e 


These two variables ρ and e change during the transient, as a function of mass and energy transfer among the neighbouring elements. EUROPLEXUS computes these transfers automatically.


There are two additional parameters besides the four mandatory ones. These are respectively the ratio of specific heats (γ), and the apecific heat at constant volume (Cv), which allow to obtain the temperature (θ).

θ = 
e
Cv
 

Programming example relative to MFLIBR:
      SUBROUTINE MFLIBR(NUM,TT,XMAT,SIG,DEPS,EDOT,RO,EINT,DSIG,CSON,
     &                  ECR,X,IEL,IDIM,NBN)
*
*     ---------------------------------------------------------------
*
*          materiau libre (fluide)                   m.lepareux 11.86
*
*     ---------------------------------------------------------------
*
*    entree :
*          num        = numero de reperage du materiau utilisateur
*          tt         = temps du calcul
*          sig        = contraintes au debut du pas
*          deps       = accroissement des deformations
*          edot       = vitesse de deformation
*          ro         = masse volumique courante
*          eint       = energie interne massique courante
*          x          = coordonnees des nbn noeuds
*          iel        = numero de l'element
*          idim       = dimension (2=2d ou axis , 3=3d)
*          nbn        = nombre de noeuds de l'element
*          xmat(1)    = masse volumique initiale
*          xmat(2)    = pression initiale
*          xmat(3)    = pression de reference
*          xmat(4)    = energie interne massique initiale
*          xmat(5:)   = parametres de l'utilisateur
*    sortie :
*          dsig       = increments de contraintes
*          cson       = vitesse du son (pour la stabilite)
*          ecr(1)     = pression
*          ecr(2)     = masse volumique
*          ecr(3:7)   = emplacements libres
*
*  attention !  le materiau 903 est utilise par le benchmark
*                               "bm_flu_1d_libr.epx"
*
      IMPLICIT NONE
*
*---   variables globales :
      INTEGER, INTENT(IN)  :: NUM,IEL,NBN,IDIM
      REAL(8), INTENT(IN)  :: TT,XMAT(*),SIG(*),DEPS(*),EDOT(*),RO,EINT,
     &                        X(IDIM,NBN)
      REAL(8), INTENT(OUT) :: DSIG(*),CSON
      REAL(8), INTENT(INOUT) :: ECR(*)
*
*---   variables locales :
      REAL(8) :: ROZR,PZER,PREF,PABS,PR,CV,GAMA,TRE
*
*
      SELECT CASE (NUM)
      CASE(903)
*--         cas d'un gaz parfait :
        PREF = XMAT(3)                        ! PRESSION DE REFERENCE
        GAMA = XMAT(5)                        ! GAMMA DU GAZ
        CV   = XMAT(6)                        ! CHALEUR MASSIQUE
        PABS = RO * (GAMA -1D0) * EINT        ! PRESSION ABSOLUE
        CSON = SQRT(GAMA*PABS/RO)             ! VITESSE DU SON
        PR   = PABS - PREF                    ! PRESSION RELATIVE
        TRE  = EINT/CV  - 273.15D0            ! TEMPERATURE
*--         increments de contrainte (1d)
        DSIG(1) = -PR -SIG(1)
*--         remplissage des "ecr" :
        ECR(1) = PABS
        ECR(2) = RO
        ECR(3) = CSON
        ECR(4) = TRE
*
      CASE DEFAULT
*----               routine use to write
        CALL ERRMSS('MFLIBR','ROUTINE UTILISATEUR NON PROGRAMMEE')
        STOP ' "MFLIBR" ABSENT'
      END SELECT
*
      END

7.6.34  FREE MATERIAL OF TYPE MATERIAL POINT

C.226


Object:


This directive introduces a user-defined constitutive behaviour of type material point (“POINT MATERIEL”).


Syntax:

   "LIBR" "PMAT" num  "MASS" m  < "PARA"  a b c ... >  /LECTURE/

"PMAT" num

Indicates that the free material of type “POINT MATERIEL” has the user-specified index num.
"MASS" m

Mass of the material point element.
"PARA"...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The number num enables several materials chosen by the user to be recognized. The single parameter “MASS” is mandatory.


The user specifies his material’s parameters after the keyword “PARAM”. When EUROPLEXUS finds the keyword “LECTURE”, it considers that the list of parameters is terminated, whatever the number of values that have been read.


However, the total number of parameters for this material may not exceed 100, including the single mandatory value (m).


If there are no additional parameters besides the mandatory one, the keyword “PARAM” may be omitted.


The parameters are used within the subroutine “MPLIBR” that must be written by the user, compiled and linked with the code libraries to produce a special code executable before launching the run.


The only element that accepts the free material of type “POINT MATERIEL” is "PMAT", that is always 3-D.


Be careful to respect the conventions chosen to rank the tensor components according to the 3-D cases. See page G.20 for further explanations.


The user can store for each element (and each integration point), the values he wants (up to 10) in the ECR table. The ten locations are free.


Examples:


The following example, taken from the standard benchmark "bm_str_terlun", treats the case of two pointwise masses that attract each other according to the universal gravitation law.


The material data are as follows:

MATERIAUX

!--                                  cte G    nbr   pt_lune
LIBRE  PMAT 101  MASS 1.00    PARAM  1.14e4    1       2
                 LECT  terre TERM
!--                                  cte G    nbr   pt_terre
LIBRE  PMAT 101  MASS 0.0123  PARAM  1.14e4    1       2
                 LECT  lune  TERM
!                 param(1) = constante de gravitation
!                 param(2) = nbr de noeuds attires par cet element
!                 param(3) = liste des noeuds (ici un seul)


In this case there are two materials, whose user index is the same (101), but which have different parameters. Lines starting by a “!” are comments.


The used units are adapted to the treated problem. For masses, the reference is the earth mass, for lengths the earth radius and for times the day.


There are three additional parameters besides the mandatory one, that are respectively the gravity constant, the number of nodes subjected to gravity (here just one) and the index of the concerned node.


Programming example relative to MPLIBR:
      SUBROUTINE MPLIBR(NUM,T,PARAM,AMAS,ECR,X,U,F,V,DTSTAB)
*
*     ---------------------------------------------------------------
*
*          materiau libre pour les points mat.       m.lepareux 08-95
*
*     ---------------------------------------------------------------
*
*    entree :
*             num       : numero de reperage pour l'utilisateur
*             t         : temps
*             param     : tableau des parametres du mat. libre
*             amas      : masse de l'element
*             x         : coordonnees
*             u         : deplacements
*             v         : vitesses
*    sortie :
*             ecr       : tableau des parametres du materiau
*             f         : forces internes
*
*  attention !  le materiau 101 est utilise par le benchmark
*                               "bm_str_terlun.epx"
*
      IMPLICIT NONE
*
*---    variables globales :
      INTEGER, INTENT(IN)  :: NUM
      REAL(8), INTENT(IN)  :: T,PARAM(*),AMAS,X(3),U(3),V(3)
      REAL(8), INTENT(OUT) :: F(3)
      REAL(8), INTENT(INOUT) :: ECR(*),DTSTAB
*
*---    variables locales :
      INTEGER LON,NOD,NBR,II
      REAL(8) GG,FF,R(3),R2,R3,AMB,XB(3),AUX,EPSI,BM(3)
      REAL(8) CX,SS,ROL,V2,VV,COEF
*
*
      SELECT CASE (NUM)
      CASE (101)
!---     loi de gravitation universelle :
!--      (l'element affecte de ce materiau agit sur les noeuds designes)
!--          param(2+1:2+nbr)   ! numeros des noeuds designes
         GG    = PARAM(1)       ! CONSTANTE G DE GRAVITATION
         NBR   = PARAM(2)       ! NOMBRE DE NOEUDS SOUMIS A L'ATTRACTION
         DTSTAB = 1000.
         EPSI = 0.01
*
         F(:) = 0D0
         DO II=1,NBR
           NOD = PARAM( 2 + II )
           CALL QUIDNE( 0,NOD,LON,XB )   ! XB = POSITION DU NOEUD CIBLE
           CALL QUIDNE( 5,NOD,LON,BM )
           AMB = BM(1)                   ! MASSE DU NOEUD CIBLE
*
           R(:) = X(:) - XB(:)
           R2 = R(1) * R(1)  +  R(2) * R(2)  +  R(3) * R(3)
           R3 = R2 * SQRT(R2)
           FF = GG * AMAS * AMB / R3
           AUX = SQRT( R3 / ( GG * AMB )  )
           DTSTAB = MIN( DTSTAB , AUX * EPSI )
*
           F(:) = F(:) + R(:) * FF
         END DO
      CASE DEFAULT
         CALL ERRMSS('MPLIBR','NUMERO DE MATERIAU LIBRE INCONNU')
         STOP ' MPLIBR'
!
      END SELECT
*
      END

7.6.35  FREE MATERIAL OF TYPE MECHANISM

C.228


Object:


This directive introduces a user-defined constitutive behaviour of mechanism type (“MECANISME”).


Syntax:

   "LIBR" "MECA" num   < "PARA"  a b c ... >  /LECTURE/

"MECA" num

Indicates that the free material of type “MECANISME” has the user-specified index num.
"PARA"...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The number num enables several materials chosen by the user to be recognized. There are no mandatory parameters.


The user specifies his material’s parameters after the keyword “PARAM”. When EUROPLEXUS finds the keyword “LECTURE”, it considers that the list of parameters is terminated, whatever the number of values that have been read.


However, the total number of parameters for this material may not exceed 100.


If there are no parameters the keyword “PARAM” may be omitted.


The parameters are used within the subroutine “MMLIBR” that must be written by the user, compiled and linked with the code libraries to produce a special code executable before launching the run.


The only element that accepts the free material of type “MECANISME” is "MECA", that is an element with two nodes and 6 degrees of freedom per node.


The main interest of this free material is to allow the user to specify arbitrary relations (in matricial form) between the displacements of the two nodes and the applied forces. For example, it is possible to enter a symmetric stiffness matrix in order to model a complicated support (78 values). However, it must be noted that the relations must be specified in (or converted to) the global reference frame, and that they stay constant during the whole transient calculation.


The user can store for each element (and each integration point), the values he wants (up to 10) in the ECR table. The ten locations are free.


Examples:


The following example, taken from the standard benchmark "bm_str_meca_lbr", treats the very simple case of springs in translation and rotation.


The 78 values are specified in the global reference frame, and the principal axex are parallel to the global ones. The translational stiffness is KT = 1E3, and the rotational one is KR = 4E6. The free material has the user-specified index 905.


The material data are as follows:

MATERIAUX

   LIBRE  MECA  905  PARAM
       1e3
       0.0  1e3
       0.0  0.0  1e3
       0.0  0.0  0.0  4e6
       0.0  0.0  0.0  0.0  4e6
       0.0  0.0  0.0  0.0  0.0  4e6
      -1e3  0.0  0.0  0.0  0.0  0.0  1e3
       0.0 -1e3  0.0  0.0  0.0  0.0  0.0  1e3
       0.0  0.0 -1e3  0.0  0.0  0.0  0.0  0.0  1e3
       0.0  0.0  0.0 -4e6  0.0  0.0  0.0  0.0  0.0  4e6
       0.0  0.0  0.0  0.0 -4e6  0.0  0.0  0.0  0.0  0.0  4e6
       0.0  0.0  0.0  0.0  0.0 -4e6  0.0  0.0  0.0  0.0  0.0  4e6
                LECT  L_meca TERM


Programming example relative to MMLIBR:
      SUBROUTINE MMLIBR(NUM,TT,NBPAR,XMAT,X,DU,F,XMA,V,DFX,
     &                  ECR,SIG,DEPS,PI,DWINT,IEL,DTSTAB)
*
*     ------------------------------------------------------------------
*
*             materiau libre mecanisme                m.lepareux 12-00
*
*     ------------------------------------------------------------------
*
*    entree :
*          num        = numero de reperage du materiau utilisateur
*          tt         = temps du calcul
*          nbpar      = nombre de parametres utilisateur
*          xmat(1: )  = parametres du materiau
*          x(1:3,1:2) = coordonnees des 2 noeuds
*          du(1:12)   = deplacements des 2 noeuds
*          xma(1:12)  = masses des 2 noeuds
*          v(1:12)    = vitesses des 2 noeuds
*          dfx(1:12)  = deplacements cumules des 2 noeuds
*          sig(1:6)   = forces internes au debut du pas
*                       en fait : sig = 0.5 * (f2 - f1)
*          deps(1:6)  = deplacement relatif : deps = (u2 - u1)
*          iel        = numero de l'element
*    sorties :
*          f(1:12)    = forces internes appliquees aux 2 noeuds
*          ecr(:)     = variables internes (emplacements libres)
*          pi(1:6)    = forces internes a la fin du pas
*          dwint      = travail des forces internes
*          dtstab     = pas de stabilite
*
*  attention !  le materiau 905 est utilise par le benchmark
*                               "bm_str_meca_lbr.epx"
*
      IMPLICIT NONE
*
*---   variables globales :
      INTEGER, INTENT(IN)    :: NUM,IEL,NBPAR
      REAL(8), INTENT(IN)    :: TT,XMAT(*),X(3,2),DU(12),XMA(12),
     &                          V(12),DFX(12),SIG(6),DEPS(6)
      REAL(8), INTENT(OUT)   :: F(12),PI(6),DWINT
      REAL(8), INTENT(INOUT) :: ECR(*),DTSTAB
*
*---   variables locales :
      INTEGER :: K,I,II
      REAL(8) :: R_K(12,12),RT(3),RR(3),DT(12)
*
*
      SELECT CASE (NUM)
      CASE(905)
        IF(NBPAR /= 78) THEN
          CALL ERRMSS('MMLIBR','IL FAUT 78 VALEURS')
          STOP ' MMLIBR'
        ENDIF
*
*--         construction de la matrice de raideur :
        II = 0
        DO K=1,12
          DO I=1,K
            II = II+1
            R_K(K,I) = XMAT(II)
            R_K(I,K) = R_K(K,I)
          END DO
        END DO
*
*--         calcul direct des forces internes :
        F(:) = 0D0
        DO K=1,12
          DO I=1,12
            F(K) = F(K) + R_K(K,I)*DFX(I)
          END DO
        END DO
*
*--          nouvelles forces internes (pour calculer wint)
        DO K=1,6
          PI(K) = 0.5D0 * (F(K+6) - F(K))
        END DO
*
*--          travail des forces internes (pendant le pas de temps)
        DWINT = 0D0
        DO K=1,6
          DWINT = DWINT + 0.5D0*(SIG(K)+PI(K))*DEPS(K)
        END DO
*
*--          ECR : variables internes (allongement)
        DO K=1,3
          RT(K) = DFX(K+6) - DFX(K)
          RR(K) = DFX(K+9) - DFX(K+3)
        END DO
        ECR(1) = SQRT(RT(1)*RT(1) + RT(2)*RT(2) + RT(3)*RT(3))
        ECR(2) = SQRT(RR(1)*RR(1) + RR(2)*RR(2) + RR(3)*RR(3))
*
*--          calcul du pas de stabilite :
        DTSTAB = 1000D0
        DO K=1,12
          DT(K) = SQRT(XMA(K)/R_K(K,K))
          DTSTAB = MIN(DTSTAB,2*DT(K))
        END DO
*
      CASE DEFAULT
        CALL ERRMSS('MMLIBR','ROUTINE UTILISATEUR NON PROGRAMMEE')
        STOP ' "MMLIBR" ABSENT'
      END SELECT
*
      END

7.6.36  FREE MATERIAL OF TYPE BOUNDARY CONDITIONS

C.230


Object:


This directive introduces a user-defined constitutive behaviour of the boundary condition type (“CONDITION AUX LIMITES"”).


Syntax:

   "LIBR" "CLIM" num  "PREF" pref  < "PARA"  a b c ... >  /LECTURE/

"CLIM" num

Indicates that the free material of type “CONDITION AUX LIMITES” has the user-specified index num.
"PREF" pref

Reference pressure.
"PARA"...

Key-word used to introduce a series of additional parameters.
LECTURE

List of the elements concerned.

Comments:


The number num enables several materials chosen by the user to be recognized. The only mandatory parameter is pref.


The user specifies his material’s parameters after the keyword “PARAM”. When EUROPLEXUS finds the keyword “LECTURE”, it considers that the list of parameters is terminated, whatever the number of values that have been read.


However, the total number of parameters for this material may not exceed 100, including the single mandatory value pref.


If there are no additional parameters besides the mandatory one, the keyword “PARAM” may be omitted.


The parameters are used within the subroutine “CLIBRE” that must be written by the user, compiled and linked with the code libraries to produce a special code executable before launching the run.


The elements that accept the free material of type "CONDITION AUX LIMITES" are "CL1D" and "CLTU", which are respectively an element with one node and one dof and an element with one node and 7 dofs.


The main interest of this free material is to allow the user to specify boundary conditions applied to the ‘fluid’ degree of freedom of these elements, e.g. in order to model a special device mounted along a pipeline. In the case of "CLTU", only the 7-th dof is affected. The first 6 dofs concern the structure and are not affected.


The user can store for each element (and each integration point), the values he wants (up to 10) in the ECR table. For homogeneity with the other materials, the following data will be stored in the first two locations of the ECR table :

ECR(1) = DP : variation of pressure due to the device

ECR(2) = Density of the donor element


The eight other locations are free.


Examples:


The following example, taken from the standard benchmark "bm_cir_conteneur_eau", concerns the case of the brutal opening of a pressure container.


The container top is detached from the body and the opening (assumed circumferential) grows as the top moves away. The motion is parallel to the axis Ox. As a consequence of the detachment, the cross-section of the diaphragm across which the internal fluid passes is gradually increased, and the corresponding pressure drop is modified accordingly, as a function of the top distance.

The free material is identified by the index 906. Lines starting by a “!” are comments.


The material data are as follows:

MATERIAUX

      LIBRE  CLIM   906    PREF 10E5
             PARAM     1      25       22     0.1857
!--                  ptfond  ptcouv   eldon    diam
                      90e5     10e5    0.0       1.0
!--                  pamon     pext    tau      ksi idel'cik (sortie)
             LECT  esort TERM
!
!      materiau libre 906 (ouverture circonferentielle) :
!               param(1) = numero du premier point
!               param(2) = numero du second  point
!               param(3) = numero de l'element donneur
!               param(4) = diametre du tube
!               param(5) = pression amont initiale
!               param(6) = pression externe
!               param(7) = constante de temps pour l'ouverture
!               param(8) = perte de charge en sortie (idel'cik)
!


Programming example relative to CLIBRE:
      SUBROUTINE CLIBRE(NUNU,PREF,PARAM,AIRE,RHO,PAMON,VN,T,ECR,DP)
*
*     ------------------------------------------------------------------
*
*             materiau libre pour el. cl1d         m.lepareux 08-95
*
*     ------------------------------------------------------------------
*
*     attention !
*
*      le materiau nunu = 906 est utilise par "bm_cir_conteneur_eau.epx"
*
*    entree (ne pas les modifier) :
*             nunu      : numero de reperage pour l'utilisateur
*             pref      : pression de reference (obligatoire)
*             param     : tableau des parametres du mat. libre
*             aire      : section de la tuyauterie
*             rho       : masse volumique amont
*             pamon     : pression amont
*             vn        : vitesse du fluide dans la tuyauterie
*             t         : temps
*    sortie :
*             dp        : variation de pression due a l'appareil
*             ecr(1)    : affecte a dp
*             ecr(2)    : affecte a rho amont
*             ecr(3:9)  : selon utilisateur
*
*
*     les ecr libres permettent la sortie graphique
*     des grandeurs qui leur sont affectees
*
      IMPLICIT NONE
*
*--  variables globales :
      INTEGER, INTENT(IN)  :: NUNU
      REAL(8), INTENT(IN)  :: PREF,AIRE,RHO,PAMON,VN,T,PARAM(*)
      REAL(8), INTENT(OUT) :: ECR(*),DP
*
      REAL(8), PARAMETER :: ZERO=1D-6, RMIN=1D-3, RS2MIN=1.005D0
      INTEGER, PARAMETER :: LON1=7
*
*--  variables locales :
      INTEGER NP1,NP2,LON,NELDON,KAS
      REAL*8  DIAM,PZERO,PAVAL,TAU,PEXT,VAL1(LON1),VAL2(LON1),DIST,SECT,
     &        RAP,RS2,XKZ,PSEUIL,P0,XK,Q0,PP,ZMACH,
     &        DPE,DPK,ROVK,DPMAX,ROVN,XKSI,CSON
      LOGICAL OUVERT
!
!
      SELECT CASE (NUNU)

      CASE (906)
!---       diaphragme pour une ouverture progressive
        NP1    = NINT(PARAM(1))   ! NUMERO DU PREMIER POINT
        NP2    = NINT(PARAM(2))   ! NUMERO DU DEUXIEME POINT
        NELDON = NINT(PARAM(3))   ! NUMERO DE L'ELEMENT DONNEUR
        DIAM   = PARAM(4)         ! DIAMETRE DU TUBE
        PZERO  = PARAM(5)         ! PRESSION AMONT INITIALE
        PAVAL  = PARAM(6)         ! PRESSION EXTERNE
        TAU    = PARAM(7)         ! CONSTANTE DE TEMPS POUR L'OUVERTURE
        XKSI   = PARAM(8)         ! PERTE DE CHARGE EN SORTIE (IDEL'CIK)
!
        OUVERT = .TRUE.
!
!--        on va chercher les deplacements des 2 noeuds :
        CALL QUIDNE (1,NP1,LON,VAL1)
        CALL QUIDNE (1,NP2,LON,VAL2)
          IF(LON > LON1) STOP ' CLIBRE : DIM INSUFFISANTES'
        DIST = ABS( VAL2(1) + VAL1(1) )
        SECT = 3.1416 * DIAM * DIST
        RAP = SECT / AIRE
!
!--          le rapport des sections (rap) est limite a RMIN
!                              (cas des petites ouvertures) :
        IF( RAP .LT. RMIN ) THEN
          RAP = RMIN
          OUVERT = .FALSE.
        ENDIF
        RS2 = 1 / ( RAP*RAP )
!
!--          rs2 est limite a rs2min  (cas des grandes ouvertures) :
        IF(RS2 < RS2MIN) THEN
          RS2 = RS2MIN
          RAP = SQRT(1/RS2MIN)
        ENDIF
!
!--        perte de charge (idel'cik) :
        XK = RS2 * XKSI
!
!-----    si tau .ne. 0 la pression aval chute progressivement :
!           (a condition que pamon > paval)
!
        PSEUIL = PZERO - PAVAL
        IF(TAU.GT.ZERO .AND. PSEUIL.GT.ZERO*PZERO) THEN
          PEXT = PAVAL + PSEUIL*EXP( -T / TAU)
        ELSE
          PEXT = PAVAL
        ENDIF
!
        DPMAX = PAMON - PREF
        IF(OUVERT) THEN
          DPE = PEXT - PREF
          DPK =  0.5*XK * RHO * VN*VN
        ELSE
          DPE = PAMON - PREF
          DPK = 0
        ENDIF
        DP = DPE + DPK
        IF(DP > DPMAX) DP = DPMAX
!
        ECR(1) = DP + PREF
        ECR(2) = RHO
        ECR(3) = RHO*VN      ! PRODUIT RHO*VN (DEBIT MASSIQUE UNITAIRE)
        ECR(4) = PEXT        ! PRESSION DE SORTIE ( PEXT OU PCRIT )
        ECR(5) = DIST        ! DISTANCE ENTRE LES FRAGMENTS
        ECR(6) = XK          ! COEF. DE PERTE DE CHARGE
!
!-----   coefficient de stabilite ( xk * rho * vn ) :
        ROVK = ABS(ECR(6)*ECR(3))
!
!--   on arrete le calcul quand pamon < pext :
        IF( PAMON < PEXT )   CALL TILT
!
      CASE DEFAULT
        CALL ERRMSS('CLIBRE','ROUTINE UTILISATEUR NON PROGRAMMEE')
        STOP ' "CLIBRE" ABSENT'
      END SELECT
!
      RETURN
      END

7.6.37  FREE PARTICLE MATERIAL

C.240


Object:


This directive allows users to define their own constitutive laws for the particle elements (BILLE).


