Elasto(-visco)-plastic damage law of anisotropic materials for solid elements at variable temperature
Mechanical analysis of thermo-elasto(-visco)-plastic-damage orthotropic solids undergoing large strains, plastic mixed hardening and damage isotropic hardening are assumed.
Prepro: LADAM.F
Lagamine: ADAM2S.F, ADAM2E.F, ADAM2A.F, ADAM3D.F
| Plane stress state | YES |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 235 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing. |
| Line 1 (9I5) | |
|---|---|
| NTEMP | number of temperature at which material data are given (one temperature is possible) |
| NINTV | number of sub-steps used to integrate numerically the constitutive equation in a time step |
| MTHER | 1, for adiabatic case (uncoupled model) others, for coupled model |
| IVISC | 1, for EVP law others, for EP law |
| MMATE | 1, for brittle material others, for ductile material |
| NTRAN | 0 always It was the old wrong way to use material principal axes different from the global axes. In such a case, you must use local axes, see control parameters |
| MNINTV | Max. of number of sub-steps (0$\rightarrow$100) |
| MITERA | number of sub-iteration (0$\rightarrow$10) |
| MUTIP | number of multiplicator for sub-steps (0$\rightarrow$2) |
2D Case
| Line 1 (7G10.0) | |
|---|---|
| ECROU | 0 for isotropic hardening 1 for kinematic hardening [0,1] for mixed hardening |
| COEFQ | TAYLOR-QUINNEY's coefficient (q) |
| DNMAX | 0 for EP without damage (0,1) $rightarrow$ Max. damage value at initial fracture otherwise $\rightarrow$ 0.95 limit damage value |
| PROC | precision of iteration (0 $\rightarrow$1.D-3) |
| TEMP0 | initial temperature |
| ANGLE | Angle between the 1-2 principal axes of material and X-Y axes of co-ordinate. Only for 2D |
| THICK | thickness for plane state. |
3D Case
| Line 1 (7G10.0) | |
|---|---|
| ECROU | 0 for isotropic hardening 1 for kinematic hardening [0,1] for mixed hardening |
| COEFQ | TAYLOR-QUINNEY's coefficient (q) |
| DNMAX | 0 for EP without damage (0,1) $rightarrow$ Max. damage value at initial fracture otherwise $\rightarrow$ 0.95 limit damage value |
| PROC | precision of iteration (0 $\rightarrow$1.D-3) |
| TEMP0 | initial temperature |
| TRAN11 | gradient of material principal direction in global coordinate |
| TRAN12 | |
| Line 2 (7G10.0) | |
| TRAN13 | gradient of material principal direction in global coordinate |
| TRAN21 | |
| TRAN22 | |
| TRAN23 | |
| TRAN31 | |
| TRAN32 | |
| TRAN33 | |
Both cases
| Line 1 (6G10.0) | |
|---|---|
| TEMP | temperature |
| ROC | heat capacity per unit volume (used when MTHER = 1) |
| VISCO | viscosity parameter (unit: time). |
| ALPHAT1 | thermal expansion coefficient in 1 direction |
| ALPHAT2 | thermal expansion coefficient in 2 direction |
| ALPHAT3 | thermal expansion coefficient in 3 direction |
| Line 2 (6G10.0) | |
| E1 | YOUNG's modulus in 1 direction |
| RP01 | yield limit of uniaxial tension in 1 direction |
| ET1 | elasto-plastic tangent modulus in 1 direction |
| ANU12 | POISSON's ratio in 1-2 plane |
| RD01 | initial damage limit in 1 direction |
| DT1 | damage tangent modulus in 1 direction |
| Line 3 (6G10.0) | |
| E2 | YOUNG's modulus in 2 direction |
| RP02 | yield limit of uniaxial tension in 2 direction |
| ET2 | elasto-plastic tangent modulus in 2 direction |
| ANU23 | POISSON's ratio in 2-3 plane |
| RD02 | initial damage limit in 2 direction |
| DT2 | damage tangent modulus in 2 direction |
| Line 4 (6G10.0) | |
| E3 | damage tangent modulus in 2 direction |
| RP03 | yield limit of uniaxial tension in 3 direction |
| ET3 | elasto-plastic tangent modulus in 3 direction |
| ANU13 | POISSON's ratio in 1-3 plane |
| RD03 | initial damage limit in 3 direction |
| DT3 | damage tangent modulus in 3 direction |
| Line 5 (3G10.0) | |
| G12 | shear elastic modulus in 1-2 plane |
| RP012 | yield limit in 1-2 plane |
| GT12 | elasto-plastic shear tangent modulus in 1-2 plane |
| Line 6 (3G10.0) | |
| G23 | shear elastic modulus in 2-3 plane |
| RP023 | yield limit in 2-3 plane |
| GT23 | elasto-plastic shear tangent modulus in 2-3 plane |
| Line 7 (3G10.0) | |
| G13 | shear elastic modulus in 1-3 plane |
| RP013 | yield limit in 1-3 plane |
| GT13 | elasto-plastic shear tangent modulus in 1-3 plane |
6 for the 3D state
4 for the other cases
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
For the 3-D state:
| SIG(1) | $\sigma_{XX}$ |
| SIG(2) | $\sigma_{YY}$ |
| SIG(3) | $\sigma_{ZZ}$ |
| SIG(4) | $\sigma_{XY}$ |
| SIG(5) | $\sigma_{XZ}$ |
| SIG(6) | $\sigma_{YZ}$ |
For the other cases:
| SIG(1) | $\sigma_{XX}$ |
| SIG(2) | $\sigma_{YY}$ |
| SIG(3) | $\sigma_{XY}$ |
| SIG(4) | $\sigma_{ZZ}$ |
28 for the 3D state
26 for the other cases
| Q(1) | element thickness (t) in plane stress state 1 in plane strain state circumferential strain rate $\dot{\varepsilon_\theta}$ in axisymmetric state 0 in 3D state |
| Q(2) | 0 if the current state is elastic 1 if the current state is elasto-plastic |
| Q(3) | 0 if the current state is not damage 1 if the current state is damage |
| Q(4) | initial temperature |
| Q(5) | equivalent plastic strain ($\varepsilon_{eq}$) |
| Q(6) | equivalent damage ($d_{eq}$) |
| Q(7) | plastic hardening level (R) |
| Q(8) | damage hardening level (B) |
| Q(9) | damage in 1 direction of material ($D_{1}$) |
| Q(10) | damage in 2 direction of material ($D_{2}$) |
| Q(11) | damage in 3 direction of material ($D_{3}$) |
| Q(12) | equivalent stress ($\sigma_{eq}$) |
| Q(13) | plastic work per unit volume ($W_p$) |
| Q(14) | damage work per unit volume ($W_d$) |
| Q(15) | part of the dissipated power converted into heat ($\dot{Q}$) |
| Q(16) | total strain energy per unit volume ($W_t$) (elastic + plastic + damage) |
| Q(17) | fracture criteria |
| Q(22) | |
| Q(23) | back stresses for kinematic and mixed hardening |
| Q(N) | (N = 28 for 3-D state, = 26 for other cases) |