C.100  May 17
This instruction enables the user to enter the properties of
various materials.
"MATE" ( < "LOI" numldc > . . . )
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.
Do not forget the corresponding dimensioning (GBA_0070).
C.100  Aug 13
The material models are (in alphabetical order):
number name ref law of behaviour 74 ABSE 53 ADCJ 7.8.25 hypothetical core disruptive accident with law of type JWL for the bubble 34 ADCR 7.8.19 containment accident (fast neutrons) 47 ADFM 7.8.32 advectiondiffusion fluid 71 APPU 7.5 Material for elements of type PPUI 32 ASSE motor asservissement (meca) 11 BETO 7.7.12 concrete (NAHAS model) 57 BILL 7.8.26 LIBRE (user’s free particle material), or FLUIDE (isothermal fluid particle: c = cte) 29 BL3S 7.7.61 reinforced concrete for discrete elements 20 BLMT 7.7.13 DYNAR LMT Concrete 75 BOIS 7.7.27 wood for shock adsorbing (only compression) 121 BPEL 7.7.13 model for prestressing cableconcrete friction 114 BREC 7.8.12 data for pipeline break 59 BUBB 7.8.38 Balloon model for air blast simulations 89 CAMC 7.7.44 Modified Camclay material 8 CAVI isothermal fluid with cavitation 68 CDEM 7.8.39 Discrete Equation Method for Combustion 64 CHAN 7.7.22 Multilayer with the CHANGCHANG criterion 51 CHOC 7.8.22 Shock waves, RankineHugoniot equation 21 CLVF 7.9.33 Boundary conditions for finite volumes 90 CLAY 7.7.45 Modified Camclay material (backward fully implicit algorithm, viscoplastic regularization) 88 COMM 7.7.43 Composite material (linear orthotropic), Ispra implementation 113 CREB 58 CRIT 7.7.18 damage criteria calculation : PY (damage of type P/Y), DUCTile (ductile damage) 100 CRTM 7.7.57 Composite manufactured by RTM process 109 DADC 7.7.16 Dynamic Anisotropic Damage Concrete 110 DEMS 7.8.40 Discrete Equation Method for Two Phase Stiffened Gases 38 DONE 7.7.40 viscoplastic material 111 DPDC 7.7.17 dynamic plastic damage concrete 87 DPSF 7.7.42 Drucker Prager with softening and viscoplastic regularization 83 DRPR 7.7.51 Drucker Prager Ispra model 12 DRUC 7.7.6 DruckerPrager 19 DYNA 7.7.7 dynamic Von Mises isotropic ratedependent 22 EAU 7.8.9 twophase water (liquid + vapour) 115 ENGR 7.7.20 elastic gradient damage material 105 EOBT 7.7.19 anisotropic damage of concrete 49 EXVL 7.8.20 hydrogen explosion Van Leer 17 FANT 7.7.30 phantom: ignore the associated elements 27 FLFA 7.8.15 rigid tube bundles 86 FLMP 7.8.35 Fluid multiphase 7 FLUI 7.8.2 isothermal fluid ( c = cte ) 36 FLUT 7.8.30 fluid, to be specified by the user 93 FOAM 7.7.52 Aluminium foam (for crash simulations) 80 FUNE 7.7.46 specialized cable material (no compression resistance) 9 GAZP 7.8.4 perfect gas 118 GGAS 7.8.1 generic ideal gas material 44 GLAS 7.7.60 glass with strainrate effect 116 GLIN 7.7.3 generic linear material 92 GLRC 7.7.53 Plasticity with kinematic softening for orthotropic shells. Global plastic criterion. 52 GPDI 7.8.23 diffusive perfect gas Van Leer 117 GPLA 7.7.4 generic plastic material 48 GVDW 7.8.28 Van Der Waals gas 40 GZPV 7.8.24 perfect gas for Van Leer 28 HELI 7.8.10 helium 3 HILL 7.7.59 Isotropic plasticity associated with a HILL criterion and with a orthotropic elastic behaviour 95 HYPE 7.7.54 hyperelastic material (Model of MooneyRivlin, HartSmith and Ogden) 16 IMPE 7.9 impedance 43 IMPV 7.9.21 impedance Van Leer 4 ISOT 7.7.7 isotropic Von Mises 108 JCLM 7.7.65 JohnsonCook with Damage LemaitreChaboche for SPHC 91 JPRP 7.12 for bushing elements 50 JWL 7.8.21 explosion (JonesWilkinsLee model) 66 JWLS 7.8.29 Explosion (JonesWilkinsLee for solids) 72 LEM1 7.7.9 Von Mises isotropic coupled with damage (type Lemaitre) 13 LIBR 7.7.31 free (material defined by the user) 1 LINE 7.7.1 linear elasticity 23 LIQU 7.8.14 incompressible (or quasi) fluid 70 LMC2 7.7.11 Von Mises isotropic coupled with damage (Lemaitre) with strainrate sensitivity 63 LSGL 7.7.62 laminated security glass material 26 MASS 7.7.29 mass of a material point 85 MAZA 7.7.15 Mazarslinear elastic law with damage 82 MCFF 7.8.34 multicomponent fluid material (farfield) 81 MCGP 7.8.33 multicomponent fluid material (perfect gas) 60 MCOU 7.7.21 Linear multilayer homogenised through the thickness 45 MECA 7.10 mechanism associated to articulated systems 33 MHOM 7.8.16 homogenization 97 MINT 7.7.55 Material for interface element 31 MOTE motor force or couple (meca) 25 MULT 7.8.13 multiple materials (coupled monodim.) 10 NAH2 7.8.7 sodiumwater reaction 18 ODMS 7.7.26 nonlinear damage with orthotropy (ODM) 42 ORTE 7.7.25 linear damage with orthotropy 41 ORTH 7.7.23 linear orthotropic in user system 46 ORTS 7.7.24 linear elastic orthotropic with local reference frame 2 PARF 7.7.7 perfectly plastic Von Mises 56 PARO 7.8.11 friction and heat exchange for pipeline walls 96 PBED particle bed 6 POST postrupture (beton) 69 PRGL 7.8.27 Porous jelly for the particles 39 PUFF 7.8.17 equation of state of type "PUFF" 123 RESG 7.7.4 Material for RL3D spring element in the global reference frame 61 RESL 7.7.1 Material for RL3D spring element in the local reference frame 125 RIGI 7.7.67 Rigid material (for rigid bodies) 54 RSEA 7.9.13 reaction sodiumwater with three constituents 103 SG2P 112 SGBN 104 SGMP 107 SLIN 7.7.64 Linear Damage for SPHC 99 SLZA 7.7.56 SteinbergLundZerilliArmstrong 106 SMAZ 7.7.63 Mazars Damage for SPHC 24 SOUR 7.8.6 imposed pressure in a continuum element 30 STGN 7.7.8 Steinberg  Guinan 102 STIF 94 SUPP 7.6 support 101 TAIT 5 TETA 7.7.7 Von Mises dependent upon temperature 98 TVMC 7.7.58 elastoplastic short fibres with damage 37 VM1D 7.7.39 material for elements of type "ED1D" 35 VM23 7.7.38 Von Mises elastoplastic radial return 2/4/5/19 VMIS 7.7.7 Von Mises materials 76 VMJC 7.7.47 JohnsonCook 78 VMLP 7.7.48 LudwigPrandtl 79 VMLU 7.7.49 Ludwik 84 VMSF 7.7.41 Von Mises with softening and viscoplastic regularization 77 VMZA 7.7.50 ZerilliArmstrong 120 VPJC 7.7.66 viscoplastic JohnsonCook 67 ZALM 7.7.10 ZerilliArmstrong with damage LemaitreChaboche
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):
==================================== 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 uptodate 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).
C.105
This directive allows to read the material data from an
auxiliary file.
"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".
C.106
This directive allows adding a localised damping on some
d.o.f.s of some particular nodes.
"AMORTISSEMENT" ( /LECDDL/ "BETA" beta "FREQ" freq /LECTURE/ )
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 cutoff frequency:
f_{c}=β f will be damped in a pseudoperiodic 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 F_{amort} of the form:
F_{amort} = − 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).
C.108
This directive allows to model nonlinear 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.
"APPUI" [ "RESS" ; "AMOR" ] [ "TRAN" ; "ROTA" ] "CMPX" cmpx "CMPY" cmpy "CMPZ" cmpz "COEF" coef "NUFO" nufo <"MASS" mass> <"INCR" incr> <"DECX" decx> <"DECY" decy> /LECTURE/
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.E4):
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) )
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).
C.109
This directive allows to model a complex nonlinear 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.
"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/
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 keyword 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):
F_{x} = k_{x} f_{1}(D_{x}) + a_{x} f_{2}(V_{x}) 
If the displacement (or the velocity) is positive, the function
f1 (or f2) must be negative in order to obtain a correct reaction.
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.
C.110
This option enables materials with a linear elastic
behaviour to be used.
"LINE" "RO" rho "YOUN" young "NU" nu <"VISC" visc "KRAY" kray "MRAY" mray> /LECTURE/
This option may be repeated as many times as necessary.
The components of the ECR table are as follows:
ECR(1): pressureECR(2): Von Mises criterion
ECR(1): Von Mises criterion (membrane)ECR(2): Von Mises criterion (membrane + bending)
ECR(1): Von Mises criterion (bending)ECR(2): Von Mises criterion (membrane + bending + torsion)
ECR(1): elastic strainECR(2): Von Mises criterion
C.111
This directive allows to model a complex nonlinear twonode 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 (twonode 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 nonzero 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.
"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/
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 keyword 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):
F_{x} = k_{x} f_{1}(D_{x}) + a_{x} f_{2}(V_{x}) 
If the displacement (or the velocity) is positive, the function
f1 (or f2) must be negative in order to obtain a correct reaction.
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.
C.112
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 7.7.1, VM23 7.7.38) for the elements used.
"GLIN" "RO" rho "YOUN" young "NU" nu /LECTURE/
The output variables are according to the material in which the generic material is converted.
C.113
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 7.7.7, VM23 7.7.38) for the elements used.
"GPLA" "RO" rho "YOUN" young "NU" nu "ELAS" sige ... ... "TRAC" npts*( sig eps ) /LECTURE/
The output variables are according to the material in which the generic material is converted.
C.114
This directive allows to model a complex nonlinear twonode 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 (twonode 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.
"RESG" <[ "KX" kx ; "KY" ky ; "KZ" kz ] "NFKT" nufo1> <[ "AX" ax ; "AY" ay ; "AZ" az ] "NFAT" nufo2> /LECTURE/
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 keyword 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):
F_{x} = k_{x} f_{1}(D_{x}) + a_{x} f_{2}(V_{x}) 
If the displacement (or the velocity) is positive, the function
f1 (or f2) must be negative in order to obtain a correct reaction.
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.
This option enables to specify materials with a perfect
elastoplastic behaviour (DruckerPrager criterion).
"DRUC" "RO" rho "YOUNG" young "POISSON" nu ... ... "TRACTION" sigt "COMPRESSION" sigc ... ... < "FRACTURE" pf > /LECTURE/
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 DruckerPrager 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 nonexistant 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 DruckerPrager 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.
The different components of the ECR table are as follows:
ECR(1): pressureECR(2): Von Mises
ECR(3): equivalent plastic strain
ECR(4): D.P. criterion ( always <= 0 )
ECR(5): cohesion (becomes nonexistant in the case of brittle rupture)
This subdirective enables materials with an elastoplastic
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.
"VMIS" $[ "PARF" . . . ; "ISOT" . . . "DYNA" . . . "TETA" . . . ]$
This subinstruction 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 material.
"VMIS" "PARF" "RO" rho "YOUN" young "NU" nu "ELAS" sige ... ... /LECTURE/
The law of behaviour is described by the following diagram of stresses and strains:
The components of the ECR table are as follows:
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(1): Von Mises criterion (membrane)
ECR(2): Von Mises criterion (membrane + bending)
ECR(3): plastic strain
ECR(1): elastic strain
ECR(2): Von Mises criterion
ECR(3): plastic strain
"VMIS" "ISOT" "RO" rho "YOUN" young "NU" nu "ELAS" sige ... <FAIL fail LIMI limi> ... "TRAC" npts*( sig eps ) /LECTURE/
fail = 1 for a criterion based upon Von Mises stress (membrane + bending + torsion),
fail = 2 for a criterion based upon plastic strain.
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.
The components of the ECR table are as follows:
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit
ECR(1): pressure
ECR(2): Von Mises criterion
ECR(3): plastic strain
ECR(7): new elastic limit
ECR(1): Von Mises criterion (membrane)
ECR(2): Von Mises criterion (membrane + bending)
ECR(3): plastic strain
ECR(7): new elastic limit
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(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)
C.135
Isotropic Von Mises material depending on strain rate.
"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/
fail = 1 for a criterion based upon Von Mises stress (membrane + bending + torsion),
fail = 2 for a criterion based upon plastic strain.
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 s1 and P = 10 (Forrestal and Sagartz 1978).
For ordinary steel, it is usually assumed:
D = 40 s1 and P = 5 (Symonds 1965).
For titanium TI50A, the values suggested are:
D = 120 s1 and P = 9 (Symonds et Chon 1974).
For aluminum alloys, some authors use
D = 6500 s1 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 ISPRACADARACHE):
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/ 104 ) ** ALFAY
The dynamic increase factor for the ultimate stress is given by:
SIG_U(dyna) = SIG_U(stat) * DIF_U DIF_U = ( EPSP / 104 ) ** 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,
TwentyEighth 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}.
For all formulations, the strain rate EPSP is filtered with a first order lowpass 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.
The components of the ECR table are as follows:
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
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