Syntax:

    "BILLE  $  "LIBR" num  "RO" rho  $

            ...  < "FONC"  numfon >

            ...  < "PARA"  a b c ... >  /LECTURE/


num

Number of the material used for the particle elements.
rho

Density.
numfon

Number of the function used.
"PARA" ...

Introduces a series of complementary parameters.
LECTURE

List of the concerned elements.

Comments:


The number (num) allows to distinguish between several user-defined materials.


The rho parameter is mandatory.


The number (numfon) allows to identify the function used for the interaction.


The complementary parameters introduced by "PARA" may be as many as needed. EUROPLEXUS recognizes the end of the parameters when the "LECTURE" keyword is encountered.


The subroutine "MBLIBR", to be written by the user, computes the interaction forces between neighbouring particles of the "BILLE" element considered, starting from the quantities at the beginning of the step, which are known. Consult the following example for a list of the available variables.


The only element type accepting this material is "BILLE".


The user may store for each element the variables of his choice within the ECR table (up tp 7 values). However, for uniformity with the other materials, it is advised to use the first two slots as follows:

         Fluid :                           Continuum structure:

           ECR(1) = Pressure                  ECR(1) = Pressure
           ECR(2) = Density                   ECR(2) = Von Mises

Example:


Two new materials of the fluid type are defined: a material of type acoustic fluid, and the other depending upon the distance between two neighbouring particles.


The corresponding data will be, for example:

         "BILL" "LIBR" 1 "RO" 1000 "PARA" 1000   /LECTURE/

         "BILL" "LIBR" 2 "RO"  800 "FONC" 1      /LECTURE/



Programming example for routine MBLIBR:

      SUBROUTINE MBLIBR(XMAT,DINI,DIST,A,B,C,NVOIS,NUMVOI,DVX,DVY,DVZ,
     * ROCOUR,IEL,INOE,INOEV,IPFONC,TABFON,T,DT1,FORCE,SIG,ECR)
C
C ----------------------------------------------------------------------
C
C                         MATERIAU "BILLE" "LIBRE"
C
C                                                        R.GALON 02/91
C ---------------------------------------------------------------------
C
C
C      ENTREE :
C      ------
C           XMAT(1)     =  MASSE VOLUMIQUE INITIALE
C           XMAT(2)     =  NUMERO DE REPERAGE DU MATERIAU UTILISATEUR
C           XMAT(3)     =  NUMERO DE LA FONCTION ASSOCIEE
C           XMAT(4:  )  =  AUTRES PARAMETRES DU MATERIAU
C           DINI        =  DIAMETRE INITIAL DE LA BILLE
C           DIST        =  DISTANCE SEPARANT LES 2 BILLES EN INTERACTION
C           A           =  COSINUS DIRECTEUR SUIVANT X DE LA LIAISON
C           B           =  COSINUS DIRECTEUR SUIVANT Y DE LA LIAISON
C           C           =  COSINUS DIRECTEUR SUIVANT Z DE LA LIAISON
C           NVOIS       =  NOMBRE DE BILLES VOISINES DE LA BILLE TRAITEE
C           NUMVOI      =  NUMVOI-IEME BILLE EN INTERACTION
C           DVX         =  VITESSE RELATIVE DES 2 BILLES DE LA LIAISON
C                          SUIVANT X
C           DVY         =  VITESSE RELATIVE DES 2 BILLES DE LA LIAISON
C                          SUIVANT Y
C           DVZ         =  VITESSE RELATIVE DES 2 BILLES DE LA LIAISON
C                          SUIVANT Z
C           ROCOUR      =  MASSE VOLUMIQUE ASSOCIEE A LA LIAISON
C           IEL         =  NUMERO DE L ELEMENT TRAITE
C           INOE        =  NUMERO DU NOEUD ASSOCIE A L ELEMENT IEL
C           INOEV       =  NUMERO DU NOEUD VOISIN DE LA BILLE
C           IPFONC      =  POINTE SUR LA TABLE DE FONCTION
C           TABFON      =  TABLE DE FONCTION ASSOCIEE AU MATERIAU
C           T           =  TEMPS DE CALCUL
C           DT1         =  INCREMENT DE TEMPS DE CALCUL
C
C
C      SORTIE :
C      ------
C           FORCE(1:3)  =  FORCES A APPLIQUER A LA BILLE TRAITEE
C           SIG(1:6)    =  CONTRAINTES A LA FIN DU PAS (FACULTATIF)
C           ECR(1:10)   =  EMPLACEMENTS LIBRES
C
C      REMARQUE : - DEUX BILLES SEPAREES DE PLUS DE 1.3 * DINI SONT
C      --------     SUPPOSEES NE PAS POUVOIR INTERAGIR ENTRE ELLES.
C
C                 - ON CUMULE TOUJOURS LES FORCES CAR ELLES PROVIENNENT
C                   DE L INTERACTION DE TOUTES LES BILLES VOISINES DE LA
C                   BILLE TRAITEE.
C
      IMPLICIT REAL*8(A-H,O-Z)
C
      DIMENSION XMAT(*),ECR(*),FORCE(*),TABFON(*),SIG(*),IPFONC(2,*)
C
C
      NUM = XMAT(2)
C
      IF(NUM.NE.1) GOTO 20
C
C --------- CAS D UN MATERIAU DE TYPE FLUIDE
C           ================================
      RO = XMAT(1)
      CSON = XMAT(4)
C ------ POUR LA PREMIERE BILLE EN INTERACTION ON INITIALISE PAR EXEMPLE
C       LA MASSE VOLUMIQUE ET LA PRESSION MOYENNE DE L ELEMENT BILLE IEL
      IF(NUMVOI.EQ.1)THEN
            ECR(1)=0.
            ECR(2)=0.
            SIG(1)=0.
            SIG(2)=0.
            SIG(3)=0.
      ENDIF
C ------ DRO = VARIATION DE LA MASSE VOLUMIQUE
      DRO = ROCOUR - RO
      P = DRO * CSON * CSON
      DVOL = (ROCOUR/RO) -1.D0
      DP2 = DINI**3 / (DIST*(1.D0 + DVOL))
C
C ------ COEFICIENT DE PONDERATION POUR UN RESEAU HEXAGONAL DE BILLES
      COEF = SQRT(2.D0)/4.D0
C
C ------ COEFICIENT DE PONDERATION POUR UN RESEAU CUBIQUE DE BILLES
C     COEF = 1.D0
C ------ FORCE DANS LA DIRECTION DE LA LIAISON APPLIQUEE A LA BILLE
      FN = - DP2 * COEF * P
C ------ ON PROJETTE LA FORCE DANS LE REPERE GLOBAL
      FORCE(1) = FORCE(1) + A * FN
      FORCE(2) = FORCE(2) + B * FN
      FORCE(3) = FORCE(3) + C * FN
C ------ CONTAINTES DANS L ELEMENT (PRESSIONS)
C
      SIG(1) = SIG(1) + P/NVOIS
      SIG(2) = SIG(2) + P/NVOIS
      SIG(3) = SIG(3) + P/NVOIS
      SIG(4) = 0.
      SIG(5) = 0.
      SIG(6) = 0.
C ------ MASSE VOLUMIQUE MOYENNE
      ECR(1) = ECR(1) + ROCOUR/NVOIS
C ------ PRESSION MOYENNE
      ECR(2) = ECR(2) + P/NVOIS
      RETURN
C
C
 20   CONTINUE
C
C --------- FORCE DEFINIE PAR UNE FONCTION
C           ==============================
C
C   REMARQUE : ON SUPPOSE ICI QUE LA FORCE AGISSANT SUR L ELEMENT BILLE
C              EST FONCTION UNIQUEMENT DE LA DISTANCE SEPARANT LES 2
C              BILLES EN INTERACTION (LA FONCTION EST DEFINIE PAR LA
C              DIRECTIVE "FONC".
C
      IFONC = XMAT(3)
C
C ------ FN EST LA FORCE CORRESPONDANT A UNE DISTANCE DIST SEPARANT LES
C        2 BILLES EN INTERACTION (ELLE EST APPLIQUEE A L ELEMENT IEL)
C
      CALL FFONCT(IFONC,DIST,FN,IPFONC,TABFON)
C
C ------ ON PROJETTE LA FORCE DANS LE REPERE GLOBAL
C
      FORCE(1) = FORCE(1) + A * FN
      FORCE(2) = FORCE(2) + B * FN
      FORCE(3) = FORCE(3) + C * FN
C
C ------ DISTANCE MOYENNE DANS ECR(1) PAR EXEMPLE OU TOUTE AUTRE VALEUR
C        QUE L ON DESIRE CONSERVER
C
      ECR(1) = ECR(1) + DIST/NVOIS
C
      RETURN
      END

7.6.38  VON MISES (ISPRA IMPLEMENTATION)

C.241


Object:


This option enables to choose the Von Mises material with the implementation developed at Ispra. Elasto-plasticity is implemented via a radial return algorithm. Only isotropic hardening is activated to date. There is no dependency on temperature nor on strain rate.


Syntax:

    "VM23"  "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige ...
              <"FAIL" $[ VMIS ; PEPS ; PRES ; PEPR ]$ "LIMI" limit>
              "TRAC" npts*(sig eps)
              /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
FAIL

Optional keyword: introduces an element failure model, represented by a failure criterion and a by failure limit value. The available failure criteria are: VMIS for a criterion based upon Von Mises stress (isotropic criterion), PEPS for a criterion based upon the principal strain (see caveat below), PRES for a criterion based upon the hydrostatic stress, PEPR for a criterion based upon the principal strain if the hydrostatic stress is positive (traction): if the hydrostatic stress is negative (compression) there is no failure.
limit

Optional parameter, indicates the failure limit for the chosen criterion.
"TRAC"

This key-word announces the yield curve.
npts

Number of points (except the origin) defining the yield curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig, eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may not increase from one segment to the following one.


4/ - When using a failure criterion based upon the principal strains (PEPS or PEPR) be aware that the criterion is based upon the cumulated strains. These are usually a good approximation of the total strains for elements using a convected reference frame for the stresses and strains (such as e.g. plate, shell or bar elements). The approximation is likely to be very bad, instead, for continuum-like elements, at least when there are large rotations.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): sound speed

ECR(6): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.39  VM1D MATERIAL

C.242


Object:


This is the material to be used for the interface elements of type ED1D (see INT.80).


Syntax:

    "VM1D"  "PT1D" pt1d /LECTURE/


pt1d

Associated node index in the 1-D model.

Comments:


Note that when several ED1D elements are present in a coupled 1-D/multi-D calculation, then each ED1D element must have a separate VM1D material, because the material is used to carry the information of the associated 1-D node to each one ED1D element (pt1d).


Outputs:


The components of the ECR table are as follows :

ECR(1) : unused

ECR(2) : unused

ECR(3) : unused

ECR(4) : unused

ECR(5) : unused

ECR(6) : unused

7.6.40  DONE MATERIAL

C.243


Object:


This is a viscoplastic material model mostly used to describe the sensitivity of commonly used stainless steels (e.g. AISI 304 and 316) to the rate of loading. It uses the theory of viscoplasticity based on total strain and overstress. To date, it is limited to small strains.


Syntax:

    "DONE"  "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige ...
      ...  "VIS1" vis1  "VIS2" vis2  "VIS3" vis3  ...
      ...  "VIS4" vis1  "VIS5" vis2  "VIS6" vis3  ...
      ...  "TRAC" npts*(sig eps) /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
vis1,..,vis6

Viscous coefficients.
"TRAC"

This key-word announces the yield curve (static).
npts

Number of points (except the origin) defining the static yield curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig, eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the static yield curve may not increase from one segment to the following one.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): x-overstress

ECR(6): y-overstress

ECR(7): xy-overstress

ECR(8): z-overstress

ECR(9): previous time

ECR(10): yz-overstress

ECR(11): xz-overstress


Let P represent the point of intersection (in the equivalent stress - equivalent strain space) between the unloading path and the equilibrium stress-strain curve.

ECR(12): total x-strain at point P

ECR(13): total y-strain at point P

ECR(14): total z-strain at point P

ECR(15): total xy-strain at point P

ECR(16): total yz-strain at point P

ECR(17): total xz-strain at point P

ECR(18): equivalent total strain at point P

ECR(19): old equivalent total strain

ECR(20): EPSC (equivalent strain parameter)


EPSC is defined by the cyclic hardening law. It corresponds to the distance between point P and the new origin in the strain direction.

ECR(21): current cumulative value of number of crossings of the unloading path with the equilibrium stress-strain diagram

ECR(22): new x-stress at point P

ECR(23): new y-stress at point P

ECR(24): new xy-stress at point P

ECR(25): new z-stress at point P

ECR(26): new yz-stress at point P

ECR(27): new xz-stress at point P

ECR(28): new equivalent stress at point P

ECR(29): old equivalent stress

ECR(30): old equilibrium equivalent stress

ECR(31): old (Young’s modulus * total strain)

ECR(32): sound speed


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.41  VON MISES WITH VISCOPLASTIC REGULARIZATION

C.244


Object:


This directive enables to choose an elastoplastic constitutive theory with Von Mises yield surface, associative flow rule, and isotropic hardening or softening, including a viscoplastic regularization. Elasto-plasticity is implemented via a radial return algorithm.


For more information about the theory, please refer to: J.C. Simo, J.G. Kennedy and S. Govindjee, "Non-Smooth Multisurface Plasticity and Viscoplasticity. Loading/Unloading Conditions and Numerical Algorithms", Int. J. Num. Meth. Eng., Vol 26, pp. 2161-2185 (1988).


Syntax:

    "VMSF"  "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige "ETA" eta
      ...  "TRAC" npts*(sig eps) /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
eta

Viscoplastic parameter (relaxation time).
"TRAC"

This key-word announces the yield curve.
npts

Number of points (except the origin) defining the yield curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may become negative in the softening part of the curve.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): x-stress before viscoplastic correction

ECR(6): y-stress before viscoplastic correction

ECR(7): xy-stress before viscoplastic correction

ECR(8): z-stress before viscoplastic correction

ECR(9): yz-stress before viscoplastic correction (3D only)

ECR(10): xz-stress before viscoplastic correction (3D only)

ECR(11): current time

ECR(12): sound speed


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.42  DRUCKER PRAGER WITH VISCOPLASTIC REGULARIZATION

C.245


Object

This directive enables to choose an elastoplastic constitutive theory with Drucker Prager yield surface, associative or non-associative flow rule, including hardening or softening, and a viscoplastic regularization.


This material is part of the models developed by the CESI team (formerly at ENEL, Milano) in collaboration with JRC.


The regularization technique is the same as the one implemented in the VMSF material, see: J.C. Simo, J.G. Kennedy and S. Govindjee, "Non-Smooth Multisurface Plasticity and Viscoplasticity. Loading/Unloading Conditions and Numerical Algorithms", Int. J. Num. Meth. Eng., Vol 26, pp. 2161-2185 (1988).


The model uses two parameters, alfa and c, related to the angle and the cohesion parameters of the classical Drucker Prager model. These two parameters are not constant in general, but depend on the plastic strain. Hardening and/or softening are thus possible.


References

More information on the formulation of this material model may be found in reference [120].


Syntax

    "DPSF"  "RO" rho  "YOUN" young  "NU" nu
            "ALF1" alf1 "C1" c1 "BETA" beta "ETA" eta
            <"FAIL" $[ PEPS ; PEPR ]$ "LIMI" limit >
            "TRAA" npta*(alfa epsp)
            "TRAC" npts*(c    epsp) /LECTURE/


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
alf1

First value ("yield limit") of the TRAA curve for the alfa parameter, see below.
c1

First value ("yield limit") of the TRAC curve for the c parameter, see below.
beta

Parameter indicating whether the model is associative or non associative. If the alfa parameter (given by the "TRAA" directive below) does not depend upon the plastic strain, and beta=alf1, then an associative rule is taken. Otherwise, the law is non associative. E.g., beta=0 corresponds to return along a cylinder.
eta

Viscoplastic parameter (relaxation time).
FAIL

Optional keyword: introduces an element failure model, represented by a failure criterion and a by failure limit value. The available failure criteria are: PEPS for a criterion based upon the principal strain (see caveat below), PEPR for a criterion based upon the principal strain if the hydrostatic stress is positive (traction): if the hydrostatic stress is negative (compression) there is no failure.
limit

Optional parameter, indicates the failure limit for the chosen criterion.
"TRAA"

This key-word announces the curve defining the variation of the alfa parameter with the plastic strain.
npta

Number of points defining the curve.
alfa

Value of the alfa parameter.
epsp

Corresponding value of the plastic strain.
"TRAC"

This key-word announces the curve curve defining the variation of the c parameter with the plastic strain.
npts

Number of points defining the curve.
c

Value of the c parameter.
epsp

Corresponding value of the plastic strain.
LECTURE

List of the elements concerned.

Comments:


When using a failure criterion based upon the principal strains (PEPS or PEPR) be aware that the criterion is based upon the cumulated strains. These are usually a good approximation of the total strains for elements using a convected reference frame for the stresses and strains (such as e.g. plate, shell or bar elements). The approximation is likely to be very bad, instead, for continuum-like elements, at least when there are large rotations.


The parameter ETA can be effectively used to obtain a mesh size independence in case of static or quasi-static calculations. The parameter is very sensitive in case of dynamic simulations and must be set with care. It is recommended to set this parameter to 0 in case of fast dynamic simulations.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): cohesion

ECR(5): x-stress before viscoplastic correction

ECR(6): y-stress before viscoplastic correction

ECR(7): xy-stress before viscoplastic correction

ECR(8): z-stress before viscoplastic correction

ECR(9): yz-stress before viscoplastic correction (3D only)

ECR(10): xz-stress before viscoplastic correction (3D only)

ECR(11): current time

ECR(12): alfa

ECR(13): zone (sigma - tau plane)

ECR(14): yield (f=alfa*sigma+tau-cohe), >0 if plast

ECR(15): failure flag (0=virgin Gauss Point, 1=failed Gauss Point).

ECR(16): sound speed


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.43  COMPOSITE MATERIAL (LINEAR OTHOTROPIC) ISPRA IMPLEMENTATION

C.246


Object:


The option is used to enter materials with a linear orthotropic behaviour into a coordinate system defined by the user. The model is suitable to represent e.g. composite materials.


Syntax:

    "COMM"  "RO"  rho    "YG1"  yg1    "YG2"   yg2  "YG3" yg3
            "NU12" nu12  "NU13" nu13   "NU23" nu23
            "G12"  g12   "G13"  g13    "G23" g23
            /LECTURE/


rho

Density of the material.
yg1

Young’s modulus along direction 1.
yg2

Young’s modulus along direction 2.
yg3

young’s modulus along direction 3.
nu12

Poisson’s ration between direction 1 and 2.
nu 13

Poisson’s ration between direction 1 and 3.
nu23

Poisson’s ratio between direction 2 and 3.
g12

Shear modulus between direction 1 and 2.
g13

Shear modulus between direction 1 and 3.
g23

Shear modulus between direction 2 and 3.
LECTURE

List of the elements concerned.

Comments:


This option may be repeated as many times as necessary.


The associated orthotropy directions are to be specified via the COMP ORTS directive (see page C.97).


Outputs:


The different components of the ECR table are as follows:

ECR(1) : current hydrostatic pressure (1/3(SX+SY+ST))

ECR(2) : current equivalent stress (von Mises)

ECR(3) : current equivalent plastic strain

ECR(4) : current yield stress

ECR(5): sound speed

ECR(6): angle alpha between lamina coordinate 1 and orthotropy direction 1

ECR(7): 10.

ECR(8): 10.

7.6.44  MODIFIED CAM-CLAY MATERIAL

C.247


Object

The directive is used to enter materials with a modified Cam-clay behaviour. The model is suitable to represent e.g. cohesive soil materials.


Although the model includes some treatment of the water possibly present in soils, the use of this feature is strongly discouraged because the modeling appears somewhat inconsistent in that case: for example, water motion within the soil is not treated, water pressure is not taken into account to compute internal forces, and finally the calculation of masses seems inconsistent. To model a dry soil, just leave out the keyword ROW: then the code assumes ρw=0, the value given for ρ is the density of the (dry) soil alone, and the value given for zf, if any, is irrelevant.


References

More information on the formulation of this material model may be found in reference [147].


Syntax

    CAMC  RO ro |[ NU nu ; G g ]|
          M m     LAM lam   K k    E e   <ROW row>
          K0 k0   OCR ocr
          |[ ZF zf SLEV slev GRAV grav  ;  PRES pres ]|
          /LECT/


ro

Initial density ρ of the soil (including the water, if any: but see the comments above and below).
nu

Poisson’s coefficient ν. If this value is given, then the shear modulus G may not be given and the calculation is done with constant Poisson’s coefficient (G will vary accordingly).
g

Shear modulus G. If this value is given, then ν may not be given and the calculation is done with constant shear modulus (ν will vary accordingly).
m

Critical state parameter M. Corresponds to the CLAY model’s M parameter. For the physical meaning, see the Remarks below.
lam

Isotropic consolidation modulus (λ).
k

Unloading-reloading modulus (κ).
e

Initial void ratio e, defined as: e=VVoids / VSolid.
row

Water density ρw. Use 0.0 for dry soils, or just leave out this keyword since the default value is 0.0. Note that in this case the value for ρ given above indicates the density of the (dry) soil alone.
k0

Coefficient of earth pressure at rest (K0).
ocr

Overconsolidation ratio Ocr: (Ocr=1 for normal-consolidated soil).
zf

Upper level of water, i.e. water surface “vertical” coordinate (y in 2D, z in 3D). Used to compute the in-situ (initial) stress and hardening state. This quantity is unused, and thus any value may be given, e.g. zf=0, if the user has specified ρw=0 (dry soil).
slev

Upper level of soil, i.e. soil surface “vertical” coordinate (y in 2D, z in 3D). Used to compute the in-situ (initial) stress and hardening state.
grav

Acceleration of gravity along the “vertical” coordinate (y in 2D, z in 3D). Used to compute the in-situ (initial) stress and hardening state.
pres

Initial hydrostatic (uniform) pressure state. Note that here (but not for stresses SIG etc.) a positive value should be used to indicate an initial compression (negative stress).
LECTURE

List of the elements concerned.

Comments

This option may be repeated as many times as necessary.


This material model seems unable to start from initial stress-free conditions, so that in-situ (initial) stresses should always be specified.


The initial in-situ conditions (stresses and some of the ECR components) for elements using this material are computed by using the parameters (zf, slev, grav) or pres. One and only one of these two sets must be given. In the following discussion, the term “vertical” refers to the y-coordinate in 2D, to the z-coordinate in 3D calculations.

A) If pres (p) is specified, then the initial state is uniform hydrostatic stress (−p) all over the current CAMC material. This is typical, e.g., of simple one-element tests to check the behaviour of the constitutive law, or of simple laboratory experiments.

In this case, the code simply sets:

σ1=−p    ,    σ2=−p    ,    σ3=−p.

B) If (zf, slev, grav) are specified, then the initial conditions are computed as follows. The model assumes a horizontally stratified (homogeneous) soil, the lower part of which may contain water. The quantities zf and slev are the vertical coordinates of the upper water and soil levels, respectively. Normally it should be slev>zf so that the soil layer between zf and slev is dry (no water) while the soil below that level is saturated by water.

For each element with the current CAMC material, the code computes the vertical coordinate of its centroid zc. Then the vertical stress due to the soil weight (effective stress) is:

σv = −g(ρ−ρw)(slevzc), 

where ρ is the density of the wet soil (soil plus water), ρw is the density of the water. Thus, the difference between the two is the density of the (dry) soil. The vertical stress may not be positive:

σv=MINv,0). 

The horizontal stress is given by:

σh=K0σv

where K0 is the k0 parameter specified above. Then, the code sets:

σ1h    ,    σ2h    ,    σ3v.

In addition to soil (effective) stresses, the water pressure (hydrostatic) is also evaluated:

pw = −gρw(zfzc). 

The water pressure may not be positive:

pw=MIN(pw,0). 

This quantity is stored in ECR(7). Note, however, that the water pressure does not contribute to internal forces in the CAMC model: only the effective (soil) stresses are used.

Note also that if (zf, slev, grav) are specified one should also probably specify a “global” gravity term (equal to the value of g given above) by means e.g. of the CHAR CONS GRAV directive, in order to have (at least approximate) equilibrium in the initial configuration. In addition, suitable boundary conditions must also be prescribed along the envelope of the CAMC soil region.


Outputs

The different components of the ECR table are as follows:

ECR(1) : current hydrostatic pressure 1/3 tr (σ)

ECR(2) : square root of the second invariant of the deviatoric stress tensor J2′ (i.e. square root of Von Mises equivalent stress)

ECR(3) : current void ratio

ECR(4) : hardening parameter Pc (isotropic consolidation pressure)

ECR(5): sound speed

ECR(6): water overpressure (u)

ECR(7): initial water pressure (p0), p = p0 + u (p is the total water pressure)

ECR(8): volumetric strain (єV = єx + єy + єz)

ECR(9): deviatoric strain
єd = √2/3[(єx−єy)2+ (єy−єz)2+ (єy−єz)2]+ (γxy2 + γyz2 + γxz2)


The components of the stress tensor are as follows:

SIG(1): σx

SIG(2): σy

SIG(3): σz

SIG(4): τxy

SIG(5): τyz (only 3D)

SIG(6): τxz (only 3D)


Remarks

Let M1 be the ratio between the second invariant of the stress tensor J2 and the first invariant of the stress tensor J1 at critical state (i.e. for stress points which lie on the failure surface). This is the quantity which is usually available from tests.


Let M2 be the ratio between the second invariant of the deviatoric stress tensor J2′ and the first invariant of the stress tensor J1 at critical state.


The M parameter defined above in the input syntax corresponds to M1. However, note that in the model description of the CAMC material the quantity g(θ) corresponds rather to M2.


The following relation holds between the two quantities: M2 = M1 / √3.


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements)

7.6.45  MODIFIED CAM-CLAY MATERIAL WITH VISCOPLASTIC REGULARIZATION

C.248


Object

The option is used to enter materials with a modified Cam-clay behaviour. The model is suitable to represent e.g. (dry) soil materials. The main differences with respect to the CAMC material are that:

Like for the CAMC material, the user may choose between a calculation with constant shear modulus and one with constant Poisson’s coefficient.


References

More information on the formulation of this material model may be found in reference [123].


Syntax

    CLAY  RO ro |[ NU nu ; G g ]|
          M m     LAM lam   K k   P0 p0
          K0 k0
          < BETA beta > < NUM num >
          |[ SLEV slev GRAV grav  ;  PRES pres ]|
          /LECT/


ro

Initial density ρ of the (dry) soil. Water content is not taken into account by this model.
nu

Poisson’s coefficient ν. If this value is given, then G may not be given and the calculation is done with constant Poisson’s coefficient (G will vary accordingly).
g

Shear modulus G. If this value is given, then ν may not be given and the calculation is done with constant shear modulus (ν will vary accordingly).
m

Critical state parameter M. Corresponds to the CAMC model’s M parameter. For the physical meaning, see the Remarks below.
lam

First loading slope (λ). This is the slope of the normal consolidation line, divided by the reference volume Vλ. The normal consolidation line is defined in the plane [V, ln(P)], where V is the so-called specific volume (V = 1 + e, e being the void ratio i.e. the volune of the voids divided by volume of the solid). Vλ is the specific volume at unit pressure. P is the pressure.
k

Unloading-reloading slope κ. This is the slope of the unloading-reloading line, divided by the reference volume Vλ. The unloading-reloading line is defined in the plane [V, ln(P)], where V is the so-called specific volume (V = 1 + e, e being the void ratio i.e. the volune of the voids divided by volume of the solid). Vλ is the specific volume at unit pressure. P is the pressure.
p0

Initial value of the hardening parameter p0.
k0

Coefficient of earth pressure at rest (K0).
beta

Relaxation modulus β for the viscoplastic regularization. If β=0, then no regularization is performed. By default, the code assumes β=0.
num

Index (integer) n used by the initialization routine INICLA in order to set some initial properties of the soil (initial stresses and initial hardening parameters). By default, the program assumes n=0.
slev

Upper level of soil, i.e. soil surface “vertical” coordinate (y in 2D, z in 3D). Used to compute the in-situ (initial) stress and hardening state.
grav

Acceleration of gravity along the “vertical” coordinate (y in 2D, z in 3D). Used to compute the in-situ (initial) stress and hardening state.
pres

Initial hydrostatic (uniform) pressure state. Note that here (but not for stresses SIG etc.) a positive value should be used to indicate an initial compression (negative stress).
LECTURE

List of the elements concerned.

Comments

This option may be repeated as many times as necessary.


The initial in-situ conditions (stresses and some of the ECR components) for elements using this material are computed by using the parameters (slev, grav) or pres. One and only one of these two sets must be given. In the following discussion, the term “vertical” refers to the y-coordinate in 2D, to the z-coordinate in 3D calculations.

A) If pres (p) is specified, then the initial state is uniform hydrostatic stress (−p) all over the current CLAY material. This is typical, e.g., of simple one-element tests to check the behaviour of the constitutive law, or of simple laboratory experiments.

In this case, the code simply sets:

σ1=−p    ,    σ2=−p    ,    σ3=−p.

B) If (slev, grav) are specified, then the initial conditions are computed as follows. The model assumes a horizontally stratified (homogeneous) soil in dry conditions, i.e. containing no water. The quantity slev is the vertical coordinate of the upper soil level.

For each element with the current CLAY material, the code computes the vertical coordinate of its centroid zc. Then the vertical stress due to the soil weight (effective stress) is:

σv = −gρ(slevzc), 

where ρ is the density of the (dry) soil. The vertical stress may not be positive:

σv=MINv,0). 

The horizontal stress is given by:

σh=K0σv

where K0 is the k0 parameter specified above. Then, the code sets:

σ1h    ,    σ2h    ,    σ3v.

Note that if (slev, grav) are specified one should also probably specify a “global” gravity term (equal to the value of g given above) by means e.g. of the CHAR CONS GRAV directive, in order to have (at least approximate) equilibrium in the initial configuration. In addition, suitable boundary conditions must also be prescribed along the envelope of the CLAY soil region.


Outputs

The different components of the ECR table are as follows:

ECR(1) : current hydrostatic pressure 1/3(σxyz)

ECR(2) : current bulk modulus

ECR(3) : second invariant of the deviatoric cumulated strain

ECR(4) : hardening parameter p0

ECR(5): sound speed

ECR(6): current value of the shear modulus G

ECR(7): current value of the Poisson’s coefficient ν


The components of the stress tensor are as follows:

SIG(1): σx

SIG(2): σy

SIG(3): σz

SIG(4): τxy

SIG(5): τyz (only 3D)

SIG(6): τxz (only 3D)


Remarks

Let M1 be the ratio between the second invariant of the stress tensor J2 and the first invariant of the stress tensor J1 at critical state (i.e. for stress points which lie on the failure surface). This is the quantity which is usually available from tests.


Let M2 be the ratio between the second invariant of the deviatoric stress tensor J2′ and the first invariant of the stress tensor J1 at critical state.


The M parameter defined above in the input syntax corresponds to M1. However, note that in the model description of the CLAY material (An Implementation of the Cam-Clay Elasto-Plastic Model Using a Backward Interpolation and Visco-Plastic Regularization, Technical Note I.96.239) the quantity M corresponds rather to M2.


The following relation holds between the two quantities: M2 = M1 / √3.


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.46  FUNE (SPECIALIZED CABLE MATERIAL)

C.250


Object:


This model represents an elastoplastic cable, with no resistance in compression, and should be used in conjunction with special cable elements FUN2 (in 2D) and FUN3 (in 3D). The material is elasto-plastic in traction.


Syntax:

   "FUNE"  "RO" rho  "YOUN" young  "NU" nu  "ELAS" sige "ERUP" erup ...
       ...  "TRAC" npts*(sig eps) /LECTURE/
rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
erup

Rupture strain.
"TRAC"

This key-word announces the yield curve (in traction).
npts

Number of points (except the origin) defining the yield curve.
sig

Stress.
eps

Total strain (elastic + plastic).
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may not increase from one segment to the following one.


Outputs:


The components of the ECR table are as follows:

ECR(1): (free) (was total longitudinal strain of the cable element)

ECR(2): (free) (was total lateral strain of the cable element)

ECR(3): plastic longitudinal strain of the cable element

ECR(4): current yield stress in traction (0 if broken)

ECR(5): sound speed


Note that in order to post-process the total strains (which were formerly unappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.47  JOHNSON-COOK MODEL

C.251


Object:


In the Johnson-Cook model Elasto-plasticity is implemented via a radial return algorithm. Only isotropic hardening is activated to date and strain-rate dependency is included in the model. However, no temperature effects are included in the present implementation.


References

The implementation of this material model is described in reference [167].


The Johnson-Cook constitutive relation is given by:

σeq = 
A1 + A2 
εeqp
λ2



1 + λ1 ln


εeqp
εeq,refp
 






1 − θm 
    (2)

where:


The Johnson-Cook model is a simple empirical generalization of Ludwik’s constitutive law (see VMLU on page C.253), represented by the first term of the above equation, trying to account for strain-rate effects (included in the second term of the equation) and for temperature effects (third and last term). The “reference” strain rate is the minimum plastic strain rate for which calibration of the model has been made.


In Johnson-Cook’s model the Ludwik’s law (first term) is multiplied by a function of the equivalent plastic strain rate. The form of this function is related to the often made experimental observation that the increase in flow stress is a logarithmic function of the strain rate.


The reference (or minimum) equivalent plastic strain rate εeq,refp is the value of equivalent plastic strain rate under which the material behaves in a “static” (i.e., strain-rate independent) way. In practice, in the code, when the equivalent plastic strain rate is below this value, only the static part of the model is considered. The parameters equivalent plastic strain rate and λ1 are interconnected.


Syntax:

   "VMJC"  "RO" rho  "YOUN" young  "NU" nu "COA1" coa1
           "COA2" coa2 "CLB1" clb1 "CLB2" clb2 "SRRF" srrf
          <"FAIL" $[ "VMIS" "LIMI" limit ;
                     "DPLS" "LIMI" limit ;
                     "JOCO" "COD1" cod1 "COD2" cod2 "COD3" cod3 "COD4" cod4
                  ]$ >
     ...  /LECTURE/
rho

Density of the material.
young

Young’s modulus (elastic phase).
nu

Poisson’s ratio.
coa1

1st constant (A1) in the Johnson-Cook model.
coa2

2nd constant (A2) in the Johnson-Cook model.
clb1

3rd constant (λ1) in the Johnson-Cook model.
clb2

Hardening coefficient (λ2) of the Johnson-Cook model.
srrf

Reference strain rate (εeq,refp) of the Johnson-Cook model.
FAIL

Optional keyword: introduces an element failure model. The available failure criteria are: VMIS for a criterion based upon the equivalent Von-Mises stress, DPLS for a criterion based upon the equivalent plastic strain, JOCO for the so-called Johnson-Cook criterion based upon an equivalent plastic strain, depending on the strain rate and the triaxiality ratio. See comments below.
limit

Optional parameter, indicates the failure limit for the VMIS or PLAS criterion.
cod1

Optional parameter, 1st constant (D1) in the Johnson-Cook failure criterion.
cod2

Optional parameter, 2nd constant (D2) in the Johnson-Cook failure criterion.
cod3

Optional parameter, 3rd constant (D3) in the Johnson-Cook failure criterion.
cod4

Optional parameter, 4th constant (D4) in the Johnson-Cook failure criterion.

LECTURE

List of the elements concerned.

Comments:


The Johnson-Cook failure criterion is given by:

εpf = 
D1 + D2 exp
D3 σ*




1 + D4 ln


εeqp
εeq,refp
 





    (3)

where:


The damage parameter D triggers failure when it reaches 1. It is computed as:

D = 
Δ εp
εpf
    (4)

Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von-Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): sound speed

ECR(6): equivalent strain rate (Von-Mises)

ECR(7): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)

ECR(8): damage parameter for the Johnson-Cook failure criterion


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.48  LUDWIG-PRANDTL MODEL

C.252


Object:


This directive enables to choose the Ludwig-Prandtl model, a purely elasto-plastic model implemented at Ispra. Elasto- plasticity is implemented via a radial return algorithm. Only isotropic hardening is activated to date. There is no dependency on temperature but strain rate effects are included.


References

The implementation of this material model is described in reference [167].


Syntax:

   "VMLP"  "RO" rho  "YOUN" young  "NU" nu "COA1" coa1
           "COA2" coa2 "CLB1" clb1 "CLB2" clb2 "CLB3" clb3
           "CLB4" clb4
     ...  /LECTURE/
rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
coa1

1st constant in the Ludwig-Prandtl model.
coa2

2nd constant in the Ludwig-Prandtl model.
clb1

3rd constant in the Ludwig-Prandtl model.
clb2

4th constant in the Ludwig-Prandtl model.
clb3

5th constant in the Ludwig-Prandtl model.
clb4

6th constant in the Ludwig-Prandtl model.
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may not increase from one segment to the following one.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): sound speed

ECR(6): equivalent strain rate (Von Mises)


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.49  LUDWIK MODEL

C.253


Object:


This directive enables to choose the Ludwik model, a purely elasto-plastic model implemented at Ispra. Elasto-plasticity is implemented via a radial return algorithm. Only isotropic hardening is activated to date. There is no dependency on temperature nor on strain rate.


References

The implementation of this material model is described in reference [167].


Syntax:

   "VMLU"  "RO" rho  "YOUN" young  "NU" nu "ELAS" sige ...
           "COA2" coa2 "COEN" coen
     ...  /LECTURE/
rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit.
coa2

Plastic threshold value.
coen

Hardening coefficient.
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may not increase from one segment to the following one.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): sound speed


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.50  ZERILLI-ARMSTRONG MODEL

C.254


Object:


This directive enables to choose the Zerilli-Armstrong model with the implementation developed at Ispra. Elasto-plasticity is implemented via a radial return algorithm. Only isotropic hardening is activated to date and strain-rate dependency is included. However, no dependency on temperature exist in the present version of the model.


References

The implementation of this material model is described in reference [167].


Syntax:

   "VMZA"  "RO" rho  "YOUN" young  "NU" nu  "COA1" coa1 ...
           "COA2" coa2 "COA3" coa3 "COA4" coa4 "CLB1" clb1
           "CLB2" clb2 "CLB3" clb3
     ...  /LECTURE/
rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
coa1

1st coefficient of the Zerrilli-Armstrong model.
coa2

2nd coefficient of the Zerilli-Armstrong model.
coa3

3rd coefficient of the Zerilli-Armstrong model.
coa4

4th coefficient of the Zerilli-Armstrong model.
clb1

1st hardening coefficient of the Zerilli-Armstrong model.
clb2

2nd hardening coefficient of the Zerilli-Armstrong model.
clb3

3rd hardening coefficient of the Zerilli-Armstrong model.
LECTURE

List of the elements concerned.

Comments:


1/ - The young parameter defines Young’s modulus during an elastic phase.


2/ - The points (sig,eps) may have any position; however, concerning the first point, there must be a compatibility between the coordinates, Young’s modulus and the elastic limit.


3/ - The slope of the yield curve may not increase from one segment to the following one.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3): current equivalent plastic strain

ECR(4): current yield stress

ECR(5): sound speed

ECR(6): equivalent strain rate (Von Mises)


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.51  DRUCKER-PRAGER WITH HYDROSTATIC POST-FAILURE (JRC)

C.255


Object:


This directive enables to specify a Drucker-Prager material. The material behaves in a linear elastic way until failure is reached, and thereafter it behaves like a fluid (i.e. it resists only to compression). Failure occurs when the stress point in the J1-√J2 space reaches the failure line (a straight line) of equation:

J2
=K−α J1

where J1xyz is the first invariant of the stress tensor and J2′ is the second invariant of the deviatoric stress tensor:

J2′=
1
3
x2 + σy2 + σz2 −σx σy −σx σz −σy σz) + τxy2 + τxz2 + τyz2

The constant K is the intersection of the failure line with the vertical axis and represents the failure stress of the material in pure shear (e.g. in torsion): it is also called cohesion.

The constant α is the slope of the failure line (tangent of the angle) and is also called the internal friction angle.

After failure is reached, the material behaves like a liquid: all tangential stresses are set to zero and the normal stresses are set to equal (hydrostatic) values if the material is under compression (negative volumetric strain), or to zero if the material is under traction (positive volumetric strain).

Due to its postulated after-failure behaviour, this material is not “erodable”. That is, when failure is reached, even at all Gauss points of an element, the element is not removed from the calculation because it contributes to the solution with its post-failure (hydrostatic) behaviour. Of course, this only makes sense as long as the failed material remains confined (so that a hydrostatic pressure can build up in it).


References:

The material model is described in reference [13]. Note that although the material model had been originally denoted as a Mohr-Coulomb model, in reality it is a Drucker-Prager material. In fact, the yield surface corresponding to the expression given above (using J2′) is a cone with circular cross section (and not with hexagonal cross-section) in principle stress space.


Syntax:

    "DRPR"  "RO" ro "YOUN" youn "NU" nu "COHE" cohe "FRIC" fric
            /LECTURE/


ro

Density.
youn

Young’s modulus.
nu

Poisson’s ratio.
cohe

Failure stress K in pure shear, e.g. in torsion (cohesion).
fric

Slope α of the failure line in the J1-√J2 diagram (internal friction angle).
/LECTURE/

Numbers of the elements concerned.

Outputs:


The different components of the ECR table are as follows:

ECR(1): current J1 invariant (σ123).

ECR(2): current √J2 invariant.

ECR(3): failure flag (0=not failed, 1=failed).

ECR(4): sound speed


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.52  ALUMINIUM FOAM

C.256


Object:


This option enables to specify an aluminium foam material and follows the Deshpande-Fleck model as implemented at NTNU, Trondheim (N).


References:

More information on the formulation of this material model may be found in the following references:

1. V.S. Deshpande and N.A. Fleck, Isotropic models for metallic foams, J. Mech. Phys. Solids 48 (2000), pp. 1253–1283.

2. A. Reyes, O. S. Hopperstad, T. Berstad, A. G. Hansen, M. Langseth, Constitutive modeling of aluminum foam including fracture and statistical variation of density, European Journal of Mechanics – A/Solids, Vol 22, pp 815–835, 2003.


The stresses are calculated by using the following equation:

σ=σp
e
eD
2ln(
1
1−(e/eD)β
)

The parameter eD is taken from the recent foam density ρf and the density of the pure material ρf0 by using this equation

eD=1−
ρf
ρf0

The parameter α defines the shape of the yield surface and can be calculated by using the plastic Poission’s ratio νp:

α2=
9
2
(1−2νp)
(1+νp)

The parameter γ is the initial hardening factor by reaching the plastic regime. The parameters α2 and β can be taken by a best fit of the experimental curve.


Syntax:

    FOAM  RO_F ro_f  YOUN youn  NU   nu    SIGP sigp  RO_0 ro_0
          ALFA alfa  GAMM gamm  ALF2 alf2  BETA beta <DERF derf>
          <EF ef> <SF sf> <RNUM rnum> <WC wc>
          /LECTURE/


ro_f

Initial density of the foam material, i.e. considering the voids.
youn

Young’s modulus (initial).
nu

Poisson’s coefficient (initial).
sigp

Yield stress.
ro_0

Initial density of the material, not considering the voids (pure material, ρf0).
alfa

Shape of the yield surface (see above).
gamm

Initial hardening factor by reaching the plastic regime.
alf2

Scale factor (material constant).
beta

Shape factor (material constant).
derf

Switch to choose the derivation of Fi in the model: 0 means numerical derivation, while 1 means normal derivation. The default is 1.
efail

Critical volumetric failure strain. A Gauss point fails if the volumetric strain exceeds efail. By default it is 0.0, meaning that the volumetric strain failure criterion is not active.
sfail

Critical failure stress. A Gauss point fails if the maximum principal stress exceeds sfail for a number of (consecutive) time steps greater than rnum (see next parameter). By default it is 0.0, meaning that the maximum principal stress failure criterion is not active.
rnum

Number of (consecutive) time steps with maximum principal stress exceeding sfail needed for a Gauss point to fail. By default it is ∞, meaning that the maximum principal stress failure criterion is not active.
wc

Critical failure energy (Cockcroft-Latham criterion). A Gauss point fails if the fracture energy exceeds wc. By default it is 0.0, meaning that the Cockcroft-Latham failure criterion is not active.
/LECT/

List of the concerned elements.

Outputs:


The components of the ECR table are as follows:

ECR(1): Equivalent plastic strain (єeq)

ECR(2): Von Mises effective plastic strain (єe)

ECR(3): Volumetric strain (єm)

ECR(4): Equivalent stress (σeq)

ECR(5): Von Mises effective stress (σe)

ECR(6): Mean stress (σm)

ECR(7): Isotropic hardening variable (R)

ECR(8): Iteration counter

ECR(9): (Y)

ECR(10): sound speed

ECR(11): first principal stress (ps1)

ECR(12): second principal stress (ps2)

ECR(13): third principal stress (ps3)

ECR(14): counter of the consecutive number of steps where ps1 > sfail

ECR(15): Cockcroft-Latham damage accumulation (W) when energy-based damage is activated and ps1 > sfail

ECR(16): “universal” damage parameter (D). May be used in combination with AMR?

ECR(17): Gauss point failure flag: 1 = virgin, 0 = failed.

7.6.53  GLRC: REINFORCED CONCRETE FOR SHELLS

C.260


Object:


This material is designed to model reinforced concrete shells, possibly with prestressing and steel liner. It consists in a resultant variables constitutive law, using both plasticity (double JOHANSEN’s criterion with a kinematic softening) and damage (to take into account concrete cracking). For information about this model see references [866], [867].


New syntax for non-linear GLRC material (elastoplastic with or without damage):

    "GLRC" < "DAMA" > < "SHEA" >
           "RO"   rho
           "H"    thickness
           "EB"   yconcrete  "NUB"  pconcrete
           "NLIT" nblayer * ( |[ "NAPP" ("EA" ysteel  < "FY" tsteel >
                                         "OMX" ax       "OMY" ay
                                         "RX"  rx       "RY"  ry       ) ;
                                 "PREC" ( "EA" ysteel  < "FY" tsteel >
                                          "OMX" ax       "OMY" ay
                                          "RX"  rx       "RY"  ry       ) ;
                                 "LINR" ( "EA" ysteel  < "FY" tsteel >
                                          "OMLR" epliner "NULR" nuliner
                                          "RLR"  rliner                 ) ]| )
         < "OMT"  atrast       "EAT"  ytrast  >
         < "BT1"  shear1       "BT2"  shear2  >

         < "BTD1" sheard1      "BTD2" sheard2 >
         < "TSD"  tsheard >

         < "FT"   tconcrete  < "GAMM" gamma   >
           "QP1"  qslope1      "QP2"  qslope2 >

           "C1N1" pragmemb1x "C1N2" pragmemb1y "C1N3" pragmemb1xy
           "C2N1" pragmemb2x "C2N2" pragmemb2y "C2N3" pragmemb2xy
           "C1M1" pragbend1x "C1M2" pragbend1y "C1M3" pragbend1xy
           "C2M1" pragbend2x "C2M2" pragbend2y "C2M3" pragbend2xy

      $[    "FC"   cconcrete                    ;
         (  "MP1X"  < "FONC" >  plaslim1x
            "MP1Y"  < "FONC" >  plaslim1y
            "MP2X"  < "FONC" >  plaslim2x
            "MP2Y"  < "FONC" >  plaslim2y
          < "D1X"     "FONC"    dplaslim1x  >
          < "D1Y"     "FONC"    dplaslim1y  >
          < "D2X"     "FONC"    dplaslim2x  >
          < "D2Y"     "FONC"    dplaslim2y  >
          < "DD1X"    "FONC"    ddplaslim1x >
          < "DD1Y"    "FONC"    ddplaslim1y >
          < "DD2X"    "FONC"    ddplaslim2x >
          < "DD2Y"    "FONC"    ddplaslim2y > ) ]$

         < "PREX" nprecx  "PREY" nprecy  >

         < "KRAY" kray    "MRAY" mray    >

           /LECTURE/


rho

Density of the plate material (concrete and steel).
thickness

Thickness of the concrete (thickness of the plate).
yconcrete

Young’s modulus of the concrete material.
ypoisson

Poisson’s ratio of the concrete material.
NAPP

Keyword for the description of bending steel reinforcement (steel grid).
PREC

Keyword for the description of prestressing.
LINR

Keyword for the description of the steel liner.
ysteel

Young’s modulus of the steel material.
tsteel

Yield stress of the steel. Used to calculate automatically the generalized Johansen criterion (when the plaslim functions are not specified).
ax, ay

Areas (per meter of plate) of the reinforcement layer in the x and y directions (m2/m).
rx, ry

Nondimensional position of the layer in the x and y directions (−1 ≤ r ≤ 1).
epliner

Thickness of the liner.
nuliner

Poisson’s ratio of the liner steel.
rliner

Nondimensional position of the liner (−1 ≤ rliner ≤ 1).
shear

Coefficients of the elastic shear matrix (for elements that take into account the transverse shear like Q4GR or Q4GS):


Tx 
Ty
 

=

shear1
0shear2
 



γx 
γy
 

When the shear coefficients are not specified, they are calculated, for Q4GR and Q4GS elements, using the following expression:
T = k 
h
2
 (
Eb
1+νb
+EaT ωT) γ
with:

If the keyword SHEA is specified then a nonlinear evolution of the shear force is taken into account ([880]). This nonlinear evolution can be compared to an elastoplastic constitutive law. Beyond a shear force defined by TSD, the shear force evolves according to a linear slope whose stiffness is defined through the keywords BTD1 and BTD2 and plate elements are then subjected to irreversible deformations.