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
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
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
Von Mises isotropic material dependent upon the temperature.
"VMIS" "TETA" "RO" rho < "NU" nu >... ... "NBCOURBE" nc*( "TETA" ti "YOUNG" yg <"NUT"> nut ... ... "TRAC" npts*( sig eps ) ) /LECTURE/
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 temperaturedependant Poisson coefficient or not
which can be sufficient in case of steels for example.
The components of the ECR table are as follows:
ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : equivalent plastic strain
ECR(1) : pressure
ECR(2) : Von Mises criterion
ECR(3) : equivalent plastic strain
ECR(1) : Von Mises criterion (membrane)
ECR(2) : global Von Mises criterion (membrane + bending)
ECR(3) : equivalent plastic strain
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.
"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/
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.
The various components of the ECR table are as follows:
ECR(1) : hydrostatic pressureECR(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
C.147
This directive allows to describe the behaviour of an elastoplastic 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.
"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/
A detailed description of the model can be found in the report
DMT/98026A, available on request.
The components of the ECR table are as follows for Continuum elements:
ECR(1) : pressureECR(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.
C.148
This directive allows to describe the behaviour of an ZirelliArmstrong 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.
"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/
The components ov the ECR table are as follows for Continuum elements:
ECR(1) : pressureECR(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.
C.149
This directive allows to describe the behaviour of an elastoplastic material that may undego some damage, according to the LemaitreChaboche 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
"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/
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/98036A, available on request.
The components of the ECR table are as follows for Continuum elements :
ECR(1) : pressureECR(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.
C.150
This option is used to define materials such as concrete, soil,
rock, etc.
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 keyword, 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.
The data can be classified in 4 groups.
"BETON" "RO" rho "YOUN" young "NU" nu < "ALPH" alph > < "PREC" prec >
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 >
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 threedimensional 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.
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 (sig1sig3,
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 workhardening. 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 workhardening.
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 sig1sig3   lcdpcd . . . . . . . . *  * .  * . lctpct . . . .*  * .  * .  * . lcs  . * .  * * .  * * . * * . O .> eps1 epcs epcd
"LCS" lcs "EPCS" epcs < "LBIC" lbic > or < "LCT" lct "PCT" pct > < "LCD" lcd "PCD" pcd "EPCD" epcd >
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
The different components of the ECR table are as follows:
ECR(1): hydrostatic pressureECR(2): Von Mises criterion
ECR(3): equivalent plastic strain
ECR(4): crack angle in the (XY) 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).
All values are given in S.I. units.
RO = 2.400E+03 Kg / m3 YOUN = 37000E+06 Pa NU = 0.2100000 ALPH = 1.200E05 PREC = 1.000E03
BETA = 0.1000000 LTR = 4.440E+06 Pa EPTR = 3.600E04
LCS = 44.400E+06 Pa EPCS = 1.200E02 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 = 6.000E02
LPH = 134.887E+06 Pa PENT = 7088.120E+06 Pa
C.151
Isotropic viscodamage and viscoplastic concrete material.
"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/
1/  BE CAREFUL the initial porosity influence the real young modulus
Km=YOUNG/(3*(12*NU))
Gm=YOUNG/(2*(1+NU))
2/  Compressibily and shear moduli with porosity f (MoriTanaka)
Kporo=4*XKm*XGm*(1f)/(4*XGm+3*XKm*f)
Gporo=XGm*(1f)/(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/(1D)*(FNT/MVP)**NVP * dFNT/dSIG
5/  Porosity evolution:
Df = K * f/(1f) * (FNT/MVP)**NVP
f(t+dt) = f(t) + df
6/  Damage threshold function in tension and compression:
FDi = (EPSE  ED0  1/Ai*(Di/(1Di))**(1/Bi))
7/  Damage evolution in tension and compression:
Di= (FDi/MDi)**NDi
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
C.152
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 Coulombtype 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.
"BPEL" "FRLI" phil "FRCO" phic /LECTURE/
This material can be used with RNFR element (nonlinear frictional spring) only.
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.
C.153
Isotropic linear elastic with a modified Mazars damage for concrete and brittle rupture materials.
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 CHUZELMARMOT, "Caractérisation expérimentale et simulation
numérique d’impacts de glace à haute vitesse",
Thèse de doctorat, Université MEGA de Lyon  INSA Lyon, 2009.
"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/
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.
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
C.154  Feb 13
Concrete material with induced anisotropic damage represented by one damage variable and modelling biaxial behaviour.
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 LaMSIDUMR EDF/CNRS/CEA (2012)[817]
"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/
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
DPDC A threeinvariant 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.
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)
All values must be given in SI units.
"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/
Beware! ftr should be such that: 0.06 < ftr < 0.11
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(1722): Components of elastoplastic stress tensor
ECR(2328): Components of viscoplastic stress tensor
ECR(2934): 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
C.160
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 (TulerButcher) is available.
"CRIT" $[ "TULE" <"SIGL" sigl > <"EPSL" epsl > <"TAUL" taul > "SIGS" sigs "LAMB" lamb <"KER" ker > ]$ /LECTURE/
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, SteinbergGuinan 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 TulerButcher is given by the following expression where
σ_{1},σ_{2},σ_{3} representing the principal stresses:
∫ 
 (Max(σ_{1},σ_{2},σ_{3})−σ_{s})
^{λ} dt < ker 
The results stored in the ECR table (5 values) are, according
to the material type:
TulerButcher :
ECR(1) = Maximum principal stress
ECR(2) = Maximum principal deformation
ECR(3) = Octahedral shear stress
ECR(4) = Volume deformation
ECR(5) = TulerButcher criterion
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 .472845E2 476.26E6 7.2835E2 518.51E6 15.700E2 538.03E6 21.607E2 550.24E6 26.083E2 LECT TOUS LOI 3 CRIT TULE SIGS 1E7 LAMB 1.0 LECT TOUS
C.161
Concrete material with induced anisotropic damage.
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.
"EOBT" "RO" rho "YOUN" young "NU" nu "K0" k0 "K1" k1 "K2" k2 "ECRB" ecrb "ECRD" ecrd < "DC" dc > < "DM" dm > /LECTURE/
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
C.162
This section describes an elasticdamage material with gradient regularization. The development is still in progress and a more detailed presentation can be found in [902], [903].
This model can be used to predict crack initiation and propagation in a quasibrittle 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 XFEM 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 fracturetype 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 boundconstrained (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.
"ENGR" "RO" rho "YOUN" young "NU" nu "GC" gc [ "ELL" ell ; "SIGM" sigm ] < "LAW" law "TC" tc "AC" ac > /LECTURE/
a(α)=(1−α)^{2} , w(α)=w_{1}α 
a(α)=(1−α)^{2} , w(α)=w_{1}α^{2} 
a(α)=(1−α)^{2} , w(α)=w_{1}  ⎛ ⎝  1−(1−α^{2})  ⎞ ⎠ 
No public ECR components are available for output.
C.165
This directive allows to define materials obtained by
homogenisation through the thickness of different
layers (or plies) each having a linear orthotropic behaviour.
"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" 
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.
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 shellECR(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 shellECR(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)
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
C.170
This directive allows to define composite materials using
the CHANGCHANG 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.
"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"
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 keywords 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.
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 fibermatrix delamination.
C.181
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 (JLemaitre, LChaboche. Ed: Dunod, 1986).
"ORTH" "RO" rho "YG1" yg1 "YG2" yg2 "YG3" yg3 "NU12" nu12 "NU13" nu13 "NU23" nu23 "G12" g12 "G13" g13 "G23" g23 /LECTURE/
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.
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.
C.182
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 (JLemaitre, LChaboche. Ed: Dunod, 1986).
Stress and strain are expressed in the user coordinate system.
"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/
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):
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.
C.183
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 : d_{1},d_{2},d_{3},d_{12},d_{13},d_{23}. 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.
D_{nc} = dc < 
 > 
ḋ = 
 ⎛ ⎝  1−e^{−a<Dnc−d>}  ⎞ ⎠ 
This material behavior has been studied in [911].
"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/
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)):
The different components of the ECR table are as follows, for the
continuum elements:
ECR(1): Pressure (1/3σ_{kk}).
ECR(2): Von Mises criterion.
ECR(3:7) : Unused.
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.
C.184
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 : d_{1}^{m},d_{2}^{m},d_{3}^{m} (direction 1, 2 and 3), and 4 fiber
damages : d_{1}^{f},d_{2}^{f},d_{3}^{f},d_{4}^{f} (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.
The Onera damage model (ODM) is theorized in [910]. It’s implementation in Europlexus is studied in [911].
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−e^{−a<Dnc−d>}  ⎞ ⎠ 
The constitutive law is :
C_{eff}^{−1}=S_{eff}=S_{0} + 
 η_{i} d_{i}^{m} H_{0i}^{m}+ 
 d_{j}^{f} H_{0j}^{f} = C_{matrix}^{−1} + 
 d_{j}^{f} H_{0j}^{f} 
[σ] = C_{matrix}.[є] − C_{eff}.[є_{residual}] 
where the matrix 6x6 S_{0} and H_{0}^{i} are defined as:
Compliance S_{0}: S_{0}(1,1)=1/E_{1}^{0}, S_{0}(2,2)=1/E_{2}^{0}, S_{0}(3,3)=1/E_{3}^{0} ; S_{0}(1,2)=−ν_{12}/E_{1}^{0}, S_{0}(1,3)=−ν_{13}/E_{1}^{0}, S_{0}(2,3)=−ν_{23}/E_{2}^{0} ; S_{0}(4,4)=1/G_{12}^{0}, S_{0}(5,5)=1/G_{23}^{0}, S_{0}(6,6)=1/G_{13}^{0}, and 0 otherwise.
Matrix damage effect tensors H_{0}^{m1}, H_{0}^{m2}, H_{0}^{m3}:
H_{0}^{m1}: H_{0}^{m1}(1,1)=h_{1}^{n}/E_{1}^{0} , H_{0}^{m1}(4,4)= h_{1}^{p}/G_{12}^{0},
H_{0}^{m1}(6,6)= h _{1}^{pn}/G_{13}^{0}, and 0 otherwise.
H_{0}^{m2}: H_{0}^{m2}(2,2)=h_{2}^{n}/E_{2}^{0} , H_{0}^{m2}(4,4)= h_{2}^{p}/G_{12}^{0},
H_{0}^{m2}(5,5)= h_{2}^{pn}/G_{23}^{0}, and 0 otherwise.
H_{0}^{m3}: H_{0}^{m3}(3,3)=h_{3}^{n}/E_{3}^{0} , H_{0}^{m3}(5,5)= h_{3}^{p}/G_{23}^{0},
H_{0}^{m3}(6,6)= h_{3}^{pn}/G_{13}^{0}, and 0 otherwise.
Fiber damage effect tensors H_{0}^{f1}, H_{0}^{f2}, H_{0}^{f3}, H_{0}^{f4}:
H_{0}^{fi}: H_{0}^{fi}(1,1)=hf_{1}^{i}/E_{1}^{0} , H_{0}^{fi}(2,2)=hf_{2}^{i}/E_{2}^{0} , H_{0}^{fi}(3,3)=hf_{3}^{i}/E_{3}^{0} ,
H_{0}^{fi}(1,2)=H_{0}^{fi}(2,1)=hf_{4}^{i}.S_{0}(1,2) , H_{0}^{fi}(1,3)=H_{0}^{fi}(3,1)=hf_{5}^{i}.S_{0}(1,3) ,
H_{0}^{fi}(2,3)=H_{0}^{fi}(3,2)=hf_{6}^{i}.S_{0}(2,3) ,
H_{0}^{fi}(4,4)= hf_{7}^{i}/G_{12}^{0}, H_{0}^{fi}(5,5)= hf_{8}^{i}/G_{23}^{0}, H_{0}^{fi}(6,6)= hf_{9}^{i}/G_{13}^{0}.
Then, the matrix thermodynamic forces y_{i}^{n},y_{i}^{t} are computed in function of positive strain
as following:
y_{i}^{n}= 1/2 C_{ii}^{0}.є_{i}^{+}.є_{i}^{+} for i ∈ 1,2,3
and y_{1}^{t}= (b_{1}.C_{66}^{0}.є_{13}^{+}.є_{13}^{+} + b_{2}.C_{44}^{0}.є_{12}^{+}.є_{12}^{+}),
y_{2}^{t}= (b_{3}.C_{55}^{0}.є_{23}^{+}.є_{23}^{+} + b_{4}.C_{44}^{0}.є_{12}^{+}. є_{12}^{+}),
y_{3}^{t}= (b_{5}.C_{66}^{0}.є_{13}^{+}.є_{13}^{+} + b_{6}.C_{55}^{0}.є_{23}^{+}.є_{23}^{+}).
The fiber thermodynamic forces y_{f}^{i} are computed in function of strain as following:
y_{f}^{1}= 1/2 C_{0}(1,1).є_{1}^{+}.є_{1}^{+}, y_{f}^{2}= 1/2 C_{0}(1,1).є_{1}^{−}.є_{1}^{−},
y_{f}^{3}= 1/2 C_{0}(2,2).є_{2}^{+}.є_{2}^{+}, y_{f}^{4}= 1/2 C_{0}(2,2).є_{2}^{−}.є_{2}^{−}.
The damage law is the following :
d_{i}=max  ⎛ ⎝  g_{i}(y_{i}),d_{i}^{0}  ⎞ ⎠ 
where
g_{i}=d_{ci}  ⎛ ⎜ ⎝  1− e 
 ⎞ ⎟ ⎠ 
and if : Δ є_{i}^{f} ≤ є_{i} ,
η_{i}=1 
if : −Δ є_{i}^{f} ≤є_{i} ≤ Δ є_{i}^{f},
η_{i}= 
 ⎛ ⎜ ⎜ ⎝  1−cos  ⎛ ⎜ ⎜ ⎝ 