When the values of the damaged shear coefficients sheard1 and sheard2 are not specified, they are calculated using the following expression:

sheard1 = sheard2 = k 
h
2
 (
EaT
100
 ωT)
atrast

Area (per square meter of plate) of the transverse reinforcement (m2/m2). Used to calculate the elastic shear coefficients when shear are not specified.
ytrast

Young’s modulus of the steel material for transverse reinforcement. Used for the computation of the elastic shear coefficients when shear are not specified. Default value is the standard ysteel value.
tconcrete

Tensile strength of concrete (tensile stress). Must be positive. Used to calculate the bending cracking moment. Used only for damage.
qslope1 qslope2

Slopes quotient for positive and negative bending. The quotient is supposed to be the slope of the (curvature,moment) graph after cracking over the slope before cracking. Used only for damage.
Qp = 
peac
pebc
with:
gamma

Damage computation parameter which characterizes the slope of the (curvature,moment) graph during cracking. gamma can be considered as the slope during cracking over the slope before cracking. If gamma > 0, the slope increases. If gamma < 0, the slope decreases and the stability is not warranted. In any case, we must have gamma < qslope1 and gamma < qslope2. Default value is zero. Used only for damage.
γ = 
pedc
pebc
with:
pragmemb, pragbend

Prager coefficients corresponding to the matrices linking the plastic strain and curvature to the back membrane force and the backmoment.
n = CN1 є1p + CN2 є2p 
m = CM1 κ1p + CM2 κ2p 
with:
C = 
pe pp
pe − pp
with:
cconcrete

Compressive strength of concrete. Used to calculate automatically the generalized Johansen criterion (when the plaslim functions are not specified).
plaslim

Functions used in the generalized Johansen criterion. They describe the "beam" plastic limit moment depending on the membrane force. When they are not specified, they are automatically calculated and interpolated.
plaslim1x plaslim2x

Positive and negative plastic limit moments for a perfect bending in the x-direction (referring to the orthotropic axes of the shell element). If the directive "FONC" is used, plaslim1x or plaslim2x are integers referring to a function number (function of Nx). We should have usually plaslim1x > plaslim2x.
plaslim1y plaslim2y

Positive and negative plastic limit moments for a perfect bending in the y-direction (referring to the orthotropic axes of the shell element). If the directive "FONC" is used, plaslim1y or plaslim2y are integers referring to a function number (function of Ny). We should have usually plaslim1y > plaslim2y.
dplaslim1x dplaslim2x dplaslim1y dplaslim2y

Function number of the first derivative of plaslim1x, plaslim2x, plaslim1y and plaslim2y plastic limit functions. They are used when the membrane plasticity is taken into account and when they cannot be computed directly from the plaslim1x, plaslim2x, plaslim1y and plaslim2y functions.
ddplaslim1x ddplaslim2x ddplaslim1y ddplaslim2y

Function number of the second derivative of plaslim1x, plaslim2x, plaslim1y and plaslim2y plastic limit functions. They are used when the membrane plasticity is taken into account and when they cannot be computed directly from the plaslim1x, plaslim2x, plaslim1y, plaslim2y or dplaslim1x, dplaslim2x, dplaslim1y, dplaslim2y functions.
nprecx, nprecy

Prestressing force in the x and y directions (should be negative since it is normally a compression force).
kray, mray

Rayleigh’s stiffness and mass proportional damping coefficients, used only by finite elements of the following types: DKT3, T3GS, Q4GS. Default values: kray=0, mray=0. For information about Rayleigh’s damping see reference [862].
LECTURE

List of the elements concerned.

Syntax for perforation analysis (always used with the new syntax) :

    "GLRC" < "DAMA" > "PERF" < "SHEA" >
           "RO"   rho
           "H"    thickness
           "EB"   yconcrete  "NUB"  pconcrete
           "NLIT" nblayer * ( |["NAPP" ( "EA" ysteel  < "FY" tsteel >
                                         "FS"  tsteelp
                                         "OMX" ax       "OMY" ay
                                         "RX"  rx       "RY"  ry       ) ;
                                "PREC" ( "EA" ysteel  < "FY" tsteel >
                                         "FS"  tsteelp
                                         "OMX" ax       "OMY" ay
                                         "RX"  rx       "RY"  ry       ) ;
                                "LINR" ( "EA" ysteel  < "FY" tsteel >
                                         "FS"  tsteelp
                                         "OMLR" epliner "NULR" nuliner
                                         "RLR"  rliner                 ) ]| )
           "OMT"  atrast    <  "EAT"  ytrast  >   "FST"  tsteelp_t
         < "BT1"  shear1       "BT2"  shear2  >

         < "BTD1" sheard1      "BTD2" sheard2 >
         < "TSD"  tsheard >

         < "FT"   tconcrete  < "GAMM" gamma   >
           "QP1"  qslope1      "QP2"  qslope2 >

           "FC"   cconcrete  "PHI"  friction   < "NUFC" eff_factor >
         < "NPER" nper >

           "C1N1" pragmemb1x "C1N2" pragmemb1y "C1N3" pragmemb1xy
           "C2N1" pragmemb2x "C2N2" pragmemb2y "C2N3" pragmemb2xy
           "C1M1" pragbend1x "C1M2" pragbend1y "C1M3" pragbend1xy
           "C2M1" pragbend2x "C2M2" pragbend2y "C2M3" pragbend2xy

      <    "MP1X"  < "FONC" >  plaslim1x
           "MP1Y"  < "FONC" >  plaslim1y
           "MP2X"  < "FONC" >  plaslim2x
           "MP2Y"  < "FONC" >  plaslim2y
         < "D1X"     "FONC"    dplaslim1x  >
         < "D1Y"     "FONC"    dplaslim1y  >
         < "D2X"     "FONC"    dplaslim2x  >
         < "D2Y"     "FONC"    dplaslim2y  >
         < "DD1X"    "FONC"    ddplaslim1x >
         < "DD1Y"    "FONC"    ddplaslim1y >
         < "DD2X"    "FONC"    ddplaslim2x >
         < "DD2Y"    "FONC"    ddplaslim2y >    >

         < "PREX" nprecx  "PREY" nprecy  >

         < "KRAY" kray    "MRAY" mray    >

           /LECTURE/


cconcrete

Compressive strength of concrete. Used to calculate automatically the generalized Johansen criterion (when the plaslim functions are not specified). Mandatory for perforation analysis.
friction

Friction angle of concrete (degrees). Mandatory for perforation analysis.
tsteelp, tsteelp_t

Limit stress of steel (for each layer and for transverse reinforcement). Mandatory for perforation analysis.
eff_factor

Effectiveness factor for concrete. When not specified, a default value is taken.
nper

Frequency of verification of the perforation criterion. Default value is 1 (every time step).

For information about the perforation criterion see references [864], [866].


Old syntax for the standard material (without damage):

    "GLRC" "OLD"
           "RO" rho "BN11" memb11     "BN12" memb12
                    "BN22" memb22     "BN33" memb33
                    "BM11" bend11     "BM12" bend12
                    "BM22" bend22     "BM33" bend22
                  < "BC11" coup11 > < "BC12" coup12 >
                  < "BC22" coup22 > < "BC33" coup22 >
                  < "BT1"  shear1 > < "BT2"  shear2 >
                  < "C1N1" pragmemb1x "C1N2" pragmemb1y "C1N3" pragmemb1xy >
                  < "C2N1" pragmemb2x "C2N2" pragmemb2y "C2N3" pragmemb2xy >
                    "C1M1" pragbend1x "C1M2" pragbend1y "C1M3" pragbend1xy
                    "C2M1" pragbend2x "C2M2" pragbend2y "C2M3" pragbend2xy
                    "MP1X"  < "FONC" >  plaslim1x
                    "MP1Y"  < "FONC" >  plaslim1y
                    "MP2X"  < "FONC" >  plaslim2x
                    "MP2Y"  < "FONC" >  plaslim2y
                  < "D1X"     "FONC"    dplaslim1x >
                  < "D1Y"     "FONC"    dplaslim1y >
                  < "D2X"     "FONC"    dplaslim2x >
                  < "D2Y"     "FONC"    dplaslim2y >
                  < "DD1X"    "FONC"    ddplaslim1x >
                  < "DD1Y"    "FONC"    ddplaslim1y >
                  < "DD2X"    "FONC"    ddplaslim2x >
                  < "DD2Y"    "FONC"    ddplaslim2y >
                    /LECTURE/
rho

Density of the material.
memb, bend, coup

Coefficients of the elastic matrix:







Nxx 
Nyy 
Nxy 
Mxx 
Myy 
Mxy
 






=






memb11memb120coup11coup120  
memb12memb220coup12coup220  
00memb3300coup33 
coup11coup120bend11bend12
coup12coup220bend12bend22
00coup3300bend33
 













єxx 
єyy 
2 єxy 
κxx − κxxp 
κyy − κyyp 
2 (κxy − κxyp)
 






When the coupling coefficients are not specified, they take the zero value.
shear

Coefficients of the elastic shear matrix (for elements that take into account the transverse shear like Q4GR or Q4GS):


Tx 
Ty
 

=

shear1
0shear2
 



γx 
γy
 

When the shear coefficients are not specified, they take the zero value. Classical assumptions in elasticity give the following expression:
T = h 
kE
2(1+ν)
 γ
with:
pragmemb, pragbend

Prager coefficients corresponding to the matrices linking the plastic strain and curvature to the back membrane force and the backmoment.
n = CN1 є1p + CN2 є2p 
m = CM1 κ1p + CM2 κ2p 
with: The membrane Prager coefficients are not mandatory. If they are not specified by the user, the model takes into account only bending plasticity. Thus it has a non-normal plasticity flow if the plastic limits vary with the membrane force. This could lead to convergence problems. But if the membrane Prager coefficients are given, both membrane and bending plasticity are taken into account. The model is in fact regularized compared to the preceding one.
plaslim1x plaslim2x

Positive and negative plastic limit moments for a perfect bending in the x-direction (referring to the orthotropic axes of the shell element). If the directive "FONC" is used, plaslim1x or plaslim2x are integers referring to a function number (function of Nx). We should have usually plaslim1x > plaslim2x.
plaslim1y plaslim2y

Positive and negative plastic limit moments for a perfect bending in the y-direction (referring to the orthotropic axes of the shell element). If the directive "FONC" is used, plaslim1y or plaslim2y are integers referring to a function number (function of Ny). We should have usually plaslim1y > plaslim2y.
dplaslim1x dplaslim2x dplaslim1y dplaslim2y

Function number of the first derivative of plaslim1x, plaslim2x, plaslim1y and plaslim2y plastic limit functions. They are used when the membrane plasticity is taken into account and when they cannot be computed directly from the plaslim1x, plaslim2x, plaslim1y and plaslim2y functions.
ddplaslim1x ddplaslim2x ddplaslim1y ddplaslim2y

Function number of the second derivative of plaslim1x, plaslim2x, plaslim1y and plaslim2y plastic limit functions. They are used when the membrane plasticity is taken into account and when they cannot be computed directly from the plaslim1x, plaslim2x, plaslim1y, plaslim2y or dplaslim1x, dplaslim2x, dplaslim1y, dplaslim2y functions.
LECTURE

List of the elements concerned.

Old syntax for the material with damage (for cracking):

    "GLRC" "OLD" "DAMA"
           "RO" rho "BN11" memb11     "BN12" memb12
                    "BN22" memb22     "BN33" memb33
                    "E"    young      "NU"   poisson
                    "MF1"  cracklim1  "MF2"  cracklim2
                    "QP1"  qslope1    "QP2"  qslope2
                    "GAMM" gamma
                  < "BT1"  shear1 > < "BT2"  shear2 >
                  < "C1N1" pragmemb1x "C1N2" pragmemb1y "C1N3" pragmemb1xy >
                  < "C2N1" pragmemb2x "C2N2" pragmemb2y "C2N3" pragmemb2xy >
                    "C1M1" pragbend1x "C1M2" pragbend1y "C1M3" pragbend1xy
                    "C2M1" pragbend2x "C2M2" pragbend2y "C2M3" pragbend2xy
                    "MP1X"  < "FONC" >  plaslim1x
                    "MP1Y"  < "FONC" >  plaslim1y
                    "MP2X"  < "FONC" >  plaslim2x
                    "MP2Y"  < "FONC" >  plaslim2y
                  < "D1X"     "FONC"    dplaslim1x >
                  < "D1Y"     "FONC"    dplaslim1y >
                  < "D2X"     "FONC"    dplaslim2x >
                  < "D2Y"     "FONC"    dplaslim2y >
                  < "DD1X"    "FONC"    ddplaslim1x >
                  < "DD1Y"    "FONC"    ddplaslim1y >
                  < "DD2X"    "FONC"    ddplaslim2x >
                  < "DD2Y"    "FONC"    ddplaslim2y >
                      /LECTURE/


DAMA

Enable the option which allows to take in account the concrete cracking by damage.
rho, shear, pragmemb, pragbend, plaslim, dplaslim, ddplaslim

Same parameters as those described for the standard GLRC material.
memb

Coefficients of the elastic matrix:



Nxx 
Nyy 
Nxy
 


=


memb11memb120  
memb12memb220  
00memb33
 





єxx 
єyy 
2 єxy
 


There is no elastic coupling between the bending and the membrane behaviour.
young, poisson

Homogenized elastic characteristics (Young’s modulus and Poisson’s ratio) for bending.
cracklim1 cracklim2

Positive and negative cracking limit moments.
qslope1 qslope2

Slopes quotient for positive and negative bending. The quotient is supposed to be the slope of the (curvature,moment) graph after cracking over the slope before cracking.

Comments:


All the limit plastic moments must be defined carefully. When they are declared as functions (using "FONC"), the domain defined as plaslim1-plaslim2 > 0 must be a close convex domain: note particularly that the program tries to find two intersections of plaslim1 and plaslim2.

When the limit plastic functions are not defined as polynomial (e.g. when "LSQU" is not used), the program requires prolongation of the functions: it is necessary to compute the elastic predictor which can be located outside the close convex elastic domain.

The first and second derivative of the limit plastic functions can be surely computed from the original limit plastic functions (i.e. without using the functions associated with the "D1", "D2", "DD1" and "DD2" directives) when these limit plastic functions are polynomials (see "LSQU" 9.1 to use table functions as polynomials).

After (and never before) the definition of the material characteristics ("MATE" directive), the orthotropy characteristics of the elements are mandatory. The syntax is:

    "COMP"  "ORTS"   vx vy vz   /LECTURE/

See the "ORTS" directive for more details.


Outputs:


The components of the ECR table are as follows:

Plastic strain and curvature (єp and κp) in the orthotropic axes:
ECR(1): єxp

ECR(2): єyp

ECR(3): 2 × єxyp

ECR(4): κxp

ECR(5): κyp

ECR(6): 2 × κxyp


Energy dissipated during plasticity:
ECR(7): plastic dissipation per Gauss point. The sum of ECR(7) on all Gauss points of the element gives the plastic dissipation in the element.

Damage parameters:
ECR(8): D1/D1max for positive bending

ECR(9): D2/D2max for negative bending


Energy dissipated during damage:
ECR(10): damage dissipation per Gauss point. The sum of ECR(10) on all Gauss points of the element gives the damage dissipation in the element.

Orthotropy caracteristics:

Membrane force and moment minus back force and backmoment (Nn and Mm) in the orthotropic axes:
ECR(14): Nxnx

ECR(15): Nyny

ECR(16): Nxynxy

ECR(17): Mxmx

ECR(18): Mymy

ECR(19): Mxymxy


Post-treatment parameters for the perforation criterion:
ECR(20): = 0 if the criterion is not reached

      = 1 if the criterion is reached in bending mode

      = 2 if the criterion is reached in shear mode

ECR(21): normalized value of the perforation criterion (>0 if the criterion is reached)

ECR(22): nx (components of the vector which is

ECR(23): ny   normal to the failure plan,

ECR(24): nz     in the global reference frame)

7.6.54  HYPERELASTIC MATERIAL

C.261


Object:


This sub-directive enables materials with an hyperelastic behaviour to be used. Only two types of shell (Q4GS et DST3) and several solid elements (CUBE, TETR, etc.) can be used with this material. The following kinds of hyperelastic materials can be selected:

Note that a Blatz-Ko hyperelastic material model is also available, see the new BLKO material on page C.299.

For Type 1, the expression of the strain energy density corresponds to:

           W = c1*(I1-3) + c2*(I2-3) + c3*(I1-3)**2 +
               c4*(I1-3)(I2-3) + c5*(I2-3)**2 +
               c6*(I1-3)**3 + c7*(I2-3)*(I1-3)**2 +
               c8*(I1-3)(I2-3)**2 + c9(I2-3)**3 +
               c10*(I1-3)**4 + c11*(I2-3)**2*(I1-3)**3 +
               c12*(I1-3)**2(I2-3) + c13*(I1-3)(I2-3) +
               K*(Log(I3))**2


For Type 2, the expression of the strain energy density corresponds to :

W = A C(I1−3)2 dI1 + 3 B· log(I2) + K· log(I3)2     (5)

Type 3, the Ogden material can be expressed with the following equation

W = 
N
p=1
 
µp
αp

λ1αp + λ2αp + λ3αp −3 
    (6)

with the principal stretch λ.

Type 4, the Ogden material (new formulation) can be expressed with the following equation

W = 
N
p=1
 
µp
αp

λ1p + λ2p + λ3p −3 
K(J−1−lnJ)     (7)

with λ*J−1/3. K is the bulk modulus, µp and αp are the material parameters used for this expression.

Type 5, the Ogden-Storakers material can be expressed with the following equation

W = 
N
p=1
 
µp
αp

λ1αp + λ2αp + λ3αp −3 
N
p=1
 
µp
αpβp
(J−αpβp−1)     (8)

µp, αp and βp are the material parameters used for this expression.

The input parameters can be determined by the code if an experimental stress-strain curve is given, see the description below under Case parameters identification. A best-fit is done in this case in order to calculate them. The data must be provided in engineering strains from an 1-D experiment. The lateral deflection should not be limited by the experiment.

The Ogden formulation of Type 3 is not yet tested in detail. First tests show a shrinkage of the material under initially unloaded conditions. This is physically not possible. It is strongly recommended not to use this material type.

The material law uses total strains. These strains are sometimes not correct when large rotations occur.


Syntax:

Case 1 : TYPE = 1.
         "HYPE"
         "TYPE"     1
         "RO"       rho
         "CO1"      c1
           .        .
           .        .
         "CO14"     c14
         "BULK"     K
        /LECTURE/

rho

Density.
CO1

First coefficient of the potential
CO14

14st coefficient of the potential
K

Compressibility coefficient, if 0.0 incompressible material is considered
LECTURE

List of the concerned elements.

Case 2 : TYPE = 2.
         "HYPE"
         "TYPE"     2
         "RO"       rho
         "CO1"      c1
         "CO2"      c2
         "CO3"      c3
         "BULK"     K
         /LECTURE/
rho

Density.
CO1

First coefficient of the potential (=A)
CO2

Second coefficient of the potential (=B)
CO3

Third coefficient of the potential (=C)
K

Compressibility coefficient
LECTURE

List of the concerned elements.

Case 3 : TYPE = 3.
        "HYPE"
        "TYPE"     3
        "RO"       rho
        "CO1"      c1
        "CO2"      c2
        "CO3"      c3
        "CO4"      c4
        "CO5"      c5
        "CO6"      c6
        "CO7"      c7
        "CO8"      c8
        "CO9"      c9
        "CO10"     c10
        "CO11"     c11
        "CO12"     c12
        "BULK"     K
        /LECTURE/
rho

Density
CO1,CO2,CO3,CO4

Alpha coefficients of the potential (αp)
CO5,CO6,CO7,CO8

Mu coefficients of the potential (mup)
CO9,CO10,CO11,CO12

(1/D) coefficient of the potential (compressible contribution)
LECTURE

List of the concerned elements.

Case 4 : TYPE = 4.
        "HYPE"
        "TYPE"     4
        "RO"       rho
        "CO1"      c1
        "CO2"      c2
        "CO3"      c3
        "CO4"      c4
        "CO5"      c5
        "CO6"      c6
        "CO7"      c7
        "CO8"      c8
        "BULK"     K
        /LECTURE/
rho

Density
CO1,CO2,CO3,CO4

Alpha coefficients of the potential (αp)
CO5,CO6,CO7,CO8

Mu coefficients of the potential (µp)
LECTURE

List of the concerned elements.

Case 5 : TYPE = 5.
        "HYPE"
        "TYPE"     5
        "RO"       rho
        "CO1"      c1
        "CO2"      c2
        "CO3"      c3
        "CO4"      c4
        "CO5"      c5
        "CO6"      c6
        "CO7"      c7
        "CO8"      c8
        "CO9"      c9
        "CO10"     c10
        "CO11"     c11
        "CO12"     c12
        /LECTURE/
rho

Density
CO1,CO2,CO3,CO4

Alpha coefficients of the potential (αp)
CO5,CO6,CO7,CO8

Mu coefficients of the potential (µp)
CO9,CO10,CO11,CO12

Beta coefficients of the potential (βp)
LECTURE

List of the concerned elements.

Case parameters identification : TYPE = 1, 3, 4 or 5.

This case is recognized by the presennce of the PCAL keyword in the input data, as shown below.

         "HYPE"
         "TYPE"   [1|3|4|5]
         <"BULK"  k>
         <"NU"    nu>
         "PCAL"   npar
         "TRAC"   npts * (strain stress)
k

Compressibility coefficient (not used for Type 5).
nu

Poisson’s ratio (only used for Type 5).
npar

Number of parameters that should be calculated (i.e. between 1 and 4).
npts

Number of (strain, stress) couples of values given.

The type and the number of elements is irrelevant since only the material is called. (However, note that at least one element must be defined in order to run the code.) Four different models are possible: for the Mooney-Rivlin material a two-parameter model is included (CO1 and CO2); for the Ogden material a six-parameter model is included neglecting the influence of the D parameter and for the Ogden New model a six parameter model is included.

Note that as soon as the code encounters the TRAC keyword in the above syntax it reads the traction curve, then performs the parameters calibration and stops. Therefore, any parameters given after the TRAC subdirective are simply ignored. This means that if values should be set for the optional keywors BULK or NU, they must be entered before and not after the TRAC subdirective, as indicated in the syntax above.

For this reason, the usual /LECT/ at the end of the material directive is not included in the syntax (since it would not be interpreted anyway).


Range of validity

Note that the range of validity of the hyperelastic material models is as follows:


Outputs:

The components of the ECR table are as follows:

ECR(1): Pressure

ECR(2): Von Mises Stress

ECR(3): Normal transverse strain (shell elements) or tangential stiffness (solid elements)

ECR(4): Updated thickness (shell elements)

ECR(5): Initial thickness (shell elements) or initial volume (solid elements)

ECR(6): Energy potential

ECR(7): Maximum time step for the element

7.6.55  MINT: MATERIAL FOR INTERFACE ELEMENT

C.262


Object:

This directive allows to choose the material applied to interface elements. Thus, it can only be used with interface elements INT4 (2D quadrilateral), INT6 (3D triangular prism) and INT8 (3D hexahedron). The combination of such elements and material MINT forms a cohesive zone model, suitable to solve problems like delamination and debonding.
Only TYPE 2 material is functional. Three damage laws could be chosen with material TYPE 2: exponential, linear or Cachan interface meso-model.


References:

For the Cachan interface damage meso-model:

The implementation of material TYPE 2 is explained in [854].


Syntax:

"MINT" "TYPE" 2
        "CO1" co1 "CO2" co2 "CO3" co3
        "CO4" co4 "CO5" co5 "CO6" co6
        "CO7" co7 "CO8" co8 "CO9" co9
        "CO10" co10 "CO11" co11 "CO12" co12
        /LECTURE/
co1

Young’s modulus along direction 3.
co2

Shear modulus between direction 1 and 3.
co3

Shear modulus between direction 2 and 3.
co4

Critical release rate in mode 1.
co5

Critical release rate in mode 2.
co6

Critical release rate in mode 3.
co7

Power coefficient to couple the thermodynamic forces of the three modes.
co8

Thermodynamical force threshold for damage. Required for the linear damage law. Optional for the Cachan interface meso-model.
co9

Exponent n for the Cachan interface meso-model.
co10

Delay effect : parameter τ (optional).
co11

Delay effect : parameter a (optional).
co12

Maximum damage (optional, default value = 1.0).
LECTURE

List of the concerned elements.

Comments:

When damage reaches the maximum damage value co12, element stiffness becomes null. Erosion algorithm is activated with EROS keyword (see page A.30, Section 4.4).


Outputs:

The components of the ECR table are as follows:

ecr(1): Damage

ecr(2): Equivalent thermodynamic force

ecr(3): Time at which damage reaches 1.0 for failed elements

7.6.56  THE SL-ZA MODEL

C.263


Object:


This directive enables to choose the SLZA model which is an extension of both STEINBERG LUND and ZERILLI ARMSTRONG models. This model uses an expression for the internal stress that comes from the ZA model and an expression of the effective stress that comes from SL model.



Syntax:

"SLZA" "RO" rho   "YOUN" young   "NU" nu    "SIGE" sige
       "YA" ya    "YMAX" ymax    "YP" yp    "ER"   er
       "N"  n     "C1"   c1      "UK" uk    "CP"   cp
       "TM" tm    "T0"   t0      "BETA" beta
       /LECTURE/
rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
sige

Elastic limit at ambient temperature.
ya

Coeffiecient of the CEA SL-ZA model.
ymax

Coefficient of the CEA SL-ZA model.
yp

Coefficient of the CEA SL-ZA model.
er

Coefficient of the CEA SL-ZA model.
n

Coefficient of the CEA SL-ZA model.
c1

Coefficient of the CEA SL-ZA model.
uk

Coefficient of the CEA SL-ZA model.
cp

Heat capacity per unit mass of the solid.
tm

Melting temperature of the solid.
t0

Initial temperature of the solid.
beta

Taylor and Quiney coefficient.
LECTURE

List of the elements concerned.

Comments:


The expression of the elastic limit is given by:


yd=(ya+(ymaxya)((1−exp(−ep/er))n)) +yp(1−√kt/2uklog(c1/ė))


where k is the Boltzmann constant and ė is the strain rate.


Outputs:


The components of the ECR table are as follows:

ecr(1) : Hydrostatic pressure

ecr(2) : Von mises stress

ecr(3) : Equivalent plastic strain

ecr(4) = Increment of temperature

ecr(5) = Elastic limit

ecr(6) = Total strain at the last timestep

ecr(7) = Time of the last call of the element

ecr(8) = Equivalent strain rate

7.6.57  RTM composite material

C.264


Object:


This directive allows to chose a composite material made by a RTM process. The behavior is orthotropic and the 9 independant coefficents can defined by using abaques of 3 or 4 parameters. These parameters are the volumic fraction, the angle between warp and weft directions and the warp and weft ratio. The 4th parameter is the temperature which can be optionnal.


Syntax:

  "CRTM"
     "RO" rho
     "NTEM" ntem  "NVF" nvf  "NANG"  nang  "NRCT" nrct
     "PTEM" ptem  "PVF" pvf  "PANG"  pang  "PRCT" prct
        "E11" ne11
          PAR1 val-par1-1   PAR2 val-par2-1     PAR3 val-par3-1
              TABLE nval-par4
                       nval-par4 *(E11 PAR4)
        PAR1 val-par1-1 PAR2 val-par2-1   PAR3 val-par3-2
            TABL nval-par4
                       nval-par4*(E11 , PAR4)
       ...  then loop on PARA3, then PAR2 and PARA1.

        "E22" ne22
            -idem-

        "E33" ne33
            -idem-

        "G12" ng12
            -idem-

        "G13" ng13
            -idem-

        "G23" ng23
            -idem-

        "NU12" nnu12
            -idem-

        "NU13" nnu13
            -idem-

        "NU23" nnu23
            -idem-

                           /LECTURE/


rho

Density of the material.
ntem

Number of values of temperature
nvf

Number of values of volumic fraction
nang

Number of values of angle between warp and weft
nrct

Number of values of ratio between warp and weft
ptem

Number of the temperature parameter
pvf

Number of the volumic fraction parameter
pang

Number of the angle parameter
prct

Number of the ratio between warp and weft parameter
ne11

Number of the abaque for E11
val-par1-1

First value of the parameter 1
val-par2-1

First value of the parameter 2
val-par3-1

First value of the parameter 3
val-par3-2

Second value of the parameter 3
nval-par4

Number of values of parameter 4
LECTURE

List of the elements concerned.

Comments:


1/ - It is possible to suppress the temperature dependant. In this case, one can use 3 parameters (from 1 to 3).


2/ - By defining ptem, prct, pang and pvf, it is possible to declare that temperature is parameter 1, volumic fraction is parameter 2 and any combination the user likes. It permits to use as general as possible an abaque of 4 parameters.


3/ - The values of angle, volumic fraction and ration between warp and weft have to be define by using the directive RTMANG, RTMVF and RTMRCT (page C63). The temperature is defined as initial values (command INIT TETA page E80).


Outputs:


The components of the ECR table are as follows:

ECR(1) : pressure

ECR(2) : Von mises criterion

ECR(3) : modulus E11

ECR(4) : modulus E22

ECR(5) : modulus E33

ECR(6) : modulus G12

ECR(7) : modulus G13

ECR(8) : modulus G23

ECR(9) : Poisson coefficient NU12

ECR(10) : Poisson coefficient NU13

ECR(11) : Poisson coefficient NU23

7.6.58  TVMC (LOI ELASTOPLASTIQUE POUR COMPOSITES)

C.270


Object:

Ce materiau permet de modeliser le comportement elastoplastique endommageable de composites a fibres courtes.

C’est le cas par exemple des composites injectes de type thermoplastique charge de fibres (verre, carbone, ...) comme ULTEM 2100, ou encore des compositesSMC-R de type polyester charge de fibres (verre, carbone).


Cette loi est utilisable pour les elements volumiques. Elle se decompose en trois etapes :

- homogeneisation micro-mecanique,

- endommagement,

- plasticite couplee a l’endommagement.


Syntax:
  "TVMC"  "ROF" rhof  "ROM" rhom  "TAUX" taux  "EM"  em  "NUM"  num ...
     ...  "EF"  ef    "NUF" nuf   "R"    rap   "TVF" tvf "TE"   te  ...
     ...  "PH"  ph    "NF"  nf    "Y1C"  y1c   "Y2C" y2c "CRIT" choix  ...
     ...  "NFD1"  n1  "NFD2"  n2  "NFR"  n3    /LECTURE/
rhof

Masse volumique de la fibre.
rhom

Masse volumique de la resine (chargee ou non chargee).
taux

Taux de porosite.
em

Module d’Young de la matrice.
num

Coefficient de Poisson de la matrice.
ef

Module d’Young de la fibre.
nuf

Coefficient de Poisson de la fibre.
rap

Rapport de forme de la fibre (longueur sur diametre).
tvf

Taux volumique de fibres.
te

Orientation dans le plan de la fibre (inutilise ici).
ph

Orientation hors plan de la fibre (inutilise ici).
nf

Nombre d’orientations de fibres dans le plan.
y1c

Taux de restitution limite de la matrice en traction.
y2c

Taux de restitution limite de la matrice en cisaillement.
choix

Numero du critere definissant la forme de la surface de charge.
n1

Numero de la fonction definissant l’endommagement en traction-compression en X et Y .
n2

Numero de la fonction definissant l’endommagement en cisaillement.
n3

Numero de la fonction definissant la courbe de plasticite a ecrouissage isotrope.
LECTURE

List of the elements concerned.

Comments:

Le parametre "CRIT" peut prendre l’une des 4 valeurs suivantes :

1 = VON MISES,

2 = TRESCA,

3 = TSAI-HILL (en σ1 et σ4),

4 = TSAI-HILL (en σ1, σ2 et σ4),


Outputs:

The components of the ECR table are as follows:

ECR(1): pression hydrostatique,

ECR(2): Y1 = taux de restitution d’energie en traction,

ECR(3): Y2 = taux de restitution d’energie en cisaillement,

ECR(4): D1 = endommagement en traction,

ECR(5): D2 = endommagement en cisaillement,

ECR(6): deformation plastique cumulee,

ECR(7) : limite elastique courante,

ECR(8:10): inusites,

ECR(11): vitesse du son locale (pour la stabilite).

7.6.59  HILL MATERIAL MODEL

C.275


Object:


This directive enables to choose the HILL model which is a model with isotropic plasticity associated with a HILL criterion. The elastic behaviour of the material can be orthotropic.


Syntax:

"HILL" "RO" rho   "YG1" yg1   "YG2" yg2    "YG3" yg3
                  "G12" g12   "G13" g13    "G23" g23
            "NU12" nu12   "NU13" nu13    "NU23" nu23
                  "XT1" xt1   "XT2" xt2    "XT3" xt3
            "RST1" rst1   "RST2" rst2    "RST3" rst3
  "TRAC"  npts*( sig  eps )  /LECTURE/

       /LECTURE/
rho

Density of the material.
yg1

Young’s modulus - direction 1
yg2

Young’s modulus - direction 2
yg3

Young’s modulus - direction 3
g12

shear modulus - plane 12
g23

shear modulus - plane 23
g13

shear modulus - plane 13
nu12

shear modulus - plane 12
nu23

shear modulus - plane 23
nu13

shear modulus - plane 13
xt1

yield stress - direction 1
xt2

yield stress - direction 2
xt3

yield stress - direction 3
rst1

yield stress - plane 12
rst2

yield stress - plane 23
rst3

yield stress - plane 13
"TRAC"

This key-word introduces the yield curve.
npts

Number of points (except the origin) defining the yield curve.
sig

normalised stress.
eps

Equivalent plastic strain. Note that the first point must be always (1., 0.)
LECTURE

List of the elements concerned.

Outputs:


The components of the ECR table are as follows:

ecr(1) : Hydrostatic pressure

ecr(2) : Von Mises stress

ecr(3) : Equivalent plastic strain

ecr(7) : New elastic limit

7.6.60  GLASS MATERIAL

C.280


Object:


This option enables to choose a material that considers the strain rate effect of glass. A linear elastic material is used up to the failure. The failure limit PSAR uses the area under the stress-time curve (equivalent constant stress).


Syntax:

    "GLAS"  "RO" rho  "YOUN" young  "NU" nu  "CORR" corr
            "FAIL" $[ VMIS ; PEPS ; PRES ; PEPR; PSAR ]$ "LIMI" limit


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
corr

Stress corrosion fraction. Default value is 16.
FAIL

Introduces an element failure model, represented by a failure criterion and a by failure limit value. The available failure criteria are: VMIS for a criterion based upon Von Mises stress (isotropic criterion), PEPS for a criterion based upon the principal strain (see caveat below), PRES for a criterion based upon the hydrostatic stress, PEPR for a criterion based upon the principal strain if the hydrostatic stress is positive (traction): if the hydrostatic stress is negative (compression) there is no failure. PSAR for a criterion based upon equivalent constant stress of the duration of 60 s.
limit

Indicates the failure limit for the chosen criterion.

Comments:


When using a failure criterion based upon the principal strains (PEPS or PEPR) be aware that the criterion is based upon the cumulated strains. These are usually a good approximation of the total strains for elements using a convected reference frame for the stresses and strains (such as e.g. plate, shell or bar elements). The approximation is likely to be very bad, instead, for continuum-like elements, at least when there are large rotations.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3) Area under the (principal stress to the power of CORR)-time curve, the stress is dived by 1.E6 to avoid too big numbers.

ECR(4): equivalent constant stress of the duration 60 s.

ECR(5): sound speed

7.6.61  BL3S: REINFORCED CONCRETE LAW FOR DEM

C.285


Object:


This material law prescribes properties of the reinforced concrete for structures modeled with the discrete element method (DEM) via ELDI elements. Usually, both steel and concrete phases are present. Nevertheless, they may be used separately, i.e. it is possible to use only one material phase, either concrete or steel.

This model was first developed in J.Rousseau’s PhD thesis then reviewed and further developed in A.Masurel’s PhD thesis, with EDF financial support and collaboration with 3S-R Laboratory (Grenoble). For theoretical description of the laws see [873], [886].


Syntax:

  "BL3S" |[ "BETON"  "RO"   rho   "YOUN" youn  "NU"   nu
                     "T"    tens  "CO"   cohe  "PHII" phii
                     "PHIC" phic  "ADOU" adou
                   < "ALPH" alpha "BETA" beta  "GAMM" gamma >
                   < "CNEL" cnel  "CNPL" cnpl  "YUNL" yunl
                     "XI1"  xi1   "XI2"  xi2 >
                   < "ETA"  eta >
                   < "EPS1" eps1  "EPS2" eps2  "SIGC" sigc "DET2" det2
                     "FCUT" fcut >

          < "BIMA"   "YOUN" youn  "NU"   nu    "TN"   tn
                     "CN"   cn    "TE"   te    "TMAX" tmax
                     "UMAX" dmax  "PHII" phii  "PHIC" phic  >
                     /LECTURE/ ;

          < "ACIER"  "RO"   rho   "YOUN" youn  "NU"   nu
                     "T"    tens  "ECRO" sigmr "AMAX" amax
            < "BIMA" "YOUN" youn  "NU"   nu    "TN"   tn
                     "CN"   cn    "TE"   te    "TMAX" tmax
                     "UMAX" dmax  "PHII" phii  "PHIC" phic  >
                                                              >
                     /LECTURE/
         ]|

Parameters for concrete (BETON):


rho

Density of the material
youn

Young’s modulus
nu

Poisson’s ratio
tens

Maximum tensile strength (T > 0).
cohe

Cohesion
phii

Internal friction angle
phic

Contact friction angle
adou

Softening coefficient (ratio between elastic and softening slopes >0)
alpha

1st parameter for micro-macro relations K=f(E,nu,alpha,beta,gamma). The default value is 3.9 (see [879]).
beta

2nd parameter for micro-macro relations K=f(E,nu,alpha,beta,gamma). The default value is 3.03125 (see [879]).
gamma

3rd parameter for micro-macro relations K=f(E,nu,alpha,beta,gamma). The default value is 4.8115 (see [879]).
cnel

Local elastic compression limit
cnpl

Local plastic compression limit
yunl

Young’s modulus for compression unload
xi1

Softening in compression
xi2

Hardening in compression
eta

Reduced damping coefficient on concrete cohesive links if needed
eps1

First limit of the strain rate effect (under EPS1 the behavior of concrete is considered as quasi-static)
eps2

Second limit of the strain rate effect formula
sigc

Static compressive strength used to calculate the first delta exponent of the strain rate effect law (first range)
det2

Second exponent of the strain rate effect law (second range)
cfil

Cut-off frequency for the filter applied on the strain rate
LECTURE

List of the elements concerned.

Parameters for steel (ACIER):
rho

Density of the material
youn

Young’s modulus
nu

Poisson’s ratio
tens

Maximum elastic stress (T > 0).
sigmr

Maximum stress for steel
amax

Maximum allongation (%)
LECTURE

List of the elements concerned.

Parameters for steel-concrete interface (BIMA):
youn

Young’s modulus
nu

Poisson’s ratio
tn

Maximum normal tensile strength (perpendicular to the steel bar)
cn

Maximum normal compression strength (perpendicular to the steel bar)
te

Elastic limit in the tangential direction
tmax

Maximum strenght in the tangential direction
dmax

Coefficient to define maximum tangential sliding (umax=dmax*uglis)
phii

Internal friction angle
phic

Contact friction angle
LECTURE

List of the elements concerned.

Comments:


If only concrete is modeled through the discrete element formulation, the sequence open by BETON keyword should be used only. In this case, reinforcement is modeled by the beam finite element model and steel-concrete links are defined by ACBE link model.

If both the concrete and the reinforcement are modeled by discrete elements, theer properties must be defined separately (keywords BETON and ACIER respectively), and it is necessary to define also a specific behavior for the steel-concrete interface. This can be done by using a sequence of parametres introduced by the BIMA option. This option should be used only once, either with BETON or ACIER definition. If the sequence BIMA is not specified, the steel-concrete interface behaves as a concrete without taking into account the main direction of the reinforcement.

Don’t forget to use directive ARMA in CELDI to declare the steel discrete elements. ARMA calculates the main direction of the reinforcement needed to define normal and tangential forces for the BIMA links.


Outputs:


In the discrete element calculation BL3S material is used for the links. However, for post-processing purpose the number of active links and the degree of damage are reported onto the discrete elements.

The components of the ECR table are as follows:

ECR(1): number of COHE-type links per element at t=t0

ECR(2): number of BIMA-type links per element at t=t0

ECR(3): number of COHE-type links per element at tt0

ECR(4): number of BIMA-type links per element at tt0

ECR(5): degree of damage of COHE-type links per element

ECR(6): degree of damage of BIMA-type links per element

ECR(7): diameter of the discrete element.

7.6.62  LAMINATED SECURITY GLASS MATERIAL

C.290


Object:


This option enables to choose a material that considers laminated security glass. A linear elastic material is used up to the failure. After the failure, the material can react to compression but not more to tension. This material is recommended with a sandwich structure, where the interlayer can be built up with a elastoplastic material.


Syntax:

    "LSGL"  "RO" rho  "YOUN" young  "NU" nu  <"CORR" corr>
            <"FAIL" $[ VMIS ; PEPS ; PRES ; PEPR; PSAR ]$ "LIMI" limit>
            <"CR2D"> <"NEIG"> <"REDU" redu>


rho

Density of the material.
young

Young’s modulus.
nu

Poisson’s ratio.
corr

Stress corrosion fraction. Default value is 16. This value is only used by the failure criterion PASR. See following reference: Beason, W. Lynn, Morgan, James R.: Glass failure prediction model. Journal of Structural Engineering, 110 (2), pp. 197-212, 1984.
FAIL

Introduces an element failure model, represented by a failure criterion and a by failure limit value. The available failure criteria are: VMIS for a criterion based upon Von Mises stress (isotropic criterion), PEPS for a criterion based upon the principal strain (see caveat below), PRES for a criterion based upon the hydrostatic stress, PEPR for a criterion based upon the principal strain if the hydrostatic stress is positive (traction): if the hydrostatic stress is negative (compression) there is no failure. PSAR for a criterion based upon equivalent constant stress of the duration of 60 s.
limit

Indicates the failure limit for the chosen criterion.
CR2D

Introduces two-dimensional cracks, which means that the direction of the principle stress or strain is used to introduce a first crack. This crack is implemented in such a way that only the stresses normal to the crack direction are set to 0 (in the case of tension). If the failure criterion is reached for the direction parallel to the crack, then the integration point fails in both directions.
NEIG

If this material is used for 3D calculations, the glass part of the model should mainly eroded after the erosion of the interlayer. By using the keyword NEIG erosion of an element of the LSGL material is only taken into account, if a neighbour element (e.g. interlayer of another LSGL element) is already eroded.
redu

In case of hydrostatic tension, the stresses are set to 0. Using keyword REDU the decreasing of the stresses can be smoothed. The tension stresses are multiplied with the value redu, which should be less than 1.0. Default value for redu is 0.0.

Comments:


When using a failure criterion based upon the principal strains (PEPS or PEPR) be aware that the criterion is based upon the cumulated strains. These are usually a good approximation of the total strains for elements using a convected reference frame for the stresses and strains (such as e.g. plate, shell or bar elements). The approximation is likely to be very bad, instead, for continuum-like elements, at least when there are large rotations.

The material should only be used with shell elements. The third component of the stresses and strains is neglected in the calculation of the failure criterion.


Outputs:


The components of the ECR table are as follows:

ECR(1): current hydrostatic pressure

ECR(2): current equivalent stress (Von Mises)

ECR(3) Area under the (principal stress to the power of CORR)-time curve, the stress is dived by 1.E6 to avoid too big numbers.

ECR(4): equivalent constant stress of the duration 60 s.

ECR(5): sound speed

ECR(6): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)

ECR(7): angle of failure

ECR(8): status of the spalling: 0 no failure of the g.p.; -1 g.p. under compression; +1 g.p. under tension.


Note that in order to post-process the total strains (which were formerly inappropriately stored in the ECR table for JRC materials) one has to use the EPST table related to the element (like for CEA elements).

7.6.63  SMAZ: MAZARS-LINEAR ELASTIC LAW WITH DAMAGE FOR SPHC ELEMENTS

C.291


Object:

Isotropic linear elastic with Mazars damage for SPHC elements.


References:

1- Jacky MAZARS, "Application de la mécanique de l’endommagement au comportement non linéaire et à la rupture du béton de structure", Thèse de doctorat, Université Pierre et Marie Curie - Paris 6, 1984.


Syntax:
   "SMAZ" "RO"   rho  "YOUN" young  "NU"   nu   "EPSD" epsd
          "DCRI" dcri "A"    a      "B"    b
          "TAUC" tauc "CSTA" csta                          /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
epsd

Initial strain threshold.
dcri

Critical value of damage (=1 per default).
a

Parameter A of the tension law (asymptote of the curve stress-strain)
b

Parameter B of the tension law (shape of the curve stress-strain)
tauc

Characteristic time for delay-damage
csta

Parameter of the delay-damage (=1 per default)

Outputs:

The components of the ECR table are as follows:

ECR(1) : Pressure
ECR(2) : Von Mises criterion
ECR(3) : Equivalent strain
ECR(4) : Failure state (0: no failure, 1: failed)

7.6.64  SLIN: LINEAR ELASTIC LAW WITH DAMAGE FOR SPHC ELEMENTS

C.292


Object:

Isotropic linear elastic with damage for SPHC elements.


Syntax:
   "SLIN" "RO"   rho  "YOUN" young  "NU"   nu   "EPSD" epsd
          "DCRI" dcri "EPSR" epsr
          "TAUC" tauc "CSTA" csta                          /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s ratio.
epsd

Initial strain threshold.
dcri

Critical value of damage (=1 per default).
epsr

Maximum strain before failure.
tauc

Characteristic time for delay-damage
csta

Parameter of the delay-damage (=1 per default)

Outputs:

The components of the ECR table are as follows:

ECR(1) : Pressure
ECR(2) : Von Mises criterion
ECR(3) : Equivalent strain
ECR(4) : Failure state (0: no failure, 1: failed)

7.6.65  JCLM

C.293


Object :

This directive allows to describe the behaviour of an elasto-plastic material that may undego some damage, according to the Lemaitre model. There is coupling between damage and plasticity, represented by the Johnson-Cook model. The damage evolution rate is a function of the triaxiality ratio of stresses and of the equivalent plastic strain rate. A failure criterion is impicitly contained within the model: rupture occurs when the damage exceeds a critical value. Two optional parameters allow to introduce a limitation of the damage rate (thanks to the delayed damage model) in order to avoid the mesh dependency.