 ⎞ ⎟ ⎟ ⎠  ⎞ ⎟ ⎟ ⎠ 
if : є_{i} ≤ −Δ є_{i}^{f} ,
η_{i}=0 
where
Δ є_{i}^{f}=(1+a_{if}d_{i}^{m})Δ є_{i}^{0} 
"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/
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.
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.
C.185
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.
"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/
This material model is taken from the thesis of P. François:
“Plasticité du bois en compression multiaxiale : 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):
E_{c}=E_{1} . coe1 
ν_{c}= 

G_{c}= 

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).
C.186
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: E_{11}, E_{22},
E_{33}, ν_{12}, ν_{13}, ν_{23}, G_{12}, G_{13}, G_{23}. The rate dependency is
based on the following polynomial law:
X_{ij}(ε) = 
 X_{ij}^{k} (log(ε))^{k} (1) 
As for ORTS directive, stress and strain are expressed in the user coordinate system.
"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/
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):
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 12direction.
ECR(20): v5  Strain rate for shear in 23direction.
ECR(21): v6  Strain rate for shear in 13direction.
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.
C.200
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= 

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.
"MASS" xm < "YOUN" youn> < "NU" nu > /LECTURE/
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.
The different components of the ECR table are as follows:
ECR(1): integrated impulse from the originECR(2): sum of the instantaneous reaction forces.
C.210
This directive enables the elimination of elements in a mesh.
"FANT" rho /LECTURE/
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.
C.220
The directive enables the user to enter his own constitutive laws.
$ "STRU" ... $ $ "FLUI" ... $ "LIBR" $ "PMAT" ... $ < "PARA" a b c ... > /LECTURE/ $ "MECA" ... $ $ "CLIM" ... $
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.
In the examples proposed in the following pages, there are some
calls to utility routines that are available within EUROPLEXUS:
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.
This directive introduces a userdefined constitutive behaviour
of structural type (“STRUCTURE”).
"LIBR" "STRU" num "RO" rho "YOUN" young "NU" nu ... ... < "PARA" /LECPARA/ > /LECTURE/
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 2D plane, 2D axisymmetric or
3D 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) = PressureECR(2) = Von Mises
The eight other locations are free.
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
usersupplied 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”).
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/(12*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
This directive introduces a userdefined constitutive behaviour
of fluid type (“FLUIDE”).
"LIBR" "FLUI" num "RO" rho "PINI" pini "PREF" pref "EINT" ei ... ... < "PARA" /LECPARA/ > /LECTURE/
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 2D plane, 2D axisymmetric or
3D 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) = PressureECR(2) = Density.
The eight other locations are free.
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 (C_{v}), which allow to obtain
the temperature (θ).
θ = 