Syntax:
    "JCLM"  "RO" rho "YOUN" young "NU" nu
            "EPSD" epsd  "S0" s0  "DC" dc
            <"CSTA" csta "TAUC" tauc "NOCO" noco>
            "COA1" coa1 "COA2" coa2
            "CLB1" clb1 "CLB2" clb2 "SRRF" srrf /LECTURE/
rho

Density.
young

Young’s modulus.
nu

Poisson’s coefficient.
epsd

Damage threshold (i.e. equivalent plastic strain, weighted by a function of stress triaxiality, within which damage vanishes).
s0

Parameter driving the damage evolution rate.
dc

Critical damage defining the rupture criterion.
csta

Parameter of the delayed damage model
tauc

Characteristic time of the delayed damage model. (1/tauc) represents the maximum damage rate.
noco

Optional parameter indicating what to do when no convergence is reached in the material routine. The value 0 is the default and means that an error message is issued and the calculation is stopped. The value 1 indicates that the element (or more precisely, the element’s current Gauss point) is made to fail (eroded).
coa1

1st constant in the Johnson-Cook model.
coa2

2nd constant in the Johnson-Cook model.
clb1

3rd constant in the Johnson-Cook model.
clb2

Hardening coefficient of the Johnson-Cook model.
srrf

Reference strain rate of the Johnson-Cook model.
LECTURE

List of concerned elements.

Comments:

A detailed description of the damage model can be found in the report DMT/98-026A, available on request.

The implementation of the Johnson-Cook model is described in reference [167].


This material is currently restricted to SPHC elements.


Outputs:

The components ov the ECR table are as follows for Continuum elements:

ECR(1) : pressure

ECR(2) : Von Mises criterion

ECR(3) : equivalent plastic strain

ECR(4) : plasticity multiplier

ECR(5) : damage

ECR(7) : new elastic limit

When the “erosion” algorithm is activated (see page A.30, Section 4.4, keyword FAIL), an element is considered as failed if damage >= dc.

7.6.66  VPJC

C.294


Object :

This directive allows to define a Von Mises elasto-thermo-viscoplastic material with non-linear isotropic hardening governed by a modified Johnson-Cook model with explicit elastic predictor and return mapping algorithm, a Voce saturation type of hardening and a Cockcroft-Latham failure criterion. See report [372] for full details. It can be used in 3D, 2D plane strain, 2D plane stress or 2D axisymmetric cases. This material model was developed at NTNU (Trondheim, Norway).


The original Johnson-Cook model was first introduced in: G. R. Johnson and W. H. Cook. A constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures. Proceedings of the 7th International Symposium on Ballistics, Hague (1983), 541–547.


The so-called “modified” Johnson Cook material law, in which the strain-rate sensitivity term is adjusted so as to avoid non-physical softening, was introduced in: M. Ortiz and G. T. Camacho. Adaptive Lagrangian modelling of ballistic penetration metallic targets. Computer Methods in Applied Mechanics and Engineering 142 (1997), 269–301. See also: T. Børvik, O. S. Hopperstad, T. Berstad, M. Langseth. A computational model of viscoplasticity and ductile damage for impact and penetration. Eur. J. Mech. A/Solids 20 (2001), 685-712.


The Voce saturation type of hardening was proposed in: E. Voce. The relationship between stress and strain for homogeneous deformation. Journal of the Institute for Metals 74 (1948), 536–562.


The expression of the constitutive law is the following:

σy = 
A + Q1 
1 − eC1 p
+ Q2 
1 − eC2 p


1 + ṗ* 
C
1 − T*m 
    (9)

and is the product of three factors (from left to right): a strain hardening term (in square brackets), a strain-rate hardening term and a temperature softening term. The symbols indicate the following:


Temperature softening

The last term of the above equation accounts for the thermal softening of the yield stress at elevated temperatures. However, the evolution of the temperature remains to be established. The heat transfer is modelled by assuming adiabatic conditions. This implies that there is no heat transfer into or out of the system during plastic straining. The plastic energy dissipation Dp per unit volume in the form of heat (Watt per cubic meter) is given by:

Dp = χσeqṗ=ρ CTṪ     (10)

where:

From the above expression, the temperature rate Ṫ is obtained:

Ṫ = 
Dp
ρ CT
 = 
χ σeq ṗ
ρ CT
    (11)

and then this value is integrated in time at each Gauss point to obtain the current temperature at the point. The initial temperature is set to the room temperature Tr at each Gauss point. If during the calculation the temperature at a Gauss point reaches the melting temperature Tm, the Gauss point fails.


Gauss point failure and element erosion

The Cockcroft-Latham fracture criterion based on plastic work per unit volume is assumed. See: M. G. Cockcroft and D. J. Latham. Ductility and the workability of metals. Journal of the Institute of Metals 96 (1968), 33–39.

Material failure takes place at a Gauss point when a damage parameter D reaches the damage threshold Dc. The Dc parameter should be set by the user (see DC keyword below) such that 0<Dc≤ 1. The value 1 should be used when not considering damage softening. The damage is computed according to the following expression:

D = 
W
Wc
=
1
Wc
p


0
 ⟨σ1⟩ dp     (12)

where:

An element’s Gauss point is considered as failed if DDc, i.e. if the damage reaches the chosen threshold. If the “erosion” algorithm is activated (see GBA_0030, keyword EROS), an element is eroded as soon as a chosen fraction (see ldam parameter of the EROS keyword) of its Gauss points reach failure.


Syntax:
    "VPJC"  "RO" rho "YOUN" young "NU" nu "ELAS" elas
           <"TOL" tol "MXIT" mxit>
            "QR1" qr1 "CR1" cr1 "QR2" qr2 "CR2" cr2
            "PDOT" pdot "C" c
            "TQ" tq "CP" cp <"TR" tr> "TM" tm "M" m
            "DC" dc "WC" wc
           <"SOLU" solu> <"DEBU" debu> <"RESI" resi>
            /LECTURE/
rho

Density ρ. Typically in kg/m3.
young

Young’s modulus E. Typically in Pa.
nu

Poisson’s coefficient ν. Dimensionless.
elas

Initial yield stress (indicated as A above, or sometimes as σ0). Typically in Pa.
tol

Tolerance for Newton-Raphson internal iterations. Dimensionless. The default is 10−5.
mxit

Maximum number of Newton-Raphson internal iterations. The default is 50.
qr1

Material constant Q1, asymptote of the first Voce hardening term. It has the dimension of a stress, typically in Pa.
cr1

Material constant C1, hardening parameter of the first Voce hardening term. Dimensionless.
qr2

Material constant Q2, asymptote of the second Voce hardening term. It has the dimension of a stress, typically in Pa.
cr2

Material constant C2, hardening parameter of the second Voce hardening term. Dimensionless.
pdot

Reference strain rate ṗ0 for the calculation of ṗ*. Typically in s−1.
c

Material constant C, hardening parameter (exponent) of the viscous term. Dimensionless. By setting C=0 one can model a quasi-static test, in which the visco-plasticity effect is not included.
tq

Taylor-Quinney coefficient χ. Dimensionless.
cp

Specific heat capacity of the solid material CT. Typically in J/(kg·K).
tr

Room temperature Tr in K for the calculation of T*. The default is 293 K. This is also taken as the initial temperature of the material.
tm

Melting temperature Tm in K for the calculation of T*.
m

Material constant m, hardening parameter of the temperature term. Dimensionless. By using the special value m=0 the temperature softening effect is excluded from the model, i.e. the code assumes T*m=0, and therefore the temperature hardening term becomes (1−T*m)=(1−0)=1. Note also that in this case the temperature is not updated, so that it remains to the room value Tr.
dc

Upper limit Dc of the damage D when softening occurs. Dimensionless. Material failure takes place at a Gauss point when the damage parameter D reaches Dc. The Dc parameter should be set by the user such that 0<Dc≤ 1. The value 1 should be used when not considering damage softening.
wc

Failure parameter Wc of the Cockcroft-Latham failure criterion. It has the dimension of work per unit volume, i.e. [J/m3], i.e. of a stress, typically expressed in Pa. By setting Wc to a very large value the failure of the material (and the consequent element erosion, if specified by the user) can be excluded from the model.
solu

Solution algorithm. By default (or by specifying SOLU 1) a cutting plane algorithm is adopted, which requires internal Newton-Raphson iterations (up to a maximun number prescribed via MXIT). The cutting plane algorithm was originally developed for rate-independent plasticity and should be used with some care for rate-dependent plasticity models. This is due to the fact that the plastic strain rate ṗ actually increases during the iterative update scheme and reaches the correct value of ṗ only at the final iteration. The result is that the return to the dynamic yield condition F=0 occurs at strain rates that are too low. Optionally, by specifying SOLU 2, one may choose a radial return solution algorithm. The radial return method also requires internal (Newton-Raphson) iterations and is a special case of the (implicit) backward Euler return map algorithm developed for the von Mises yield criterion with the associated flow rule. In this case, the return to the yield surface from the elastic trial state is radial to the yield surface in the deviatoric (stress) plane, which significantly simplifies the algorithm and makes the algorithm exceptionally stable and accurate. Note, however, that the radial return solution algorithm cannot be used with plane stress or uniaxial stress states (but can be used in 3D, 2D axisymmetric and 2D plane strain cases).
debu

Debugging option. By default (or by specifying DEBU 0) no debugging is activated. By specifying DEBU 1, whenever the maximum number of iterations MXIT is exceeded, before stopping the complete set of input arguments to the routine is written (to machine’s precision) on the listing and on a binary file _VPJC.dat. This allows to debug the routine by reading back the data and feeding them to the material routine under debugging control. Note that activating this option will slightly slow down the execution since the complete set of input data to the routine must be stored each time the material routine is called.
resi

Optional keyword to decide waht to do when MXIT is reached without convergence. By default (or by specifying RESI 0) the code simply stops, with an error message (and stores the faulty, state if DEBU 1 has been set). By specifying RESI 1, whenever the maximum number of iterations MXIT is exceeded, the code assumes that convergence has been reached anyway and the calculation continues.
/LECT/

List of the elements concerned.

Comments:

All parameters are mandatory except TOL, MXIT and TR, which by default have the values 10−5, 50 and 293.0 K, respectively.


The various parameters can be grouped in the following classes:


Orientatively, some values of the parameters for typical materials could be as follows

The material parameters are taken from the literature. See:


Outputs:

The components of the ECR table are as follows (the name of the variable in the material routine is also given, whenever applicable):

ECR(1) : SIGMAH. Hydrostatic pressure (1/3σkk)

ECR(2) : PHI. Von Mises equivalent stress (σeq)

ECR(3) : P. Equivalent plastic strain (p)

ECR(4) : PHITRIAL. Elastic trial equivalent (von Mises) stress

ECR(5) : F. Yield function (which should be close to 0.0)

ECR(6) : R. Total hardening of the material

ECR(7) : DDLAMBDA. Change of the incremental plastic multiplier (from one time step to another)

ECR(8) : DLAMBDA. Incremental plastic multiplier

ECR(9) : NRITER. Number of iterations to obtain convergence

ECR(10) : DLAMBDA / DT. Rate of plastic multiplier increment in time

ECR(11) : D. Damage (D), i.e. fraction of voids with respect to the gross cross-sectional area

ECR(12) : Failure indicator: 1.0 = Virgin Gauss Point, 0.0 = Failed Gauss Point

ECR(13) : T. Absolute temperature (T)

ECR(14) : WE. Cockcroft-Latham damage accumulation (W)

ECR(15) : Sound speed

ECR(16) : First principal stress (σ1)

ECR(17) : Second principal stress (σ2)

ECR(18) : Third principal stress (σ3)

ECR(19) : RESNOR. Residual of the yield function, used to check convergence of the loop internal to the routine.

7.6.67  RIGI (Rigid Material)

C.295


Object :

This directive allows to define a rigid material to be associated with a rigid body. The geometrical characteristics of a rigid body are defined by using the COMP RIGI directive, see Page C.99B.


Syntax:
    "RIGI"  "RO" rho
            /LECTURE/
rho

Density ρ. Typically in kg/m3.
/LECT/

List of the elements concerned.

Comments:

All elements listed in the /LECT/ directive must belong to a rigid body declared in the COMP RIGI directive as described on Page C.99B.

The values of the density ρ is ignored by the code if the total mass, the center of gravity or the inertia tensor of the rigid body are prescribed by the user, see Page C.99B (RIGI directive) for details. However, even in this case a value for ρ must be specified in the present RIGI material for input completeness.

ECR(1) : empty at the moment.

7.6.68  DCMS (Damage in Coarsely Meshed Shells)

C.296


Object :

This directive may be used to model the onset of Damage, up to failure, in Coarsely Meshed metallic Shell (DCMS) structures. The DCMS material can only be used with shell elements, namely with elements subjected to plane stress conditions (σz=0).

For the formulation of this material see the following references:


Syntax:
    "DCMS"  "RO" rho "YOUN" young "NU" nu "ELAS" elas
            "K" k "N" n "EPSY" epsy "GF" gf
            "IMES" imes "IDAM" idam
            /LECTURE/
rho

Density ρ. Typically in kg/m3.
young

Young’s modulus E. Typically in Pa.
nu

Poisson’s coefficient ν. Dimensionless.
elas

Initial yield stress. Typically in Pa.
k

Power-law hardening coefficient.
n

Power-law hardening exponent.
n

Yield plateau strain.
gf

Fracture energy.
imes

Mesh scaling: 0 means no mesh scaling, 1 means mesh scaling.
idam

Damage coupling: 0 means no damage coupling, 1 means damage coupling.
/LECT/

List of the elements concerned.

Comments:

Blabla ...


Outputs:

The components of the ECR table are as follows (the name of the variable in the material routine is also given, whenever applicable):

ECR(1) : SIGH. Hydrostatic pressure.

ECR(2) : PHI. von Mises equivalent stress Φ.

ECR(3) : EPSP. Equivalent plastic strain єp.

ECR(4) : DAM. Damage D. The damage is limited to 0.95, that is
D=min(0.95,1−((Pu−єp)/(PuPc)).

ECR(5) : TRIAX. Triaxiality τ.

ECR(6) : YF. Yield function Yf.

ECR(7) : ITER. Number of iterations for plasticity N.

ECR(8) : ALFA. Alfa ratio α=s2/s1 where s1 is the maximum principal stress and s2 the minimum principal stress.

ECR(9) : BETA. Beta coefficient β=(2α−1)/(2−α).

ECR(10) : THICK. Element thickness t.

ECR(11) : SQRT(SAREA). Equivalent element length Le=√A.

ECR(12) : THICK/SQRT(SAREA). Thickness/length ratio t/Le.

ECR(13) : HSV(10). Integration point has reached BWH (Bressan, Williams, Hill) instability (0=no, 1=yes).

ECR(14) : PC. Plastic strain when BWH instability is reached Pc.

ECR(15) : PU. Plastic strain at element failure Pu.

ECR(16) : SIG1. First (maximum) principal stress s1 of the plane stress state.

ECR(17) : SIG2. Second (minimum) principal stress s2 of the plane stress state.

7.6.69  MOONEY-RIVLIN MATERIAL

C.297


Object:


This sub-directive defines a hyperelastic material of the Mooney-Rivlin type. An incompressible Mooney-Rivlin hyperelastic material is described by:

  W = C1(
I
1−3)+C2(
I
2−3)     (13)

where W is the strain energy density function, C1 and C2 are empirically determined material constants and:

 
I
1=J−2/3I1      I1122232     (14)
 
I
2=J−4/3I2      I212λ2222λ3232λ12     (15)
  I3=J212λ22λ32     (16)

Here I1 and I2 are the first and second invariants of the unimodular component of the left Cauchy-Green deformation tensor and:

  J=det
F
1λ2λ3     (17)

with F the deformation gradient. For an incompressible material J=1.

For a compressible Mooney-Rivlin material eq. (13) becomes:

  W = C1(
I
1−3)+C2(
I
2−3)+K(lnI3)2     (18)

with K the bulk modulus and I3 is the third invariant, given by eq. (16).

The material parameters C1 and C2 can be determined by EPX itself by a best fit procedure if a 1-D experimental stress-strain curve is available (see Parameters Calibration mode below).

The range of validity of this material model is as follows:


Syntax:

Two input syntaxes are available. The first one is for the normal use of the material model, while the second one (introduced by the special keyword PCAL, for Parameters CALibration) is used to identify the material parameters.

  "MOON" $ "RO" rho    <"BULK" k> "C1" c1 "C2" c2 <"INIS" inis>
           <"GINF" ginf> <"G1" g1> <"TAU1" tau1> <"G2" g2"> <"TAU2" tau2>
                         <"G3" g3> <"TAU3" tau3> <"G4" g4"> <"TAU4" tau4>
                         <"G5" g5> <"TAU5" tau5> <"G6" g6"> <"TAU6" tau6>
                                                                /LECT/ ;
           "PCAL" npar <"BULK" k> "TRAC" npts * (strain stress)          $

Normal mode
rho

Density.
k

Compressibility coefficient. If omitted, the code takes K=0 and an incompressible material is modelled.
c1

First coefficient of the potential C1.
c2

Second coefficient of the potential C2. If C2=0, the model becomes a Neo-Hookean material.
inis

Initial stiffness (used to compute the sound speed in the material). If omitted, the code estimates it.
ginf

g. Optional viscosity-related parameter.
g1 ... g6

g1 ... g6. Optional viscosity-related parameters.
tau1 ... tau6

τ1 ... τ6. Optional viscosity-related parameters.
/LECT/

List of the concerned elements.

Parameters Calibration mode
PCAL npar

Special keyword that activates the Parameters CALibration mode. If present, the PCAL keyword must immediately follow the MOON keyword. The npar value indicates the number of parameters that should be computed (which must be 2 for this material model).
k

Compressibility coefficient. If omitted, the code takes K=0 and an incompressible material is modelled.
TRAC

Introduces the definition of the experimental traction curve. The number of points is npts and then exactly npts couples of values must be specified, which are interpreted as stress-strain pairs.

This mode is activated by the presence of the PCAL keyword immediately following the MOON keyword in the input data, as mentioned above. A best fit is performed in order to calculate the parameters. The traction curve data must be provided in engineering terms from a purely 1-D experiment (that is, lateral strains should not be restrained in the experiment.)

In this mode, the type and the number of elements is irrelevant since the material routine is called directly from the material reading procedure. Then the code computes the best fit and stops immediately. (However, note that at least one element must be defined in order to keep EPX happy.)

For this reason, the usual /LECT/ at the end of the material directive is not included in this second syntax (since it would not be interpreted anyway.)


Outputs:

The components of the ECR table are as follows:

ECR(1): Pressure.

ECR(2): Von Mises Stress.

ECR(3): Normal transverse strain (shell elements) or tangential stiffness (solid elements).

ECR(4): Updated thickness (shell elements).

ECR(5): Initial thickness (shell elements) or initial volume (solid elements).

ECR(6): Energy potential.

ECR(7): Maximum time step for the element.

ECR(8-35): Unused.

7.6.70  OGDEN MATERIAL

C.298


Object:


This sub-directive defines a hyperelastic material of the Ogden type. The expression of the strain energy density is one of the following expressions:

  Type 1     W = 
N
p=1
 
µp
αp

λ1p + λ2p + λ3p −3 
K(J−1−lnJ)     (19)
  Type 2     W = 
N
p=1
 
p
αp2

λ1p + λ2p + λ3p −3 
K(J−1−lnJ)     (20)

where λ*J−1/3, K is the bulk modulus, µp and αp are material parameters. The present implementation can go up to 4 terms (N=4) plus the volumetric one if K≠ 0 in the expression of the potential W. At least the first term (α1, µ1) must be defined. The first form eq. (19) is the classical one, the second form eq. (20) is the one found in some codes, e.g. Abaqus.

The material parameters αp and µp can be determined by EPX itself by a best fit procedure if a 1-D experimental stress-strain curve is available (see Parameters Calibration mode below).

Note that the range of validity of this material model is :


Syntax:

Two input syntaxes are available. The first one is for the normal use of the material model, while the second one (introduced by the special keyword PCAL, for Parameters CALibration) is used to identify the material parameters.


Syntax
 "OGDE" $ "RO" rho    <"BULK" k>
                       "AL1" al1 <"AL2" al2> <"AL3" al3> <"AL4" al4>
                       "MU1" al1 <"MU2" al2> <"MU3" al3> <"MU4" al4>
                       <"INIS" inis> <"TYPE" type>
           <"GINF" ginf> <"G1" g1> <"TAU1" tau1> <"G2" g2"> <"TAU2" tau2>
                         <"G3" g3> <"TAU3" tau3> <"G4" g4"> <"TAU4" tau4>
                         <"G5" g5> <"TAU5" tau5> <"G6" g6"> <"TAU6" tau6>
                                                            /LECT/ ;
          "PCAL" npar <"BULK" k> "TRAC" npts * (strain stress)       $

Normal mode
rho

Density.
k

Compressibility coefficient. If omitted, the code takes K=0 and an incompressible material is modelled.
al1,al2,al3,al4

Alpha coefficients of the potential (αp). At least al1 must be specified.
mu1,mu2,mu3,mu4

Mu coefficients of the potential (µp). At least mu1 must be specified.
inis

Initial stiffness (used to compute the sound speed in the material). If omitted, the code estimates it.
type

Type of the formulation, i.e. either 1 for formula (19) or 2 for formula (20). If omitted, the code uses type 1, i.e. the classical formula.
ginf

g. Optional viscosity-related parameter.
g1 ... g6

g1 ... g6. Optional viscosity-related parameters.
tau1 ... tau6

τ1 ... τ6. Optional viscosity-related parameters.
/LECT/

List of the concerned elements.

Parameters Calibration mode
PCAL npar

Special keyword that activates the Parameters CALibration mode. If present, the PCAL keyword must immediately follow the OGDE keyword. The npar value indicates the number of parameters that should be computed (which must be between 1 and 4 for this material model).
k

Compressibility coefficient. If omitted, the code takes K=0 and an incompressible material is modelled.
TRAC

Introduces the definition of the experimental traction curve. The number of points is npts and then exactly npts couples of values must be specified, which are interpreted as stress-strain pairs.

This mode is activated by the presence of the PCAL keyword immediately following the OGDE keyword in the input data, as mentioned above. A best fit is performed in order to calculate the parameters. The traction curve data must be provided in engineering terms from a purely 1-D experiment (that is, lateral strains should not be restrained in the experiment.)

In this mode, the type and the number of elements is irrelevant since the material routine is called directly from the material reading procedure. Then the code computes the best fit and stops immediately. (However, note that at least one element must be defined in order to keep EPX happy.)

For this reason, the usual /LECT/ at the end of the material directive is not included in this second syntax (since it would not be interpreted anyway.)


Outputs:

The components of the ECR table are as follows:

ECR(1): Pressure.

ECR(2): Von Mises Stress.

ECR(3): Normal transverse strain (shell elements) or tangential stiffness (solid elements).

ECR(4): Updated thickness (shell elements),

ECR(5): Initial thickness (shell elements) or initial volume (solid elements).

ECR(6): Energy potential.

ECR(7): Maximum time step for the element.

ECR(8-35) : unused.

7.6.71  BLATZ-KO MATERIAL

C.299


Object:


This sub-directive defines a hyperelastic material of the Blatz-Ko type. This material is still under development.

  W = 
µ α
2
 


(I1−3) + β (I3−1/β−1) 


µ (1−α)
2
 


(
I2
I3
−3) + β (I31/β−1) 


    (21)

where W is the strain energy density function, α [0 ≤ α ≤ 1] a material constant, β=1−2ν/ν and being µ & ν the shear and the Poisson modulus respectively in small strains (in large strains it does not have physical sense).

  I1122232     (22)
  I212λ2222λ3232λ12     (23)
  I3=J2=
det
F
 
2

 
 = λ12λ22λ32     (24)

Here I1, I2 and I3 are the first, second and third invariants of the unimodular component of the left Cauchy-Green deformation tensor, J the Jacobian with F the deformation gradient. For an incompressible material J=1.

Note that for incompressibility (J=I3=1) the Blatz-Ko material have an similar expression as the Mooney-Riviln.

  W = 
µ α
2
 (I1−3) + 
µ (1−α)
2
 (I2−3)     (25)

The material parameters C1 and C2 can be determined by EPX itself by a best fit procedure if a 1-D experimental stress-strain curve is available (see Parameters Calibration mode below).

The range of validity of this material model is as follows:


Syntax:

Two input syntaxes are available. The first one is for the normal use of the material model, while the second one (introduced by the special keyword PCAL, for Parameters CALibration) is used to identify the material parameters.