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
This directive introduces a userdefined constitutive behaviour
of type material point (“POINT MATERIEL”).
"LIBR" "PMAT" num "MASS" m < "PARA" a b c ... > /LECTURE/
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 3D.
Be careful to respect the conventions chosen to rank the
tensor components according to the
3D 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.
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.
SUBROUTINE MPLIBR(NUM,T,PARAM,AMAS,ECR,X,U,F,V,DTSTAB)
*
* 
*
* materiau libre pour les points mat. m.lepareux 0895
*
* 
*
* 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
This directive introduces a userdefined constitutive behaviour
of mechanism type (“MECANISME”).
"LIBR" "MECA" num < "PARA" a b c ... > /LECTURE/
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.
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 K_{T} = 1E3, and the rotational one is
K_{R} = 4E6.
The free material has the userspecified 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
SUBROUTINE MMLIBR(NUM,TT,NBPAR,XMAT,X,DU,F,XMA,V,DFX,
& ECR,SIG,DEPS,PI,DWINT,IEL,DTSTAB)
*
* 
*
* materiau libre mecanisme m.lepareux 1200
*
* 
*
* 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
This directive introduces a userdefined constitutive behaviour
of the boundary condition type (“CONDITION AUX LIMITES"”).
"LIBR" "CLIM" num "PREF" pref < "PARA" a b c ... > /LECTURE/
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 7th 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 deviceECR(2) = Density of the donor element
The eight other locations are free.
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 O_{x}.
As a consequence of the detachment, the crosssection 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) !
SUBROUTINE CLIBRE(NUNU,PREF,PARAM,AIRE,RHO,PAMON,VN,T,ECR,DP)
*
* 
*
* materiau libre pour el. cl1d m.lepareux 0895
*
* 
*
* 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=1D6, RMIN=1D3, 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
C.240
This directive allows users to define their own constitutive
laws for the particle elements (BILLE).
"BILLE $ "LIBR" num "RO" rho $ ... < "FONC" numfon > ... < "PARA" a b c ... > /LECTURE/
The number (num) allows to distinguish between several
userdefined 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
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/
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 = NUMVOIIEME 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(AH,OZ)
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
C.241
This option enables to choose the Von Mises material with
the implementation developed at Ispra. Elastoplasticity is
implemented via a radial return algorithm. Only isotropic
hardening is activated to date. There is no dependency on
temperature nor on strain rate.
"VM23" "RO" rho "YOUN" young "NU" nu "ELAS" sige ... <"FAIL" $[ VMIS ; PEPS ; PRES ; PEPR ]$ "LIMI" limit> "TRAC" npts*(sig eps) /LECTURE/
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 continuumlike elements, at least when there are large rotations.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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 postprocess 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).
This is the material to be used for the interface elements
of type ED1D (see INT.80).
"VM1D" "PT1D" pt1d /LECTURE/
Note that when several ED1D elements are present in a coupled
1D/multiD calculation, then each ED1D element
must have a separate VM1D material, because the material is used
to carry the information of the associated 1D node to each
one ED1D element (pt1d).
The components of the ECR table are as follows :
ECR(1) : unusedECR(2) : unused
ECR(3) : unused
ECR(4) : unused
ECR(5) : unused
ECR(6) : unused
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.
"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/
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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(2): current equivalent stress (Von Mises)
ECR(3): current equivalent plastic strain
ECR(4): current yield stress
ECR(5): xoverstress
ECR(6): yoverstress
ECR(7): xyoverstress
ECR(8): zoverstress
ECR(9): previous time
ECR(10): yzoverstress
ECR(11): xzoverstress
Let P represent the point of intersection (in the equivalent
stress  equivalent strain space) between the unloading path
and the equilibrium stressstrain curve.
ECR(12): total xstrain at point PECR(13): total ystrain at point P
ECR(14): total zstrain at point P
ECR(15): total xystrain at point P
ECR(16): total yzstrain at point P
ECR(17): total xzstrain 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 stressstrain diagramECR(22): new xstress at point P
ECR(23): new ystress at point P
ECR(24): new xystress at point P
ECR(25): new zstress at point P
ECR(26): new yzstress at point P
ECR(27): new xzstress 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 postprocess 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).
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.
Elastoplasticity 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, "NonSmooth
Multisurface Plasticity and Viscoplasticity. Loading/Unloading
Conditions and Numerical Algorithms", Int. J. Num. Meth. Eng.,
Vol 26, pp. 21612185 (1988).
"VMSF" "RO" rho "YOUN" young "NU" nu "ELAS" sige "ETA" eta ... "TRAC" npts*(sig eps) /LECTURE/
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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(2): current equivalent stress (Von Mises)
ECR(3): current equivalent plastic strain
ECR(4): current yield stress
ECR(5): xstress before viscoplastic correction
ECR(6): ystress before viscoplastic correction
ECR(7): xystress before viscoplastic correction
ECR(8): zstress before viscoplastic correction
ECR(9): yzstress before viscoplastic correction (3D only)
ECR(10): xzstress before viscoplastic correction (3D only)
ECR(11): current time
ECR(12): sound speed
Note that in order to postprocess 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).
This directive enables to choose an elastoplastic constitutive theory with Drucker Prager yield surface, associative or nonassociative 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, "NonSmooth
Multisurface Plasticity and Viscoplasticity. Loading/Unloading
Conditions and Numerical Algorithms", Int. J. Num. Meth. Eng.,
Vol 26, pp. 21612185 (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.
More information on the formulation of this material model may be found in reference [120].
"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/
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 continuumlike 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 quasistatic 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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(2): current equivalent stress (Von Mises)
ECR(3): current equivalent plastic strain
ECR(4): cohesion
ECR(5): xstress before viscoplastic correction
ECR(6): ystress before viscoplastic correction
ECR(7): xystress before viscoplastic correction
ECR(8): zstress before viscoplastic correction
ECR(9): yzstress before viscoplastic correction (3D only)
ECR(10): xzstress before viscoplastic correction (3D only)
ECR(11): current time
ECR(12): alfa
ECR(13): zone (sigma  tau plane)
ECR(14): yield (f=alfa*sigma+taucohe), >0 if plast
ECR(15): failure flag (0=virgin Gauss Point, 1=failed Gauss Point).
ECR(16): sound speed
Note that in order to postprocess 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).
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.
"COMM" "RO" rho "YG1" yg1 "YG2" yg2 "YG3" yg3 "NU12" nu12 "NU13" nu13 "NU23" nu23 "G12" g12 "G13" g13 "G23" g23 /LECTURE/
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).
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.
The directive is used to enter materials with a modified Camclay 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 ρ_{w}=0, the value given for ρ
is the density of the (dry) soil alone, and the value
given for z_{f}, if any, is irrelevant.
More information on the formulation of this material model may be found in reference [147].
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/
This option may be repeated as many times as necessary.
This material model seems unable to start from initial stressfree conditions,
so that insitu (initial) stresses should always be specified.
The initial insitu 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 ycoordinate
in 2D, to the zcoordinate 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 oneelement tests to check the behaviour of the constitutive law, or of simple laboratory experiments.
In this case, the code simply sets:
σ_{1}=−p , σ_{2}=−p , σ_{3}=−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 z_{f} and s_{lev} are the vertical coordinates of the upper water and soil levels, respectively. Normally it should be s_{lev}>z_{f} so that the soil layer between z_{f} and s_{lev} 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 z_{c}. Then the vertical stress due to the soil weight (effective stress) is:
σ_{v} = −g(ρ−ρ_{w})(s_{lev}−z_{c}), 
where ρ is the density of the wet soil (soil plus water), ρ_{w} 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:
σ_{v}=MIN(σ_{v},0). 
The horizontal stress is given by:
σ_{h}=K_{0}σ_{v}, 
where K_{0} is the k0 parameter specified above. Then, the code sets:
σ_{1}=σ_{h} , σ_{2}=σ_{h} , σ_{3}=σ_{v}. 
In addition to soil (effective) stresses, the water pressure (hydrostatic) is also evaluated:
p_{w} = −gρ_{w}(z_{f}−z_{c}). 
The water pressure may not be positive:
p_{w}=MIN(p_{w},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.
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 J_{2}′ (i.e. square root of Von Mises equivalent stress)
ECR(3) : current void ratio
ECR(4) : hardening parameter P_{c} (isotropic consolidation pressure)
ECR(5): sound speed
ECR(6): water overpressure (u)
ECR(7): initial water pressure (p_{0}), p = p_{0} + u (p is the total water pressure)
ECR(8): volumetric strain (є_{V} = є_{x} + є_{y} + є_{z})
ECR(9): deviatoric strain
є_{d} = √2/3[(є_{x}−є_{y})^{2}+ (є_{y}−є_{z})^{2}+ (є_{y}−є_{z})^{2}]+ (γ_{xy}^{2} + γ_{yz}^{2} + γ_{xz}^{2})
The components of the stress tensor are as follows:
SIG(1): σ_{x}SIG(2): σ_{y}
SIG(3): σ_{z}
SIG(4): τ_{xy}
SIG(5): τ_{yz} (only 3D)
SIG(6): τ_{xz} (only 3D)
Let M_{1} be the ratio between the second invariant of the stress tensor J_{2} and the first invariant of the stress tensor J_{1} 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 M_{2} be the ratio between the second invariant of
the deviatoric stress tensor J_{2}′ and the first invariant of the
stress tensor J_{1} at critical state.
The M parameter defined above in the input syntax corresponds
to M_{1}.
However, note that in the model description of the CAMC material the
quantity g(θ) corresponds rather to M_{2}.
The following relation holds between the two quantities:
M_{2} = M_{1} / √3.
Note that in order to postprocess 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)
The option is used to enter materials with a modified Camclay 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.
More information on the formulation of this material model may be found in reference [123].
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/
This option may be repeated as many times as necessary.
The initial insitu 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 ycoordinate
in 2D, to the zcoordinate 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 oneelement tests to check the behaviour of the constitutive law, or of simple laboratory experiments.
In this case, the code simply sets:
σ_{1}=−p , σ_{2}=−p , σ_{3}=−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 s_{lev} 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 z_{c}. Then the vertical stress due to the soil weight (effective stress) is:
σ_{v} = −gρ(s_{lev}−z_{c}), 
where ρ is the density of the (dry) soil. The vertical stress may not be positive:
σ_{v}=MIN(σ_{v},0). 
The horizontal stress is given by:
σ_{h}=K_{0}σ_{v}, 
where K_{0} is the k0 parameter specified above. Then, the code sets:
σ_{1}=σ_{h} , σ_{2}=σ_{h} , σ_{3}=σ_{v}. 
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.
The different components of the ECR table are as follows:
ECR(1) : current hydrostatic pressure 1/3(σ_{x}+σ_{y}+σ_{z})ECR(2) : current bulk modulus
ECR(3) : second invariant of the deviatoric cumulated strain
ECR(4) : hardening parameter p_{0}
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): σ_{x}SIG(2): σ_{y}
SIG(3): σ_{z}
SIG(4): τ_{xy}
SIG(5): τ_{yz} (only 3D)
SIG(6): τ_{xz} (only 3D)
Let M_{1} be the ratio between the second invariant of the stress tensor J_{2} and the first invariant of the stress tensor J_{1} 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 M_{2} be the ratio between the second invariant of
the deviatoric stress tensor J_{2}′ and the first invariant of the
stress tensor J_{1} at critical state.
The M parameter defined above in the input syntax corresponds
to M_{1}.
However, note that in the model description of the CLAY material
(An Implementation of the CamClay
ElastoPlastic Model Using a Backward Interpolation and
ViscoPlastic Regularization, Technical Note I.96.239)
the quantity M corresponds rather to M_{2}.
The following relation holds between the two quantities:
M_{2} = M_{1} / √3.
Note that in order to postprocess 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).
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 elastoplastic in traction.
"FUNE" "RO" rho "YOUN" young "NU" nu "ELAS" sige "ERUP" erup ... ... "TRAC" npts*(sig eps) /LECTURE/
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.
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 postprocess 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).
In the JohnsonCook model Elastoplasticity is
implemented via a radial return algorithm. Only isotropic
hardening is activated to date and strainrate dependency is
included in the model. However, no temperature effects are
included in the present implementation.
The implementation of this material model is described in reference [167].
The JohnsonCook constitutive relation is given by:
σ_{eq} =  ⎡ ⎣  A_{1} + A_{2}  ⎛ ⎝  ε_{eq}^{p}  ⎞ ⎠  ^{λ2}  ⎤ ⎦  ⎡ ⎢ ⎢ ⎣  1 + λ_{1} ln  ⎛ ⎜ ⎜ ⎝ 
 ⎞ ⎟ ⎟ ⎠  ⎤ ⎥ ⎥ ⎦  ⎛ ⎝  1 − θ^{m}  ⎞ ⎠  (2) 
where:
The JohnsonCook 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 strainrate 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 JohnsonCook’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
ε_{eq,ref}^{p}
is the value of equivalent plastic strain rate under which the material
behaves in a “static” (i.e., strainrate 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 λ_{1} are interconnected.
"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/
The JohnsonCook failure criterion is given by:
ε_{p}^{f} =  ⎡ ⎣  D_{1} + D_{2} exp  ⎛ ⎝  D_{3} σ^{*}  ⎞ ⎠  ⎤ ⎦  ⎡ ⎢ ⎢ ⎣  1 + D_{4} ln  ⎛ ⎜ ⎜ ⎝ 
 ⎞ ⎟ ⎟ ⎠  ⎤ ⎥ ⎥ ⎦  (3) 
where:
The damage parameter D triggers failure when it reaches 1. It is computed as:
D = ∑ 
 (4) 
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(2): current equivalent stress (VonMises)
ECR(3): current equivalent plastic strain
ECR(4): current yield stress
ECR(5): sound speed
ECR(6): equivalent strain rate (VonMises)
ECR(7): failure flag (0=virgin Gauss Point, 1=failed Gauss Point)
ECR(8): damage parameter for the JohnsonCook failure criterion
Note that in order to postprocess 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).
This directive enables to choose the LudwigPrandtl model,
a purely elastoplastic 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.
The implementation of this material model is described in reference [167].
"VMLP" "RO" rho "YOUN" young "NU" nu "COA1" coa1 "COA2" coa2 "CLB1" clb1 "CLB2" clb2 "CLB3" clb3 "CLB4" clb4 ... /LECTURE/
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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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 postprocess 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).
This directive enables to choose the Ludwik model, a purely
elastoplastic model implemented at Ispra. Elastoplasticity is
implemented via a radial return algorithm. Only isotropic hardening
is activated to date. There is no dependency on temperature
nor on strain rate.
The implementation of this material model is described in reference [167].
"VMLU" "RO" rho "YOUN" young "NU" nu "ELAS" sige ... "COA2" coa2 "COEN" coen ... /LECTURE/
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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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 postprocess 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).
This directive enables to choose the ZerilliArmstrong model
with the implementation developed at Ispra. Elastoplasticity
is implemented via a radial return algorithm. Only isotropic
hardening is activated to date and strainrate dependency is
included. However, no dependency on temperature exist in the
present version of the model.
The implementation of this material model is described in reference [167].
"VMZA" "RO" rho "YOUN" young "NU" nu "COA1" coa1 ... "COA2" coa2 "COA3" coa3 "COA4" coa4 "CLB1" clb1 "CLB2" clb2 "CLB3" clb3 ... /LECTURE/
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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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 postprocess 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).
This directive enables to specify a DruckerPrager 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 J_{1}√J_{2}′ space reaches the failure line (a straight line)
of equation:
√ 
 =K−α J_{1} 
where J_{1}=σ_{x}+σ_{y}+σ_{z} is the first invariant of the stress tensor and J_{2}′ is the second invariant of the deviatoric stress tensor:
J_{2}′= 
 (σ_{x}^{2} + σ_{y}^{2} + σ_{z}^{2} −σ_{x} σ_{y} −σ_{x} σ_{z} −σ_{y} σ_{z}) + τ_{xy}^{2} + τ_{xz}^{2} + τ_{yz}^{2} 
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 afterfailure 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 postfailure (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).
The material model is described in reference [13]. Note that although the material model had been originally denoted as a MohrCoulomb model, in reality it is a DruckerPrager material. In fact, the yield surface corresponding to the expression given above (using J_{2}′) is a cone with circular cross section (and not with hexagonal crosssection) in principle stress space.
"DRPR" "RO" ro "YOUN" youn "NU" nu "COHE" cohe "FRIC" fric /LECTURE/
The different components of the ECR table are as follows:
ECR(1): current J_{1} invariant (σ_{1}+σ_{2}+σ_{3}).ECR(2): current √J_{2}′ invariant.
ECR(3): failure flag (0=not failed, 1=failed).
ECR(4): sound speed
Note that in order to postprocess 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).
This option enables to specify an aluminium foam material
and follows the DeshpandeFleck model as implemented at NTNU,
Trondheim (N).
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=σ_{p}+γ 
 +α_{2}ln( 
 ) 
The parameter e_{D} is taken from the recent foam density ρ_{f} and the density of the pure material ρ_{f0} by using this equation
e_{D}=1− 