  "BLKO" $ "RO" rho    <"ALPH" alpha> "NU" nu "MU" mu <"INIS" inis>
           <"GINF" ginf> <"G1" g1> <"TAU1" tau1> <"G2" g2"> <"TAU2" tau2>
                         <"G3" g3> <"TAU3" tau3> <"G4" g4"> <"TAU4" tau4>
                         <"G5" g5> <"TAU5" tau5> <"G6" g6"> <"TAU6" tau6>
                                                               /LECT/ ;
           "PCAL" npar <"nu" nu> "TRAC" npts * (strain stress)          $

Normal mode
rho

Density.
alpha

[ 0 ≤ α ≤ 1 ]   Material constant
nu

For small strains, Poisson modulus (ν). For large strains does not have physical sense.
mu

For small strains, Shear modulus (µ). For large strains does not have physical sense.
inis

Initial stiffness (used to compute the sound speed in the material). If omitted, the code estimates it.
ginf

g. Optional viscosity-related parameter.
g1 ... g6

g1 ... g6. Optional viscosity-related parameters.
tau1 ... tau6

τ1 ... τ6. Optional viscosity-related parameters.
/LECT/

List of the concerned elements.

Parameters Calibration mode
PCAL npar

Special keyword that activates the Parameters CALibration mode. If present, the PCAL keyword must immediately follow the MOON keyword. The npar value indicates the number of parameters that should be computed (which must be 2 for this material model).
k

Compressibility coefficient. If omitted, the code takes K=0 and an incompressible material is modelled.
TRAC

Introduces the definition of the experimental traction curve. The number of points is npts and then exactly npts couples of values must be specified, which are interpreted as stress-strain pairs.

This mode is activated by the presence of the PCAL keyword immediately following the BLKO keyword in the input data, as mentioned above. A best fit is performed in order to calculate the parameters. The traction curve data must be provided in engineering terms from a purely 1-D experiment (that is, lateral strains should not be restrained in the experiment.)

In this mode, the type and the number of elements is irrelevant since the material routine is called directly from the material reading procedure. Then the code computes the best fit and stops immediately. (However, note that at least one element must be defined in order to keep EPX happy.)

For this reason, the usual /LECT/ at the end of the material directive is not included in this second syntax (since it would not be interpreted anyway.)


Outputs:

The components of the ECR table are as follows:

ECR(1): Pressure.

ECR(2): Von Mises Stress.

ECR(3): Normal transverse strain (shell elements) or tangential stiffness (solid elements).

ECR(4): Updated thickness (shell elements).

ECR(5): Initial thickness (shell elements) or initial volume (solid elements).

ECR(6): Energy potential.

ECR(7): Maximum time step for the element.

ECR(8-35): Unused.

7.7  FLUID MATERIALS

C.300


Object:

The following directives describe fluid materials for continuum elements.


Here are the different material types:


numbernamereflaw of behaviour
34ADCR7.7.19homogeneous mixture with 3 components (1 liquid + 2 gases)
53ADCJ7.7.25hypothetical core disruptive accident with law of type JWL for the bubble
57BILL7.7.26specialised equation of state for the particle elements
59BUBB7.7.38Balloon model for air blast simulations
68CDEM7.7.39Discret Equation Method for Combustion
51CHOC7.7.22Shock waves, Rankine-Hugoniot equation
110DEMS7.7.40Discret Equation Method for Two Phase Stiffenened Gases
22EAU7.7.9two-phase water (liquid + vapour)
49EXVL7.7.20hydrogen explosion Van Leer
27FLFA7.7.15rigid tube bundles (homogeneous acoustic model)
86FLMP7.7.35Fluid multi-phase
7FLUI7.7.2isothermal fluid ( c = cte )
36FLUT7.7.30fluid, to be specified by the user
73GAZD7.7.41Detonation in gas Mixture
9GAZP7.7.4perfect gas
118GGAS7.7.1generic ideal gas material
52GPDI7.7.23diffusive perfect gas Van Leer
48GVDW7.7.28Van Der Waals gas
40GZPV7.7.24perfect gas for Van Leer
28HELI7.7.10helium
50JWL7.7.21explosion (Jones-Wilkins-Lee model)
66JWLS7.7.29Explosion (Jones-Wilkins-Lee for solids)
23LIQU7.7.14incompressible (or quasi-) fluid
82MCFF7.7.34multicomponent fluid material (far-field)
81MCGP7.7.33multicomponent fluid material (perfect gas)
33MHOM7.7.16pipe bundle (homogeneous asymptotic model)
25MULT7.7.13multiple materials (coupled monodim.)
10NAH27.7.7sodium-water reaction (1 liquid and 1 gas)
56PARO7.7.11friction and heat exchange for pipeline walls
39PUFF7.7.17equation of state of type "PUFF"
54RSEA7.8.13sodium-water reaction (1 liquid and 2 gases)
103SG2P7.7.36Multicomponent Stiffened Gases - Conservative formulation
104SGMP7.7.37Multicomponent Stiffened Gases models
24SOUR7.7.6imposed time-dependent internal pressure
102STIF7.7.5Stiffened Gas
101TAIT7.7.3Tait Equation of State
 


Comments:

These materials are detailed in the following pages.


All pressures given as parameters are absolute pressures that must account for the external pressure. If one wants to avoid an unwanted transient expansion, it is necessary to specify the reference pressure "PREF", which must be the same for all fluid materials in a calculation.


For example, for a reservoir filled with gas at the relative pressure of 10 MPa (Pint - Pext = 10 MPa), it is necessary to specify an internal pressure of 10.1 MPa if the atmospheric pressure is 0.1 MPa. Then, two cases are possible:


1) The reservoir is initially in equilibrium:

The calculation aims at simulating the response of the reservoir to an overpressure which appears later on (shock, explosion, imposed velocity ...). The reference pressure must then be: pref = 10.1 MPa, so that the reservoir remains initially in equilibrium.


2) The reservoir is not initially in equilibrium:

The calculation aims at simulating the response of the reservoir to an an internal pressure which appears abruptly. The reference pressure must then be: pref = 0.1 MPa, so that the final status be correct.

7.7.1  GENERIC IDEAL GAS

C.301


Object:

Perfect gas (P=ρ(γ−1)Einternal)
This option enables materials with a ideal gas behaviour to be used. It is an interface to convert the input to the appropriate material (GAZP 7.7.4, FLUT 7.7.30) for the elements used.


Syntax:
    "GGAS"  "RO"  rho  "GAMMA"  gamma  ["PINI"  pini | "EINI" eini]
           ...  < "PREF"  pref >   /LECTURE/
rho

Initial density.
gamma

Ratio cP/cV (supposed constant).
pini

Initial pressure.
pref

Reference pressure. Note that, by default, it is assumed pref = pini for CEA elements (GAZP) and pref=0 for JRC elements (FLUT).
/LECTURE/

List of the elements concerned.

Outputs:

The output variables are according to the material in which the generic material is converted.

7.7.2  FLUID

C.305


Object:

This option enables a fluid (liquid-like) behaviour for continuum elements to be input. The fluid (isothermal) can be perfect (no viscosity) or viscous.


The expression used to compute the absolute pressure p in the fluid is:

p = pini + (ρ − ρini)c2 

where pini is the fluid pressure in the initial state, ρ is the current density, ρini is the initial density and c is the sound speed, which is considered constant.


By default the fluid is considered “free” (i.e. fluid alone, keyword LIBR). However, it is also possible to take into account the volume occupied by some fixed internal structures (which are not meshed) by specifying the optional keyword POREUX. Such a “porosity” may be specified either in 2D or in 3D, but only for the elements of type CAR1, CUBE and PRIS.


Syntax:

    For a "free" fluid (no internal structures) :
    -------------------------------------------

    "FLUID"  < "LIBR" >   "RO" rho   "C" c   <"PINI" pini>    ...
        ...  <"PREF" pref >   <"PMIN" pmin >   <"VISC"  mu  >  ...
        ...  /LECTURE/

    For a "porous" fluid (with internal structures) :
    -----------------------------------------------

    "FLUID"  "PORE"   "RO" rho   "C" c   <"PINI" pini>    ...
      ...  <"PREF" pref >   <"PMIN" pmin >   <"VISC"  mu  >  ...
      ...  "PORO" alpha   < "SMOU" sur >   < "BETA" beta >  ...
      ...   $ "KPER" kp ; "KPX" kpx  "KPY" kpy  < "KPZ" kpz > $ ...
      ...  /LECTURE/

"LIBR"

The fluid is “free”, i.e. without internal structures. This is the default option.
"PORE"

The fluid is “porous”, i.e. it occupies just one part of the meshed volume, the rest being occupied by some fixed internal structures.
rho

Initial density ρini of the fluid.
c

Sound speed c in the fluid, considered constant.
pini

Absolute initial pressure pini in the fluid. By default, pini = 0.
pref

Absolute reference pressure pref in the fluid. By default, pref = pini (even when pini = 0).
pmin

Absolute minimum pressure pmin in the fluid. By default, pmin = 0. Obviously, it must be pminpini. The minimum density ρmin results then from the expression:
ρmin = ρini + 
pmin − pini
c2
mu

Dynamic viscosity coefficient µ (2D or 3D).
alpha

Value of the porosity: ratio of the volume occupied by the fluid with respect to the total volume.
sur

Relative wet surface (value 1 by default).
kp

Head loss coefficient by unit length, assumed isotropic.
kpx, kpy, kpz

Head loss coefficient by unit length in the direction Ox (respectively Oy, Oz).
beta

Reduced damping coefficient for high frequencies. It is zero by default, and should always be very small.
/LECTURE/

List of the elements concerned.

Comments:

The parameters RO and C are compulsory.


Role of PREF:

When the reference pressure is different from the initial one, the fluid is not in equilibrium at the beginning. This is the case e.g. when a membrane is breaking at t=0, releasing a compressed fluid. For further detail, see page C.300.


In various problems, studies relate to acoustic effects; since it is supposed that a fluid in equilibrium evolves under the effects of loading (motion of a piston, shock,...), in this case it must be: pref = pini.


If PREF is omitted, EUROPLEXUS considers that the fluid is in equilibrium and pref=pini (even when pini=0).


For a given minimum pressure pmin, the fluid pressure is always greater than or equal to that value, even if the density is decreasing. This is a very simple way to model cavitation. The default value of pmin is pmin = 0.


Viscosity:

In the presence of viscosity, the tensor of stresses in the fluid has the following form:

σ(i,j)=−P δ(i,j) +2 µ   є(i,j

with:

P : pressure

δ(i,j) : Kronecker’s symbol

є(i,j) : strain rate (derived from є(i,j))


For water at 20 degrees Celsius: µ = 0.001 SI units (Kg/(m*s)).


Porous fluid:

If the fluid is porous, the parameter PORO is mandatory. In this case an equivalent fluid is used by the code for the calculations, which occupies the entire volume of the element. However, the used variables (pressure, velocity, etc.) are those of the REAL fluid, so as to obtain directly the physical state of the fluid in the presence of internal structures.


If these internal structures generate a head loss, the parameter kp allows to model it in case this loss is isotropic. Otherwise, the parameters kpx, kpy, kpz allow to distinguish between the three directions in the global reference.


The former coefficients are given per unit length. For example, if the head loss is Δ P=0.25 bar over a length of L=2 m, for a fluid of density ρ=1000 kgm−3 with a velocity V=5 ms−1, the coefficient will be Kp=1 according to the formula:

Δ P = 
1
2
 Kp  L  ρ V2 


The parameter SMOU (relative wet surface) is obsolete and may be omitted. It is only kept for compatibility with old input files.


Correlation between bulk modulus and sound speed:

This material model can be compared to that of a fluid with constant bulk modulus (e.g. the FLUT material with NUM 9) as follows. For the latter, the absolute pressure is given by:

p = pini + Bη

where B is the bulk modulus (assumed constant and usually expressed in Pa) and η is the relative volume variation:

η = −єV = 
VVini
Vini
 = 1 − 
ρini
ρ

From these expressions one obtains:

p = pini + (ρ − ρini)
B
ρ
 

By comparing this with the pressure expression of the FLUI material, one sees that:

c = 
B
ρ
 

Therefore, strictly speaking the two models are different because in one the sound speed is assumed constant (so that the bulk modulus varies with the density) while in the other the bulk modulus is assumed constant (so that the sound speed varies with the density). However, by assuming that the density varies only slightly from the initial value ρini, one obtains the following relation between c and B:

c ≈ 
B
ρini
 

Outputs:

The components of the ECR table are as follows:

ECR(1): absolute pressure

ECR(2): density


Reference:

CEA report to appear.

7.7.3  TAIT EoS

C.307


Object:

This option enables a barotropic fluid (liquid-like) behaviour for continuum elements to be input. The Tait Equation of State (EoS) can be used to model liquids and is frequently used to model water in underwater-explosion simulations. For water, classical constants are: γ = 7.15 and b = 331 MPa.


The expression used to compute the absolute pressure P in the fluid is:

P = B 





ρ
ρref
 


γ −1 


where P is the fluid pressure, ρ is the current density and ρref is the reference density.


Syntax:

    "TAIT"    "RO" rho   "PINI" pini <"PREF" pref >   <"PMIN" pmin >
       ...    "GAMM" gamma   "B" b
       ...    /LECTURE/

rho

Reference density ρref of the fluid.
pini

Absolute initial pressure pini in the fluid.
pref

Absolute reference pressure pref in the fluid. By default, pref = pini.
pmin

Absolute minimum pressure pmin in the fluid. By default, pmin = 0. Obviously, it must be pminpini. The minimum density ρmin results then from the expression:
ρmin =  ρref



pmin
B
 + 1 


1
γ
 
gamma

first coefficient of the TAIT EoS.
b

second coefficient of the TAIT EoS.
/LECTURE/

List of the elements concerned.

Comments:

For the TAIT EoS, the initial density ρini is computed from the expression:

ρini =  ρref



pini
B
 + 1 


1
γ
 

with:

pini : initial pressure, ρref : reference density


The expression used for the sound speed is:

C=
 
γ (P + B)
ρ
 

Role of PREF:

When the reference pressure is different from the initial one, the fluid is not in equilibrium at the beginning. This is the case e.g. when a membrane is breaking at t=0, releasing a compressed fluid. For further detail, see page C.300.


In various problems, studies relate to acoustic effects; since it is supposed that a fluid in equilibrium evolves under the effects of loading (motion of a piston, shock,...), in this case it must be: pref = pini.


If PREF is omitted, EUROPLEXUS considers that the fluid is in equilibrium and pref=pini.


For a given minimum pressure pmin, the fluid pressure is always greater than or equal to that value, even if the density is decreasing. This is a very simple way to model cavitation. The default value of pmin is pmin = 0.


Outputs:

The components of the ECR table are as follows:

ECR(1): absolute pressure

ECR(2): current density

ECR(3): sound speed

7.7.4  PERFECT GAS

C.310


Object:

Euler : perfect gas (P=ρ(γ−1)Einternal);


Lagrange: adiabatic perfect gas (P=kργ).


In a 1-D case, the frictions against the walls can be taken into account, since the dissipated energy will heat up the gas (modification of the internal energy). To this end the user has to add a PARO material, which must be associated with GAZP by means of the MULT material (see pages C.370 and C.380).


Syntax:
    "GAZP"  "RO"  rho  "GAMMA"  gamma  "PINI"  pini  <"VISC" mu > ...
           ... < "CV"  cv >   < "PREF"  pref >   /LECTURE/
rho

Initial density.
gamma

Ratio cP/cV (supposed constant).
pini

Initial pressure.
mu

Dynamic viscosity of the gas (for 2-D and 3-D).
cv

Specific heat at constant volume cV (used to compute the temperature).
pref

Reference pressure. Note that, by default, it is assumed pref = pini.
/LECTURE/

List of the elements concerned.

Comments:

The reference pressure pref enables the initial state to be defined. If pref = pini, the gas is in equilibrium just before the computation starts; it will be perturbated by an external action, by the motion of a piston, for instance. If pref = 0, the problem consist in a computation with initial stresses determined by pini. This is the case when a membrane which was seperating two gases at different states disappears at the initial instant.


If cv is omitted, the temperature is not computed. If it is present, the temperature is expressed in degrees Celsius.


Outputs:

The different components of the ECR table are as follows:

ECR(1): pressure

ECR(2): density

ECR(3): velocity of sound

ECR(4): maximum pressure ever experienced

ECR(5): minimum pressure ever experienced

ECR(6): dynamic pressure: (Pdyn=1/2ρ v2)

ECR(7): temperature (if cV is not zero) in degrees Celsius

ECR(8): total specific energy (E = h + 1/2v2)

7.7.5  STIFFENED GAS

C.315


Object:

This Equation of State can be used for both liquids and gases. It takes the following form:

P = (γ −1) ρ (eq) − γ Pinf  

Where e is the internal energy per unit mass, ρ the density. γ is an empirical constant for liquids. Pinf is a constant representing the molecular attraction between molecules (liquid) and q is an additional constant. This expression is identical to the ideal gas EoS when Pinf and q is zero.


Syntax:
    "STIF" "RO"  rho  "PINI"  pini  < "PMIN"  pmin >   < "PREF"  pref >
            ...  "GAMMA"  gamma  "PI" pinf  "Q" q
            ...   /LECTURE/

rho

Initial density.
pini

Initial initial pressure.
pref

Reference pressure. Note that, by default, it is assumed pref = pini.
pmin

Absolute minimum pressure pmin in the fluid. Note that, by default, it is assumed pmin = 0.
gamma

Ratio cP/cV (supposed constant) for gases and an empirical constant for liquid.
pinf

Constant parameter for liquid to take into account molecular attraction between molecules.
q

Internal energy of the fluid at a given reference state (most time one take q = 0).
/LECTURE/

List of the elements concerned.

Comments:

The reference pressure pref enables the initial state to be defined. If pref = pini, the gas is in equilibrium just before the computation starts; it will be perturbated by an external action, by the motion of a piston, for instance. If pref = 0, the problem consist in a computation with initial stresses determined by pini. This is the case when a membrane which was seperating two gases at different states disappears at the initial instant.


The expression used for the sound speed is:

C=
 
γ (P + Pinf)
ρ
 

Outputs:

The different components of the ECR table are as follows:

ECR(1): pressure

ECR(2): density

ECR(3): sound speed

7.7.6  SOURCE

C.320


Object :

This instruction enables a time dependent pressure to be imposed, inside an element.


For fluids modelled in ALE, this material allows to create a source of mass flow, if it is used in conjunction with an imposed velocity directive. However, this source is limited to the case of a liquid (case "FLUI"), of a perfect gas ("GAZP"), of a two-phase mixture of water ("EAU") or of a liquid-gas mixture ("ADCR").


Syntax:
    "SOUR"   $ "FLUI" ... ; "GAZP" ... ; "EAU" ... ; "ADCR" ... $

       ...  < "FONC" nufo  < "FACT" coef > >  /LECTURE/

FLUI, GAZP, EAU, ADCR

This keyword indicates the source material data which are strictly identical to those of the material with the same name.

For "FLUI" see 7.7.2 page C.305, for "GAZP" see 7.7.4 page C.310, for "EAU" see 7.7.9 page C.350, for "ADCR" see 7.7.19 page C.430,

nufo

Number of the ’FONCTION’ allowing to define the pressure as a function of time
coef

Multiplying factor for the pressures given by the preceding function. By default coef=1.
LECTURE

List of the concerned elements.

Comments:

The "FONCTION" directive is described in 9.1 (page E.15).


The initial pressure, must correspond to the origin of the curve.


The element deforms only under the action of forces due to the imposed pressure (no stiffness). The temperature is assumed constant. In the case of water, for example, if the pressure increases one can pass from a liquid phase to a vapor phase, but always at the same temperature.


Outputs:

The different components of the ECR table are the same as the components for the material with the same name.

7.7.7  SODIUM-WATER REACTION (“NAH2”)

C.330


Object:


Explosion caused by water injection into liquid sodium.


In 2D or 3D, one element or more (contiguous) elements may be affected by the chemical reaction. In 1D, just one "TUBE" or "TUYA" element must be used with this material.


In 1D or 3D there are two options for the water mass flow rate:

1) imposed curve as a function of time (keyword "DEBIT")

2) calculation of a water-filled pipeline meshed by elements of type TUBE or TUYA and coupling with the sodium mesh (keyword "DCOUP").


Syntax:

    "NAH2"  "RO" rho  "C" c  "PINI" pinit    "PV" pv   "FACT" facteur
     ... < "PREF" pref > < "PMIN" pmin > < "CMIN" cmin > < "CH2" ch2 >
     ...$[ "DEBIT"  npt*(temps , debit) ;
           "DCOUP"   1     tini    qini ]$/LECTURE/


rho

Initial density (pure sodium).
c

Sound speed in the sodium.
pinit

Initial pressure.
pref

Reference pressure (see page C.300).
pv

Value of the product P*V for the unit mass of hydrogen at the initial temperature.
facteur

Number of gas moles formed starting from one mole of injected water.
ch2

Initial mass fraction for the hydrogen. By default, ch2 = 0 and as a maximum ch2 = 1.
cmin

Minimum mass fraction of the hydrogen in the pure sodium (1.E-8 by default).
pmin

Minimum pressure (zero by default).
"DEBIT"

Keyword that announces the introduction of the curve of total mass flow rate of water injected in the sodium for the whole set of elements concerned.
npt

Number of points defining the mass flow rate curve for the water.
(temps, débit)

Coordinates of the points (in axisymmetric, divide the mass flow rate by 2π, as the calculation refers to one radian).
"DCOUP"

The water mass flow rate at the outlet of a pipe is computed (1D) by directive "IMPE" "NAH2" (page C.610).
tini

Initial time.
qini

Initial mass flow rate.
/LECTURE/

List of the elements affected by the injection.

Comments:


For the dimensioning, an injection curve requires a space similar to that of a traction curve. The user will therefore have to specify "TRAC" n1 n2, with n1 the maximum number of curves to be entered (traction and injection), and n2 the maximum number of points.


In the elements affected by the reaction, it is assumed that the reaction is instantaneous, that the mixture of reacting components is always homogeneous and that the reaction is isothermal.


The "facteur" parameter allows to account for the vaporised ’soude’. If there is none, then facteur = 0.5.


If the volume fraction of hydrogen (printed as ECR(4)) is above 1, the program treats the mixture like pure hydrogen.


In a Lagrangian calculation (default option) the "NAH2" material is attached only to the elements where the reaction takes place. The "FLUI" material is used for the other elements.


In an Eulerian calculation (option "EULER" page A.30), the material "NAH2" is affected to ALL fluid elements. The mass flow rate curve for the water is only affected to the elements where the reaction occurs, for the others one must write:

        "DEBIT"  0  /LECTURE/

Outputs:


The components of the ECR table are as follows:

ECR(1) : absolute pressure

ECR(2) : density

ECR(3) : hydrogen concentration

ECR(4) : hydrogen volume occupation ratio

ECR(5) : total water mass flow rate for the set of elements

ECR(6) : water mass injected in each element

ECR(7) : sound speed in the Na+H2O mixture

ECR(8) : hydrogen mass per unit volume (in Eulerian)

ECR(10): phase indicator (1= saturated in H2; else 0)

7.7.8  SODIUM-WATER REACTION (“RSEA”)

C.340


Object:


Explosion caused by water injection into liquid sodium.


It is possible to repeat this material as many times as needed, provided the injections occur in different elements.


There are two possibilities concerning the water mass flow rate:

1) a time function is invoked (keyword "NUFO")

2) compute a water-filled pipeline meshed with TUBE or TUYA elements and coupled with the sodium mesh (keyword DCOU).