The parameter α defines the shape of the yield surface and can be calculated by using the plastic Poission’s ratio ν_{p}:
α^{2}= 


The parameter γ is the initial hardening factor by reaching the plastic regime. The parameters α_{2} and β can be taken by a best fit of the experimental curve.
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/
The components of the ECR table are as follows:
ECR(1): Equivalent plastic strain (є_{eq})ECR(2): Von Mises effective plastic strain (є_{e})
ECR(3): Volumetric strain (є_{m})
ECR(4): Equivalent stress (σ_{eq})
ECR(5): Von Mises effective stress (σ_{e})
ECR(6): Mean stress (σ_{m})
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): CockcroftLatham damage accumulation (W) when energybased 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.
C.260
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 [879], [880].
"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/
⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦  =  ⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦  ⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦ 
T = k 
 ( 
 +E_{aT} ω_{T}) γ 
If the keyword SHEA is specified then a nonlinear evolution of the shear force is taken into account ([893]). 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 
 ( 
 ω_{T}) 
Q_{p} = 

γ = 

n = CN_{1} є_{1}^{p} + CN_{2} є_{2}^{p} 
m = CM_{1} κ_{1}^{p} + CM_{2} κ_{2}^{p} 
pragmemb1x  0  0 
0  pragmemb1y  0 
0  0  pragmemb1xy 
pragmemb2x  0  0 
0  pragmemb2y  0 
0  0  pragmemb2xy 
pragbend1x  0  0 
0  pragbend1y  0 
0  0  pragbend1xy 
pragbend2x  0  0 
0  pragbend2y  0 
0  0  pragbend2xy 
C = 

"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/
For information about the perforation criterion see references [877], [879].
"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/
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦  =  ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦  ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ 
⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦  =  ⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦  ⎡ ⎢ ⎣ 
 ⎤ ⎥ ⎦ 
T = h 
 γ 
n = CN_{1} є_{1}^{p} + CN_{2} є_{2}^{p} 
m = CM_{1} κ_{1}^{p} + CM_{2} κ_{2}^{p} 
pragmemb1x  0  0 
0  pragmemb1y  0 
0  0  pragmemb1xy 
pragmemb2x  0  0 
0  pragmemb2y  0 
0  0  pragmemb2xy 
pragbend1x  0  0 
0  pragbend1y  0 
0  0  pragbend1xy 
pragbend2x  0  0 
0  pragbend2y  0 
0  0  pragbend2xy 
"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/
⎡ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎦  =  ⎡ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎦  ⎡ ⎢ ⎢ ⎣ 
 ⎤ ⎥ ⎥ ⎦ 
All the limit plastic moments must be defined carefully. When they are
declared as functions (using "FONC"), the domain defined
as plaslim1plaslim2 > 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.
The components of the ECR table are as follows:
ECR(1): є_{x}^{p}ECR(2): є_{y}^{p}
ECR(3): 2 × є_{xy}^{p}
ECR(4): κ_{x}^{p}
ECR(5): κ_{y}^{p}
ECR(6): 2 × κ_{xy}^{p}
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.
ECR(8): D_{1}/D_{1max} for positive bendingECR(9): D_{2}/D_{2max} for negative bending
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.
ECR(11): vxECR(12): vy
ECR(13): vz
ECR(11): angle defining the orthotropic axes referring to the local axes in the shell element plane.ECR(12): 10.
ECR(13): 10.
ECR(14): N_{x}−n_{x}ECR(15): N_{y}−n_{y}
ECR(16): N_{xy}−n_{xy}
ECR(17): M_{x}−m_{x}
ECR(18): M_{y}−m_{y}
ECR(19): M_{xy}−m_{xy}
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)
C.261
This subdirective 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 BlatzKo 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*(I13) + c2*(I23) + c3*(I13)**2 + c4*(I13)(I23) + c5*(I23)**2 + c6*(I13)**3 + c7*(I23)*(I13)**2 + c8*(I13)(I23)**2 + c9(I23)**3 + c10*(I13)**4 + c11*(I23)**2*(I13)**3 + c12*(I13)**2(I23) + c13*(I13)(I23) + K*(Log(I3))**2
For Type 2, the expression of the strain energy density corresponds to :
W = A  ∫  C(I_{1}−3)^{2} dI_{1} + 3 B· log(I_{2}) + K· log(I_{3})^{2} (5) 
Type 3, the Ogden material can be expressed with the following equation
W = 

 ⎛ ⎝  λ_{1}^{αp} + λ_{2}^{αp} + λ_{3}^{αp} −3  ⎞ ⎠  (6) 
with the principal stretch λ.
Type 4, the Ogden material (new formulation) can be expressed with the following equation
W = 

 ⎛ ⎝  λ_{1}^{*αp} + λ_{2}^{*αp} + λ_{3}^{*αp} −3  ⎞ ⎠  + K(J−1−lnJ) (7) 
with λ^{*}=λ J^{−1/3}. K is the bulk modulus, µ_{p} and α_{p} are the material parameters used for this expression.
Type 5, the OgdenStorakers material can be expressed with the following equation
W = 

 ⎛ ⎝  λ_{1}^{αp} + λ_{2}^{αp} + λ_{3}^{αp} −3  ⎞ ⎠  + 

 (J^{−αpβp}−1) (8) 
µ_{p}, α_{p} and β_{p} are the material parameters used for this expression.
The input parameters can be determined by the code if an experimental stressstrain curve is given, see the description below under Case parameters identification. A bestfit is done in this case in order to calculate them. The data must be provided in engineering strains from an 1D 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.
"HYPE" "TYPE" 1 "RO" rho "CO1" c1 . . . . "CO14" c14 "BULK" K /LECTURE/
"HYPE" "TYPE" 2 "RO" rho "CO1" c1 "CO2" c2 "CO3" c3 "BULK" K /LECTURE/
"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/
"HYPE" "TYPE" 4 "RO" rho "CO1" c1 "CO2" c2 "CO3" c3 "CO4" c4 "CO5" c5 "CO6" c6 "CO7" c7 "CO8" c8 "BULK" K /LECTURE/
"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/
This case is recognized by the presennce of the PCAL keyword in the input data, as shown below.
"HYPE" "TYPE" [1345] <"BULK" k> <"NU" nu> "PCAL" npar "TRAC" npts * (strain stress)
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 MooneyRivlin material a twoparameter model is included (CO1 and CO2); for the Ogden material a sixparameter 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).
Note that the range of validity of the hyperelastic material models is as follows:
The components of the ECR table are as follows:
ECR(1): PressureECR(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
C.262
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 mesomodel.
For the Cachan interface damage mesomodel:
The implementation of material TYPE 2 is explained in [867].
"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/
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).
The components of the ECR table are as follows:
ecr(1): Damageecr(2): Equivalent thermodynamic force
ecr(3): Time at which damage reaches 1.0 for failed elements
C.263
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.
"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/
The expression of the elastic limit is given by:
y_{d}=(y_{a}+(y_{max}−y_{a})((1−exp(−e_{p}/e_{r}))^{n}))
+y_{p}(1−√kt/2u_{k}log(c_{1}/ė))
where k is the Boltzmann constant and ė is the strain rate.
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
C.264
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.
"CRTM" "RO" rho "NTEM" ntem "NVF" nvf "NANG" nang "NRCT" nrct "PTEM" ptem "PVF" pvf "PANG" pang "PRCT" prct "E11" ne11 PAR1 valpar11 PAR2 valpar21 PAR3 valpar31 TABLE nvalpar4 nvalpar4 *(E11 PAR4) PAR1 valpar11 PAR2 valpar21 PAR3 valpar32 TABL nvalpar4 nvalpar4*(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/
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).
The components of the ECR table are as follows:
ECR(1) : pressureECR(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
C.270
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 compositesSMCR de type polyester charge de fibres (verre, carbone).
Cette loi est utilisable pour les elements volumiques. Elle se decompose
en trois etapes :
 homogeneisation micromecanique, endommagement,
 plasticite couplee a l’endommagement.
"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/
Le parametre "CRIT" peut prendre l’une des 4 valeurs suivantes :
1 = VON MISES,2 = TRESCA,
3 = TSAIHILL (en σ_{1} et σ_{4}),
4 = TSAIHILL (en σ_{1}, σ_{2} et σ_{4}),
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).
C.275
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.
"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/
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
C.280
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 stresstime curve (equivalent constant stress).
"GLAS" "RO" rho "YOUN" young "NU" nu "CORR" corr "FAIL" $[ VMIS ; PEPS ; PRES ; PEPR; PSAR ]$ "LIMI" limit
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 continuumlike elements, at least when there are large rotations.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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
C.285
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 3SR Laboratory (Grenoble). For theoretical description of the laws see [886], [899].
"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 "AFIL" afil > < "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/ ]
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 steelconcrete 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 steelconcrete 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 steelconcrete 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.
In the discrete element calculation BL3S material is used for the links.
However, for postprocessing 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 COHEtype links per element at t=t_{0}
ECR(2): number of BIMAtype links per element at t=t_{0}
ECR(3): number of COHEtype links per element at t ≥ t_{0}
ECR(4): number of BIMAtype links per element at t ≥ t_{0}
ECR(5): degree of damage of COHEtype links per element
ECR(6): degree of damage of BIMAtype links per element
ECR(7): diameter of the discrete element.
C.290
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.
"LSGL" "RO" rho "YOUN" young "NU" nu <"CORR" corr> <"FAIL" $[ VMIS ; PEPS ; PRES ; PEPR; PSAR; VMPR ]$ "LIMI" limit> <"CR2D"> <"NEIG"> <"REDU" redu>
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 continuumlike 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.
The components of the ECR table are as follows:
ECR(1): current hydrostatic pressureECR(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 postprocess 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).
C.291
Isotropic linear elastic with Mazars damage for SPHC elements.
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.
"SMAZ" "RO" rho "YOUN" young "NU" nu "EPSD" epsd "DCRI" dcri "A" a "B" b "TAUC" tauc "CSTA" csta /LECTURE/
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)
C.292
Isotropic linear elastic with damage for SPHC elements.
"SLIN" "RO" rho "YOUN" young "NU" nu "EPSD" epsd "DCRI" dcri "EPSR" epsr "TAUC" tauc "CSTA" csta /LECTURE/
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)
C.293
This directive allows to describe the behaviour of an elastoplastic material that may undego some damage, according to the Lemaitre model. There is coupling between damage and plasticity, represented by the JohnsonCook 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.
"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/
A detailed description of the damage model can be found in the report
DMT/98026A, available on request.
The implementation of the JohnsonCook model is described in reference [167].
This material is currently restricted to SPHC elements.
The components ov the ECR table are as follows for Continuum elements:
ECR(1) : pressureECR(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.
C.294
This directive allows to define a Von Mises elastothermoviscoplastic material with nonlinear isotropic hardening governed by a modified JohnsonCook model with explicit elastic predictor and return mapping algorithm, a Voce saturation type of hardening and a CockcroftLatham 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 JohnsonCook 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 socalled “modified” Johnson Cook material law,
in which the strainrate sensitivity
term is adjusted so as to avoid nonphysical 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), 685712.
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:
σ_{y} =  ⎡ ⎣  A + Q_{1}  ⎛ ⎝  1 − e^{−C1 p}  ⎞ ⎠  + Q_{2}  ⎛ ⎝  1 − e^{−C2 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 strainrate hardening term and a temperature softening term. The symbols indicate the following:
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 D_{p} per unit volume in the form of heat (Watt per cubic meter) is given by:
D_{p} = χσ_{eq}ṗ=ρ C_{T}Ṫ (10) 
where:
From the above expression, the temperature rate Ṫ is obtained:
Ṫ = 
 = 
 (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 T_{r} at each Gauss point. If during the calculation the temperature at a Gauss point reaches the melting temperature T_{m}, the Gauss point fails.
The CockcroftLatham 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 D_{c}. The D_{c} parameter should be set by the user (see DC keyword below) such that 0<D_{c}≤ 1. The value 1 should be used when not considering damage softening. The damage is computed according to the following expression:
D = 
 = 
 ∫ 
 ⟨σ_{1}⟩ dp (12) 
where:
An element’s Gauss point is considered as failed if D≥ D_{c}, 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.
"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/
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
VPJC RO 7850 YOUN 210.0E9 NU 0.33 ELAS 370.0E6 QR1 236.4E6 CR1 39.3 QR2 408.1E6 CR2 4.5 PDOT 5.E4 C 0.001 TQ 0.9 CP 452 TM 1800.0 M 1.0 DC 1.0 WC 473.0E6
VPJC RO 7850 YOUN 210.0E9 NU 0.33 ELAS 333.1E6 QR1 236.3E6 CR1 16.5 QR2 416.5E6 CR2 1.2 PDOT 5.E4 C 0.011 TQ 0.9 CP 452 TM 1800.0 M 0.94 DC 1.0 WC 848.0E6
VPJC RO 7850 YOUN 208.0E9 NU 0.33 ELAS 299.0E6 QR1 160.0E6 CR1 25.0 QR2 400.0E6 CR2 0.25 PDOT 5.E4 C 0.01 TQ 0.9 CP 452 TM 1993.0 M 1.0 DC 1.0 WC 1595.0E6
VPJC RO 7800.0 YOUN 2.08E11 NU 0.30 ELAS 465.5E6 mxit 20 QR1 147.0E6 CR1 10.62 QR2 665.9E6 CR2 0.50 PDOT 8.06E4 C 0.0104 TQ 0.9 CP 452.0 TM 1800.0 M 1.0 DC 1.0 WC 1562.0E6 RESI 1
VPJC RO 7850.0 YOUN 2.1E11 NU 0.33 ELAS 605E6 mxit 20 QR1 139.0E6 CR1 10.26 QR2 709.0E6 CR2 0.48 PDOT 5.E4 C 0.0166 TQ 0.9 CP 452.0 TM 1800.0 M 1.0 DC 1.0 WC 1516.0E6 RESI 1
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 80.0E6 QR1 49.3E6 CR1 1457.1 QR2 5.2E6 CR2 121.5 PDOT 5.E4 C 1.4E2 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 54.0E6
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 137.0E6 QR1 19.1E6 CR1 592 QR2 170.0E6 CR2 11.4 PDOT 5.E4 C 1.0E3 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 140.0E6
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 38.8E6 QR1 79.5E6 CR1 56.9 QR2 88.2E6 CR2 4.0 PDOT 5.E4 C 1.25E2 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 179.0E6
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 172.7E6 QR1 35.6E6 CR1 80.6 QR2 247.7E6 CR2 6.5 PDOT 5.E4 C 1.25E2 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 244.0E6
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 350.0E6 QR1 30.1E6 CR1 185.9 QR2 72.8E6 CR2 7.7 PDOT 5.E4 C 1.25E2 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 130.0E6
VPJC RO 2700 YOUN 70.0E9 NU 0.3 ELAS 292.5E6 QR1 55.3E6 CR1 317.2 QR2 31.1E6 CR2 10.0 PDOT 5.E4 C 1.25E2 TQ 0.9 CP 910.0 TM 893.0 M 1.0 DC 1.0 WC 170.0E6
The material parameters are taken from the literature. See:
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 (1/3σ_{kk})ECR(2) : PHI. Von Mises equivalent stress (σ_{eq})
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 crosssectional area
ECR(12) : Failure indicator: 1.0 = Virgin Gauss Point, 0.0 = Failed Gauss Point
ECR(13) : T. Absolute temperature (T)
ECR(14) : WE. CockcroftLatham damage accumulation (W)
ECR(15) : Sound speed
ECR(16) : First principal stress (σ_{1})
ECR(17) : Second principal stress (σ_{2})
ECR(18) : Third principal stress (σ_{3})
ECR(19) : RESNOR. Residual of the yield function, used to check convergence of the loop internal to the routine.
ECR(20) : Stress triaxiality
ECR(21) : Lode parameter
C.295
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.
"RIGI" "RO" rho /LECTURE/
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.
C.296
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 (σ_{z}=0).
For the formulation of this material see the following references:
"DCMS" "RO" rho "YOUN" young "NU" nu "ELAS" elas "K" k "N" n "EPSY" epsy "GF" gf "IMES" imes "IDAM" idam /LECTURE/
Blabla ...
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 є_{p}.
ECR(4) : DAM. Damage D. The damage is limited to 0.95, that is
D=min(0.95,1−((P_{u}−є_{p})/(P_{u}−P_{c})).ECR(5) : TRIAX. Triaxiality τ.
ECR(6) : YF. Yield function Y_{f}.
ECR(7) : ITER. Number of iterations for plasticity N.
ECR(8) : ALFA. Alfa ratio α=s_{2}/s_{1} where s_{1} is the maximum principal stress and s_{2} 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 L_{e}=√A.
ECR(12) : THICK/SQRT(SAREA). Thickness/length ratio t/L_{e}.
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 P_{c}.
ECR(15) : PU. Plastic strain at element failure P_{u}.
ECR(16) : SIG1. First (maximum) principal stress s_{1} of the plane stress state.
ECR(17) : SIG2. Second (minimum) principal stress s_{2} of the plane stress state.
C.297
This subdirective defines a hyperelastic material of the MooneyRivlin type.
An incompressible MooneyRivlin hyperelastic material is described by:
W = C_{1}( 
 _{1}−3)+C_{2}( 
 _{2}−3) (13) 
where W is the strain energy density function, C_{1} and C_{2} are empirically determined material constants and:
 _{1}=J^{−2/3}I_{1} I_{1}=λ_{1}^{2}+λ_{2}^{2}+λ_{3}^{2} (14) 
 _{2}=J^{−4/3}I_{2} I_{2}=λ_{1}^{2}λ_{2}^{2}+λ_{2}^{2}λ_{3}^{2}+λ_{3}^{2}λ_{1}^{2} (15) 
I_{3}=J^{2}=λ_{1}^{2}λ_{2}^{2}λ_{3}^{2} (16) 
Here I_{1} and I_{2} are the first and second invariants of the unimodular component of the left CauchyGreen deformation tensor and:
J=det 
 =λ_{1}λ_{2}λ_{3} (17) 
with F the deformation gradient. For an incompressible material J=1.
For a compressible MooneyRivlin material eq. (13) becomes:
W = C_{1}( 
 _{1}−3)+C_{2}( 
 _{2}−3)+K(lnI_{3})^{2} (18) 
with K the bulk modulus and I_{3} is the third invariant, given by eq. (16).
The material parameters C_{1} and C_{2} can be determined by EPX itself by a best fit procedure if a 1D experimental stressstrain curve is available (see Parameters Calibration mode below).
The range of validity of this material model is as follows:
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) $
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 1D 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.)
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(835): Unused.
C.298
This subdirective defines a hyperelastic material of the Ogden type.
The expression of the strain energy density is one of the
following expressions:
Type 1 W = 