Syntax:

    "RSEA"  "PTOT" ptot   "PNA" pna     "RONA" rhona  "CSNA" csona
            "PBU"  pbu    "ROBU" rhobu  "NBU"  nbu    "GBU" gbu
          < "PARG" parg   "ROAR" rhoar  "GAR" gar >
          < "PSAT" psat   "ROSA" rhovap >
          < "XBU"  xbu  >  < "XAR"  xar  >  < "PREF" pref >
          < "CMIN" cmin >  < "BETA" beta >
          < "VINA" vina >  < "VIBU" vibu >  < "VIAR" viar >
          < $[ "NUFO" nufo  "COEF" coef  ;  "DCOU"   1  ]$ >
          < "FACT" facteur >
              /LECTURE/


ptot

Total pressure of the mixture.
pna

Zero pressure of sodium, defining the equation of state of the liquid, by means of the following rhona and csona parameters.
rhona

Zero density of sodium.
csona

Sound speed in the sodium.
pbu

Zero pressure of the hydrogen, defining the equation of state of the gas, by means of the following rhobu and nbu parameters.
rhobu

Zero density of the hydrogen.
nbu

Polytropic coefficient of the transformation followed by the hydrogen. For an isotermal: nbu = 1.
gbu

Ratio Cp/Cv for the hydrogen.
parg

Zero pressure of the argon, defining the equation of state of this gas, by means of the following rhoar and gar parameters.
rhoar

Zero density for the argon.
gar

Ratio Cp/Cv for the argon.
psat

Saturation pressure of the sodium vapor. A priori this is very low, and allows to treat correctly the possible cavitation phenomena.
rhovap

Density of the sodium vapor.
xbu

Initial mass fraction of the hydrogen. It allows to account for the presence of gas in the considered domain.
xar

Initial mass fraction of the argon. This refers to the subdomains that are filled with argon initially, such as the cover gas region or the zones located behind membranes.
pref

Reference pressure (see page C.300).
cmin

Maximum mass fraction of gas in the sodium in order to consider it as pure (1.E-8 by default).
vina

Dynamic viscosity of sodium.
vibu

Dynamic viscosity of the gas in the bubble.
viar

Dynamic viscosity of argon.
beta

Reduced damping coefficient for high frequencies. It is zero by default, and should always be very small ( < 0.05 ).
nufo

Number of the adimensional function defined via the "FONCTION" directive of EUROPLEXUS. This function allows to describe the variation of injected water mass flow rate in time.
coef

Multiplicative factor por the precediing function. This allows to account for the units and the number of ruptured pipes.
DCOU

This keyword specifies that a coupled water flow calculation is desired. It is always followed by an integer value.
facteur

Number of gas moles formed by one mole of injected water.
/LECTURE/

List of the concerned elements.

Comments:


In the elements affected by the reaction, it is assumed that the reaction is instantaneous, and that the mixture of reacting materials is always homogeneous.


The "facteur" parameter allows to account for the vapor ’soude’. If there is none, then facteur = 0.5.


The mesh will be subdivided in as many zones as necessary, and for each of these an RSEA material will be defined, by possibly varying the initial concentrations and the total pressures, but the other parameters must be identical, so as to have exactly the same constitutive laws for the different components of each zone. Then, starting from the given concentration and the total pressure ptot, EUROPLEXUS will compute de density of the mixture. EUROPLEXUS will also recompute the gas concentrations in order to account for the sodium vapor, if psat is not zero.


The elements where the reaction occurs will be distinguished by one of two possible options: imposed injection or injection coupled with the calculation of water mass flow rate (DCOU).


If psat and rhovap are absent, or if one only of these values is given, it is the default value which is used: psat is taken equal to one thousandth of ptot. The value of rhovap is then proportional to psat, and corresponds to a monoatomic vapor at a temperature close to 300o C.


Outputs:


The components of the ECR table are as follows:

ECR(1) : absolute pressure,

ECR(2) : density of the two-phase mixture,

ECR(3) : sound speed in the mixture,

ECR(4) : void fraction,

ECR(5) : argon mass fraction,

ECR(6) : hydrogen mass fraction,

ECR(13) : water mass flow rate (dm/dt)

ECR(14) : mass of water injected since the beginning.

7.7.9  WATER

C.350


Object :

This directive allows to treat water and its vapour as an homogeneous mixture. It is also possible to treat a water vapor explosion when energy is released within liquid water.


Syntax :

    "EAU"   $[ "EQUI"                           ;
               "META"  "NBUL" nbul  "ALFN" alfn ]$   ...

       ...  "PINI"  pini   |[ "TINI" tini ; "TITR" x ]| ...
       ...  < "PREF" pref > < "BETA"  beta > ...
       ...  < "VISL"  mul   "VISV" muv   >   ...

   For a direct injection:

          $ < "ENMA" enma    "FONC" numf    ...
            ...  < "XCOR" xcor >  < "MODE" mode ; "COEF" coef >  > $
            ...  < "DPROP" dpropag   "ORIGINE"   /LECTURE/       > $

   For an injection of corium particles:

       ...$ < "DIAM" diam    "CECH"  hh     ...
                 ...   "TCOR" tcor   "VCOR" vcor   > $

   One ends this directive by:

       .../LECTURE/
EQUI

The mixture will be in equilibrium (same pressure and same temperature for the liquid and vapour phases).
META

The mixture will be metastable (same pressure but different temperatures for the liquid and vapour phases).
nbul

Number of vapour bubbles by unit volume (of the order of 1.E9).
alfn

Minimal void fraction for the nucleation of vapor bubbles (of the order of 1.E-4).
pini

Initial pressure of the mixture.
tini

Initial temperature of the equilibrium mixture (in degrees Celsius).
x

Initial mass title of the vapor, between 0 and 1. (eau=0, vapeur=1).
pref

Reference pressure (for its meaning see page C.300). By default, it is equal to the initial pressure. All reference pressures must be equal.
beta

Reduced damping coefficient for high frequencies. It is zero by default, and should always be very small ( < 0.05 ).
mul

Dynamic viscosity of the water. Recall: below 1 bar, at 25o C, mul = 9.E-4 Poiseuille or Pascal * second. This value drops rapidly as the temperature increases. By default mul = 0.
muv

Dynamic viscosity of the water vapor. Recall: below 1 bar, at 100o C, muv = 1.3E-5 Poiseuille. This value increases with the temperature. By default, muv = 0.

For a direct injection of energy in the water:
enma

Specific power injected in the water. Multiplicative coefficient (dimensional) of the following function.
numf

Number of the non-dimensional function defined by the "FONCTION" directive of EUROPLEXUS. This function allows to vary the injected power in time.
xcor

Ratio betweeen the corium mass and the water mass contained within the element. The specific power (enma) applies only to the present corium. By default, xcor = 1.
mode

Choice of the injection mode: (0, 1, 2 or 3). The meaning is explained in the comments below. By default, mode = 0.
coef

Ratio between the limit density and the initial density. This allows to limit the injection. By default, coef = 0. Is only relevant for mode = 0 or 1.
dpropag

Propagation velocity of the energy injection signal for the elements of the considered domain. By default, the injection occurs simultaneously in all such elements.
ORIGINE

This keyword announces the reading of the element in which the injection is initiated. The injection then propagates with the speed dpropag in all directions.

For an injection by means of corium particles:
diam

Diameter of the particles.
hh

Heat exchange coefficient between a corium particle and the liquid water.
tcor

Initial temperature of the corium particles.
vcor

Volume fraction occupied by the corium.
LECTURE

List of the concerned elements.

Comments :

Do not forget to create the tables of physical properties of the water by means of directive "TEAU" or "TH2O" (page C.74).


The "TH2O" table is only working with equilibrated water.


If the mixture is single-phase, one should give the pressure and the temperature, but the title is irrelevant. If the mixture is two-phase, one should give the pressure and the title: EUROPLEXUS then computes the temperature.


The damping coefficient beta allows to damp out high-frequency oscillations caused by the discretisation. By default beta is zero. However, it is advised to use beta between 0.1% et 5%. One should be aware of the inevitable attenuations of lower frequencies, especially if the mesh is coarse. In fact, the eigenfrequencies of the structure are not very different from the frequencies associated with the finite elements.


If the viscosity has to be considered, the two parameters mul and muv must be related and given together.


Energy injection:

The "MODE" parameter allows to account for the evolution of fluid close to the injection zone, in a less brutal fashion compared with directive "COEF". Its meaning is as follows:

mode = 0 : the injected energy i s independent from the fluid mass and nature,

mode = 1 : the injected energy is proportional to the mass of water, but independent from its nature of liquid or vapor,

mode = 2 : the injected energy is proportional to the mass of liquid water,

mode = 3 : the injected energy is proportional to the volume of liquid water.


Modes 2 and 3 should not be used if the pressure exceeds the critical value (Pcrit = 221 bar).


The "COEF" directive allows to limit the quantity of injected energy: if the density during the computation becomes lower than the limit density, then the injection is stopped. This directive is brutal and not advisable. It is preferable to use the "MODE" directive.


One may obtain the energy quantity released in a certain region of the mesh by means of keyword "WINJ" in directive "REGION" (page G.100).


By assigning a propagation velocity associated with an origin element allows to avoid a brutal and instantaneous injection over an extensive domain, which is irrealistic: this option is recommended in case of a steam explosion calculation.


Outputs:

The components of the ECR table are as follows:

ECR(1) : absolute pressure

ECR(2) : density of the mixture

ECR(3) : sound speed

ECR(4) : mass title of the vapor (vapor mass/total mass)

ECR(5) : temperature of the mixture for equilibrated water, liquid temperature for meta-stable

ECR(6) : enthalpy of the mixture

ECR(7) : temperature of the mixture for equilibrated water, vapor temperature for meta-stable

ECR(9) : void ratio or volume ratio of the vapor (vapor volume/total volume)


For meta-stable water:

ECR(21) : vapor relative density (vapor mass/total volume)

ECR(23) : index : 0 = equilibrium ; 1 = meta-stable

ECR(24) : specific enthalpy of the liquid water


In case of direct energy injection:

ECR(8) : power injected in the element

ECR(14) : corium mass within the element


In case of energy injection by particles:

ECR(19) : initial volume of corium within the element

ECR(20) : mean temperature of a corium particle


For a "BREC" element:

ECR(25) : Pipeline rupture area

ECR(26) : Mass flow

ECR(27) : Total ejected mass

7.7.10  HELIUM

C.355


Object :

This directive allows to treat helium and its liquid as an homogeneous mixture.


Syntax :

    "HELI"   "PINI"  pini   |[ "TINI" tini ; "TITR" x ]| ...
          ...  < "PREF" pref > < "BETA"  beta >        ...
          ...  < "VISL"  mul   "VISV" muv   >          ...
          ...   /LECTURE/
pini

Initial pressure of the mixture.
tini

Initial temperature of the equilibrium mixture (in degrees Kelvin).
x

Initial mass title of the vapour, between 0 and 1. (liquid=0, vapour=1).
pref

Reference pressure (for its meaning see page C.300). By default, it is equal to the initial pressure. All reference pressures must be equal.
beta

Reduced damping coefficient for high frequencies. It is zero by default, and should always be very small ( < 0.05 ).
mul

Dynamic viscosity of the liquid. By default mul = 0.
muv

Dynamic viscosity of the vapour. By default, muv = 0.

Comments :

Do not forget to create the tables of physical properties of helium by means of directive "THEL" (page C.75).


If the mixture is single-phase, one should give the pressure and the temperature, but the title is irrelevant. If the mixture is two-phase, one should give the pressure and the title: EUROPLEXUS then computes the temperature.


The damping coefficient beta allows to damp out high-frequency oscillations caused by the discretisation. By default beta is zero. However, it is advised to use beta between 0.1% et 5%. One should be aware of the inevitable attenuations of lower frequencies, especially if the mesh is coarse. In fact, the eigenfrequencies of the structure are not very different from the frequencies associated with the finite elements.


If the viscosity has to be considered, the two parameters mul and muv must be related and given together.


Outputs:

The components of the ECR table are as follows:

ECR(1) : absolute pressure

ECR(2) : density of the mixture

ECR(3) : sound speed

ECR(4) : mass title of the vapor (vapor mass/total mass)

ECR(5) : temperature of the mixture

ECR(6) : specific enthalpy of the mixture

7.7.11  1D WALL

C.370


Object:


This directive allows, in association with the MULT material, to account for the effects of pipe walls and cavity walls, for elements of type TUBE, TUYA or CAVI.


Syntax:

     "PARO"  $[  "RUGO"  rug    "VISC" mu                 ;
                 "RUGO"  rug    "VISL" mul    "VISV" muv  ;
                 "TPAR"  teta   "COND" cof  < "SURF" su > ;
                 "PSIL"  kl                               ;
                 "FONC"  numf < "SURF" su  >              ]$

             < "COEF" nbr >   /LECTURE/


rug

Absolute rugosity of the pipe (warning, this parameter has the dimension of a length).
mu

Dynamic viscosity (single-phase fluid).
mul

Liquid dynamic viscosity (two-phase fluid).
muv

Vapor dynamic viscosity (two-phase fluid).
teta

Wall temperature.
cof

Conductance.
su

Heat exchange surface.
kl

Head loss coefficient per unit length (1/m).
nbr

Multiplicative coefficient in the case of an assembly of identical pipes (nbr = 1 by default).
numf

Number of the FONCTION allowing to define the conductance as a function of the flow velocity of the fluid.
LECTURE

List of the elements concerned.

Comments:


The MULT material is used (page C.380) to associate the wall defined by PARO with the corresponding internal fluid.


If the internal fluid is of type NAH2, EAU or RSEA, ot is mandatory to specify the viscosities of both phases, mul for the liquid and muv for the vapor. In all other cases, the fluid is supposed to be single-phase, and only one viscosity mu will be required.


In the case of heat exchange with the wall, the keyword SURF is mandatory for the CAVI elements. For the elements of type TUBE and TUYA it may be omitted, and in this case EUROPLEXUS will compute the exchange surface starting from the geometrical characteristics of the elements.


The kl coefficient (keyword PSIL) allows to compute the head loss in the following way:

        DP = kl * long * 0.5 * rho * V ** 2


with:

DP : head loss,

long : length of the pipe,

rho : fluid density,

V : mean velocity,


Hence: kl = psi / Dh, where Dh is the hydraulic diameter.


Outputs:


The parameters associated with the wall material not included in ECR are placed after the ECR for the fluid (see the fluid documentation).


The components of the ECR table are as follows:

ECR(1) : wall temperature

ECR(2) : conductance

ECR(4) : Reynolds number

ECR(5) : psi (of the formula K = psi * L / Dh)

7.7.12  PIPE BREAK PARAMETERS

C.375


Object:


This directive allows, in association with the MULT material and elements of type BREC to enter parameters for the computation of the fluid effects after the pipe break (outlet pressure, critical mass flow rate...).


Syntax:

     "BREC" $[
               "DCRI" idcri ;
               "PIMP" ipimp < "CONT" cont "EPAI" epai >
            ]$
idcri

Mode for the critical mass flow rate computation (see comment below).
ipimp

Mode for the imposed pressure model (see comment below).
cont

Jet contraction ratio at critical section (default value: 0.84) (see comment below).
epai

Pipe thickness of the broken pipe (see comment below)



Comments:


The MULT material is used (page C.380) to associate the pipe break parameters defined by BREC with the corresponding internal fluid. Only the water material EAU is currenlty allowed for the fluid.

The keyword DCRI is used to impose a critical mass flow rate after the pipe break. Critical mass flow rate is computed using additional CL elements placed on both ends of the BREC element. Two modes are allowed:

The keyword PIMP is used to impose a pressure drop at the break with the imposed pressure being the pressure at saturated conditions, modified in order to take into account the break area [871]. This option is supposed to give a better representation of pressure wave generation at the break, focusing on the very firt instant after break opening. Two modes are allowed:

Two optional keywords CONT and EPAI can be used in conjunctin with the keyword PIMP:


For keyword DCRI, additional CL elements are needed for the mass flow rate to be calculated. If no CL elements are used, no critical mass flow rate is computed and no fow limitation is imposed. For keyword PIMP, BREC element can be used with or without CL elements, with no impact on the calculation If used, before the pipe break, the CL elements are automatically deactivated (see page D.590 for the definition of the break time).


7.7.13  MULTIPLE MATERIALS

C.380


Object:

This directive allows to assign several materials to the same element. For example, it is the case of a pipeline element, where one has to specify both the material for the internal fluid and the material of the wall plus, if necessary, a material describing the friction.


Syntax:

    "MULT"  n1  n2  < n3 > /LECTURE/


n1

Number assigned to the first material.
n2

Number assigned to the second material.
n3

Number assigned to the third material.
LECTURE

List of the elements concerned.

Comments:


The materials concerned must be defined previously, and are referenced by their law index (see LOI, page C.100). This is either the number explicitly given by the LOI keyword, or the material definition order in the input file.


In the case of "TUBE" elements, n1 will be the index of the fluid material and n2 the index of the friction material.


In the case of "TUYA" elements, the fluid must be referenced first, the wall second, and the friction third, when present. For example, if one has defined the materials in the following order: the wall material first (1), then the fluid material (2), and finally the friction material (3), the "MULT" directive must be coded as follows:

        "MULT"  2  1  3  /LECTURE/



Outputs:


The stresses and the hardening parameters will be those of the component materials. For example, for an element of pipeline, the printed stresses will be those of the associated beam (no printout of the stresses for the internal fluid), and the ECR(i) will give first the quantities related to the fluid material, then those related to the wall material.

7.7.14  LIQUID

C.390


Object:


This option enables the processing of an incompressible or quasi-incompressible fluid. The implicit algorithm of "LIAISONS" is used.


Syntax:

    "LIQU"  "RO"  rho  < "C"  c >  < "PINI"  pini >   ...
       ...  < "PREF" pref >  < "VISC" visc >  < "RUGO" rugo >
    /LECTURE/


rho

Density.
c

Velocity of sound (only for a compressible fluid).
pini

Initial pressure.
pref

Reference pressure (see page C.300).
visc

Twice the dynamic viscosity (2µ).
rugo

Absolute rugosity.
LECTURE

List of the elements concerned.

Comments:


This material only makes sense if the option "NAVIER" has been required for the definition of the problem.


If the material is incompressible, c is useless. On the contrary, c is necessary if the fluid is compressible, even at a low level. In this case c is read and then the value of (1/c2) is stored in the material property.


Warning:


It is essential to invert the connection matrix at each step. Do not forget to add the option "FREQ" 1 when using the instruction "LIAISON" (see page D.20).


Outputs:


The components of the ECR table are as follows:

ECR(1): absolute pressure of the element due to the viscous terms

ECR(2): density

ECR(3): additive term to the diagonal of BL, the connections matrix.

ECR(4): additive term to the right-hand side of the connections system

ECR(5): multiplicative term of the pressure

ECR(6): friction coefficient (see M1FROT)

ECR(7): Reynolds number

ECR(8:10): unused

7.7.15  TUBE BUNDLES

C.400


Object:


Replaces a heterogeneous medium composed by a bundle of tubes submerged in a fluid, by an equivalent homogeneous isotropic medium in the acoustic sense. The densities and sound speeds will be different along the three directions in space.


In the case of helicoidal coaxial bundles (2D axisymmetric or 3D), the axis of the bundle must be along the Oz direction, the helices have all the same axial step and are regularly spaced.


In the case of a straight bundle, (2D or 3D), the bundle axis is Oz, and a side of the base ’motif’ must be parallel to Ox or Oy.


There are two options for the definition of the three densities and of the three sound speeds:

a) The values are computed by EUROIPLEXUS as a function of the geometrical data (plane waves propagation).

b) The values have another origin, and are prescribed.


The possible combinations between options and geometries of the bundle are given in the following table:

                                              | Value of  "TYPE"|
  Geometry               |     2D      |  3D  |                 |
  Option                 | DPLA | AXIS | TRID |                 |
                         |             |      |                 |
     Triangular step     |  yes |  no  |  yes |       2*        |
     Rectangular step    |  yes |  yes |  yes |       1*        |
                         |             |      |                 |
  Imposed anisometry:    |      |      |      |                 |
     Frame  Ox,Oy,Oz     |  no  |  no  |  yes |       2         |
     Frame  Or,Ot,Oz     |  no  |  yes |  yes |1 in 3D,2 in AXIS|

    * These values are automatically affected to "TYPE" by EUROPLEXUS.



Syntax:

    "FLFA"  "RO" rho  "C" c    < "PINI"  pini >  < "PREF" pref >
                               < "PMIN"  pmin > ...

    $[ "DIAM" d  $[ "PRAD" pr  "PAXI" pa ]$ < "VISC" mu > < "COEF" coef>
                 $[ "PTRI" pt  "BASE" ba ]$                        ;

       "ROX" rox  "ROY" roy  "ROZ" roz  "CX" cx   ...
                ...  "CY" cy  "CZ" cz  "TYPE" type "TAUX" taux     ;

       "ROR" ror  "ROT" rot  "ROZ" roz  "CR" cr   ...
                ...  "CT" ct  "CZ" cz  "TYPE" type "TAUX" taux     ]$

   ...  /LECTURE/


rho

Density.
c

Sound speed.
pini

Initial pressure.
pref

Reference pressure (see meaning on page C3.300).
pmin

Minimum pressure (see meaning on page C3.305).
mu

Fluid dynamic viscosity.
coef

Multiplicative factor for the friction (= 1 by default).
d

External diameter of the tubes.
pr

Radial step of the tubes.
pa

Axial step of the tubes.
pt

Equilateral triangular step.
ba

Direction of the triangle base (ba=1 or ba=2).
rox, roy, roz

Densities along directions Ox, Oy and Oz.
cx, cy, cz

Sound speeds along directions Ox, Oy and Oz.
ror, rot, roz

Densities along directions Or, Ot and Oz.
cr, ct, cz

Sound speeds along directions Or, Ot and Oz.
type

Type of bundle: 1 = helicoidal, 2 = straight.
taux

Volume fraction of the fluid (0 < taux < 1).
LECTURE

List of the concerned elements.

Comments:


The calculation may be done in Lagrangian or in Eulerian.


To conserv the fluid mass, an apparent fluid mass is used (printed in ECR(2)), corresponding to that of a fictitious liquid that would occupy the whole volume.


The modelisation chosen for the bundle implies anisotropy effects on inertia and compressibility. For each principal direction i of the bundle, the two parameters rhoi and rhoi*ci**2 must be defined. Hence the nodal masses are quite different from those computed from the apparent density.


However, for an Eulerian calculation, the fluxes involve the mass effectively transferred from an element to the other, i.e. the code uses the density of the free fluid and the total cross section of the passage. Consequently, the computed (and printed) velocity is that of a fictitious free fluid placed at the bundle entry (entry speed). In order to estimate the mean velocity of the fluid within the tubes, it is necessary to multiply the computed velocity by the ratio between the cross-sections.


If one has to impose an absorbing boundary condition at the bundle border using elements CL2D, CL3D ou CL3T, he must care that the product rho*c be the one corresponding to the considered direction; since the CLxD take as rho the value of the neighbouring element, i.e. the apparent density of the bundle, the sound of speed must be accordingly corrected within directive "IMPE ABSO".


The presence of keyword "VISC" followed by the value of the fluid viscosity triggers the calculation of the head losses in the bundle. The formulation given by I.E.Idel’cik is adopted (Mémento des pertes de charge, Eyrolles, Paris, 1978) for the two principal directions of the bundle in the plane orthogonal to the tubes. The Blasius formula is used in the direction parallel to the tubes (the Reynolds number is then computed by means of the hydraulic diameter).


Outputs:


The components of the ECR table are as follows:

ECR(1) : absolute pressure

ECR(2) : apparent density

Then if VISC is present:

ECR(3) : half-coefficient of friction along direction Ox or Or

ECR(4) : half-coefficient of friction along direction Oy or Ot

ECR(5) : half-coefficient of friction along direction Oz

7.7.16  HOMOGENEISATION OF TUBE BUNDLES

C.410


Object:


Replaces a heterogeneous medium composed by a tube bundle surrounded by fluid, by a homogenised medium (asymptotic homogenisation method).


Syntax :

    "MHOM"  "RO"  rho  "C"  c  "EPSILON"  epsilon  "YSTAR"  ystar ...
       ...   "COEF" coef   "MTUBE" mtube  "KTUBE" ktube...
       ...    "NBTUBE"  nbtube*("BXX" bxx  "BXY" bxy  "BYY" byy ...
       ...          "CXX" cxx  "CXY" cxy  "CYY" cyy)     /LECTURE/


rho

Fluid density.
c

Sound celerity in the fluid.
epsilon

Size of the elementary cell.
ystar

Fluid surface in an increased elementary cell.
coef

Ratio y/ystar (y: total surface of the increased elementary cell).
mtube

Mass of a tube.
ktube

Stiffness of a tube.
nbtube

Number of tubes per elementary cell.