 ⎛ ⎝  λ_{1}^{*αp} + λ_{2}^{*αp} + λ_{3}^{*αp} −3  ⎞ ⎠  + K(J−1−lnJ) (19) 
Type 2 W = 

 ⎛ ⎝  λ_{1}^{*αp} + λ_{2}^{*αp} + λ_{3}^{*αp} −3  ⎞ ⎠  + 
 K (J−1)^{2} (20) 
where λ^{*}=λ J^{−1/3}, K is the bulk modulus, µ_{p} and α_{p} 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 (α_{1}, µ_{1}) 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 α_{p} and µ_{p} can be determined by EPX itself by a best fit procedure if a 1D experimental stressstrain curve is available (see Parameters Calibration mode below).
Note that the range of validity of this material model is :
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.
"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 "TRAC" npts * (strain stress) $ % <"BULK" k> % not implemented
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 1D 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.)
The components of the ECR table are as follows:
ecr(1) = Pressureecr(2) = Von misses stress
ecr(3) = Max principal Cauchy stress
ecr(4) = W (internal energy density)
ecr(5) = Von Mises natural strain
ecr(6) = Max principal natural strain
ecr(7) = Von Mises engineering strain
ecr(8) = Max principal engineering strain
ecr(9) = Max von mises stress historical
ecr(10) = Historical Max principal Cauchy stress
ecr(11) = Historical Max von Mises natural strain
ecr(12) = Historical Max principal natural strain
ecr(13) = Historical Max von Mises engineering strain
ecr(14) = Historical Max principal engineering strain
ecr(15) = Historical Max Pressure (traction)
ecr(16) = Historical Min Pressure (compression)
ecr(17) = CSON0 (sound speed estimated by new method)
ecr(18) = CSON1 (sound speed estimated like for material HYPE TYPE 4) (the maximum between CSON0 and CSON1 is retained as speed of sound)
ecr(19) = Initial Volume (needed for the calculation of the internal energy)
ecr(20) = PI1. Pressure resulting from the Prony series (only when viscosity is enabled in the materuial model)
ecr(21:23) = LAMB(1:3) Principal stretches of the element
ecr(24:29) = Sich (1:6) (only when viscosity is enabled in the materuial model)
ecr(30:35) = Si1 (1:6) (only when viscosity is enabled in the materuial model)
C.299
This subdirective defines a hyperelastic material of the BlatzKo type.
This material is still under development.
W = 
 ⎡ ⎢ ⎢ ⎣  (I_{1}−3) + β (I_{3}^{−1/β}−1)  ⎤ ⎥ ⎥ ⎦  + 
 ⎡ ⎢ ⎢ ⎣  ( 
 −3) + β (I_{3}^{1/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).
I_{1}=λ_{1}^{2}+λ_{2}^{2}+λ_{3}^{2} (22) 
I_{2}=λ_{1}^{2}λ_{2}^{2}+λ_{2}^{2}λ_{3}^{2}+λ_{3}^{2}λ_{1}^{2} (23) 
I_{3}=J^{2}=  ⎛ ⎝  det 
 ⎞ ⎠ 
 = λ_{1}^{2}λ_{2}^{2}λ_{3}^{2} (24) 
Here I_{1}, I_{2} and I_{3} are the first, second and third invariants of the unimodular component of the left CauchyGreen deformation tensor, J the Jacobian with F the deformation gradient. For an incompressible material J=1.
Note that for incompressibility (J=I_{3}=1) the BlatzKo material have an similar expression as the MooneyRiviln.
W = 
 (I_{1}−3) + 
 (I_{2}−3) (25) 
The material parameters C_{1} and C_{2} can be determined by EPX itself by a best fit procedure if a 1D experimental stressstrain curve is available (see Parameters Calibration mode below).
The range of validity of this material model is as follows:
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) $
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 1D 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.)
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(835): Unused.
C.300
The following directives describe fluid materials for continuum elements.
Here are the different material types:
number name ref law of behaviour 34 ADCR 7.8.19 homogeneous mixture with 3 components (1 liquid + 2 gases) 53 ADCJ 7.8.25 hypothetical core disruptive accident with law of type JWL for the bubble 57 BILL 7.8.26 specialised equation of state for the particle elements 59 BUBB 7.8.38 Balloon model for air blast simulations 68 CDEM 7.8.39 Discret Equation Method for Combustion 51 CHOC 7.8.22 Shock waves, RankineHugoniot equation 110 DEMS 7.8.40 Discret Equation Method for Two Phase Stiffenened Gases 22 EAU 7.8.9 twophase water (liquid + vapour) 49 EXVL 7.8.20 hydrogen explosion Van Leer 27 FLFA 7.8.15 rigid tube bundles (homogeneous acoustic model) 86 FLMP 7.8.35 Fluid multiphase 7 FLUI 7.8.2 isothermal fluid ( c = cte ) 36 FLUT 7.8.30 fluid, to be specified by the user 73 GAZD 7.8.41 Detonation in gas Mixture 9 GAZP 7.8.4 perfect gas 118 GGAS 7.8.1 generic ideal gas material 52 GPDI 7.8.23 diffusive perfect gas Van Leer 48 GVDW 7.8.28 Van Der Waals gas 40 GZPV 7.8.24 perfect gas for Van Leer 28 HELI 7.8.10 helium 50 JWL 7.8.21 explosion (JonesWilkinsLee model) 66 JWLS 7.8.29 Explosion (JonesWilkinsLee for solids) 23 LIQU 7.8.14 incompressible (or quasi) fluid 82 MCFF 7.8.34 multicomponent fluid material (farfield) 81 MCGP 7.8.33 multicomponent fluid material (perfect gas) 33 MHOM 7.8.16 pipe bundle (homogeneous asymptotic model) 25 MULT 7.8.13 multiple materials (coupled monodim.) 10 NAH2 7.8.7 sodiumwater reaction (1 liquid and 1 gas) 56 PARO 7.8.11 friction and heat exchange for pipeline walls 39 PUFF 7.8.17 equation of state of type "PUFF" 54 RSEA 7.9.13 sodiumwater reaction (1 liquid and 2 gases) 103 SG2P 7.8.36 Multicomponent Stiffened Gases  Conservative formulation 104 SGMP 7.8.37 Multicomponent Stiffened Gases models 24 SOUR 7.8.6 imposed timedependent internal pressure 102 STIF 7.8.5 Stiffened Gas 101 TAIT 7.8.3 Tait Equation of State
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.
C.301
Perfect gas (P=ρ(γ−1)E_{internal})
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 7.8.4, FLUT 7.8.30) for the elements used.
"GGAS" "RO" rho "GAMMA" gamma ["PINI" pini  "EINI" eini] ... < "PREF" pref > /LECTURE/
The output variables are according to the material in which the generic material is converted.
C.305
This option enables a fluid (liquidlike) 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 = p_{ini} + (ρ − ρ_{ini})c^{2} 
where p_{ini} is the fluid pressure in the initial state, ρ is the current density, ρ_{ini} 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.
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/
ρ_{min} = ρ_{ini} + 

The parameters RO
and C
are compulsory.
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:
p_{ref} = p_{ini}.
If PREF is omitted, EUROPLEXUS considers that the fluid is in
equilibrium and p_{ref}=p_{ini} (even when p_{ini}=0).
For a given minimum pressure p_{min}, 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 p_{min} is p_{min} = 0.
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 : pressureδ(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)).
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 K_{p}=1 according to the formula:
Δ P = 
 K_{p} L ρ V^{2} 
The parameter SMOU
(relative wet surface) is obsolete
and may be omitted. It is only kept for compatibility
with old input files.
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 = p_{ini} + Bη 
where B is the bulk modulus (assumed constant and usually expressed in Pa) and η is the relative volume variation:
η = −є_{V} = 
 = 1 − 

From these expressions one obtains:
p = p_{ini} + (ρ − ρ_{ini}) 

By comparing this with the pressure expression of the FLUI material, one sees that:
c = 


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 ρ_{ini}, one obtains the following relation between c and B:
c ≈ 


The components of the ECR table are as follows:
ECR(1): absolute pressureECR(2): density
CEA report to appear.
C.307
This option enables a barotropic fluid (liquidlike) 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 underwaterexplosion 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  ⎛ ⎜ ⎜ ⎝ 
 ^{γ} −1  ⎞ ⎟ ⎟ ⎠ 
where P is the fluid pressure, ρ is the current density and ρ_{ref} is the reference density.
"TAIT" "RO" rho "PINI" pini <"PREF" pref > <"PMIN" pmin > ... "GAMM" gamma "B" b ... /LECTURE/
ρ_{min} = ρ_{ref} 


For the TAIT EoS, the initial density ρ_{ini} is computed from the expression:
ρ_{ini} = ρ_{ref} 


with:
p_{ini} : initial pressure, ρ_{ref} : reference density
The expression used for the sound speed is:
C= 


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:
p_{ref} = p_{ini}.
If PREF is omitted, EUROPLEXUS considers that the fluid is in
equilibrium and p_{ref}=p_{ini}.
For a given minimum pressure p_{min}, 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 p_{min} is p_{min} = 0.
The components of the ECR table are as follows:
ECR(1): absolute pressureECR(2): current density
ECR(3): sound speed
C.310
Euler : perfect gas (P=ρ(γ−1)E_{internal});
Lagrange: adiabatic perfect gas (P=kρ^{γ}).
In a 1D 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).
"GAZP" "RO" rho "GAMMA" gamma "PINI" pini <"VISC" mu > ... ... < "CV" cv > < "PREF" pref > /LECTURE/
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.
The different components of the ECR table are as follows:
ECR(1): pressureECR(2): density
ECR(3): velocity of sound
ECR(4): maximum pressure ever experienced
ECR(5): minimum pressure ever experienced
ECR(6): dynamic pressure: (P_{dyn}=1/2ρ v^{2})
ECR(7): temperature (if c_{V} is not zero) in degrees Celsius
ECR(8): total specific energy (E = h + 1/2v^{2})
C.315
This Equation of State can be used for both liquids and gases. It takes the following form:
P = (γ −1) ρ (e−q) − γ P_{inf} 
Where e is the internal energy per unit mass, ρ the density. γ is an empirical constant for liquids. P_{inf} 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 P_{inf} and q is zero.
"STIF" "RO" rho "PINI" pini < "PMIN" pmin > < "PREF" pref > ... "GAMMA" gamma "PI" pinf "Q" q ... /LECTURE/
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= 


The different components of the ECR table are as follows:
ECR(1): pressure
ECR(2): density
ECR(3): sound speed
C.320
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 twophase mixture of water ("EAU") or
of a liquidgas mixture ("ADCR").
"SOUR" $ "FLUI" ... ; "GAZP" ... ; "EAU" ... ; "ADCR" ... $ ... < "FONC" nufo < "FACT" coef > > /LECTURE/
For "FLUI" see 7.8.2 page C.305, for "GAZP" see 7.8.4 page C.310, for "EAU" see 7.8.9 page C.350, for "ADCR" see 7.8.19 page C.430,
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.
The different components of the ECR table are the same as the components for the material with the same name.
C.330
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 waterfilled pipeline meshed by elements of type TUBE or TUYA and coupling with the sodium mesh (keyword "DCOUP").
"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/
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/
The components of the ECR table are as follows:
ECR(1) : absolute pressureECR(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)
C.340
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 waterfilled pipeline meshed with TUBE or TUYA elements and coupled with the sodium mesh (keyword DCOU).
"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/
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 300^{o} C.
The components of the ECR table are as follows:
ECR(1) : absolute pressure,ECR(2) : density of the twophase 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.
C.350
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.
"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/
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 singlephase, one should give the pressure
and the temperature, but the title is irrelevant.
If the mixture is twophase, one should give the pressure
and the title: EUROPLEXUS then computes the temperature.
The damping coefficient beta allows to damp out highfrequency
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.
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.
The components of the ECR table are as follows:
ECR(1) : absolute pressureECR(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 metastable
ECR(6) : enthalpy of the mixture
ECR(7) : temperature of the mixture for equilibrated water, vapor temperature for metastable
ECR(9) : void ratio or volume ratio of the vapor (vapor volume/total volume)
For metastable water:
ECR(21) : vapor relative density (vapor mass/total volume)ECR(23) : index : 0 = equilibrium ; 1 = metastable
ECR(24) : specific enthalpy of the liquid water
In case of direct energy injection:
ECR(8) : power injected in the elementECR(14) : corium mass within the element
In case of energy injection by particles:
ECR(19) : initial volume of corium within the elementECR(20) : mean temperature of a corium particle
For a "BREC" element:
ECR(25) : Pipeline rupture areaECR(26) : Mass flow
ECR(27) : Total ejected mass
C.355
This directive allows to treat helium and its liquid as an homogeneous mixture.
"HELI" "PINI" pini [ "TINI" tini ; "TITR" x ] ... ... < "PREF" pref > < "BETA" beta > ... ... < "VISL" mul "VISV" muv > ... ... /LECTURE/
Do not forget to create the tables of physical properties of helium by means of directive "THEL" (page C.75).
If the mixture is singlephase, one should give the pressure
and the temperature, but the title is irrelevant.
If the mixture is twophase, one should give the pressure
and the title: EUROPLEXUS then computes the temperature.
The damping coefficient beta allows to damp out highfrequency
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.
The components of the ECR table are as follows:
ECR(1) : absolute pressureECR(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
C.370
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.
"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/
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 singlephase, 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.
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 temperatureECR(2) : conductance
ECR(4) : Reynolds number
ECR(5) : psi (of the formula K = psi * L / Dh)
C.375
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...).
"BREC" $[ "DCRI" idcri ; "PIMP" ipimp < "CONT" cont "EPAI" epai > ]$
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 [884]. 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).
C.380
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.
"MULT" n1 n2 < n3 > /LECTURE/
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/
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.
C.390
This option enables the processing of an incompressible or
quasiincompressible fluid. The implicit
algorithm of "LIAISONS" is used.
"LIQU" "RO" rho < "C" c > < "PINI" pini > ... ... < "PREF" pref > < "VISC" visc > < "RUGO" rugo > /LECTURE/
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/c^{2}) is stored in the material property.
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).
The components of the ECR table are as follows:
ECR(1): absolute pressure of the element due to the viscous termsECR(2): density
ECR(3): additive term to the diagonal of B_{L}, the connections matrix.
ECR(4): additive term to the righthand 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
C.400
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.
"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/
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
crosssections.
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).
The components of the ECR table are as follows:
ECR(1) : absolute pressureECR(2) : apparent density
Then if VISC is present:
ECR(3) : halfcoefficient of friction along direction Ox or OrECR(4) : halfcoefficient of friction along direction Oy or Ot
ECR(5) : halfcoefficient of friction along direction Oz
C.410
Replaces a heterogeneous medium composed by a tube bundle
surrounded by fluid, by a homogenised medium (asymptotic
homogenisation method).
"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/
C.420
Equation of state of type PUFF, allowing to treat very fast mechanical
phenomena for which the material behaviour is hydrodynamic.
"PUFF" "RO" rho "MK" mk ... ... < "PINI" pini "PREF" pref > ... ... "GAMMA" gamma "D" d "S" s ... ... "GAMZ" gamz "CV" cv ... ... $[ "ES" es "SIMPLE" ; "GAM1" gam1 "N" n "EV" ev "COMPLEXE" ]$ ... ... /LECTURE/