Table of Contents
DAM-EP-TH
Description
Elastic-(visco)-plastic constitutive law fully coupled with damage for solid elements at variable temperature
The model
Mechanical analysis of thermo-elasto-(visco)-plastic-damage isotropic solids undergoing large strains, plastic mixed hardening and damage isotropic hardening are assumed.
Error in mechanical computation if elastic strain is not negligible compared to the plasticity. Small example at the end.
Files
Prepro: LZDMGC.F
Availability
| Plane stress state | YES |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | NO |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 215 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing. |
Integer parameters
| Line 1 (6I5) | |
|---|---|
| NTEMP | number of temperatures at which material date are given |
| NINTV | number of sub-steps used to integrate numerically the constitutive equation in a time step |
| 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) |
| IVISC | = 0 (EP LAW) = 1 (EVP LAW) |
Real parameters
| Line 1 (6G10.0) | |
|---|---|
| TAU | ratio of volumetric damage to deviatoric damage |
| ECROU | = 0 for isotropic hardening = 1 for kinematic hardening ∈ [0,1] for mixed hardening |
| COEFQ | TAYLOR-QINNEY'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$1.D-3) |
| THICK | thickness for plane state |
Real parameters
Repeated NTEMP times
| Line 1 (7G10.0) | |
|---|---|
| T | temperature |
| E | YOUNG's elastic modulus at temperature T |
| ANU | POISSON's ratio at temperature T |
| ALPHA | thermal expansion coefficient ($\alpha$) at temperature T |
| RP$\Phi$ | lower yield limit $\sigma_0$ at temperature T |
| ET | elasto-plastic tangent modulus ($E_t$) at temperature T1 |
| RD$\Phi$ | initial damage limit at temperature T |
| DTG | damage tangent modulus at temperature T |
| Line 2 (G10.0) | |
| VISCO | visco fluid parameter (unit : time) |
Stresses
Number of stresses
6 for 3D state
4 for the other cases
Meaning
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) | $\sigma_{ZZ}$ |
State variables
Number of state variables
28 for 3D state
26 for the other cases
List of state variables
| 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 3-D state = element thickness (t) in generalized plane 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) | generalized plastic strain ($\alpha$) |
| Q(5) | amount of current deviatoric damage (D) |
| Q(6) | plastic hardening level (R) |
| Q(7) | damage hardening level (B) |
| Q(8) | back stresses for kinematic and mixed hardening |
| Q(N) | (N = 14 for 3-D state, N = 12 for other cases) |
| Q(N+1) | equivalent plastic strain |
| Q(N+2) | equivalent stress |
| Q(N+3) | thermodynamic reaction conjugated to deviatoric damage ($Y_{d}$) |
| Q(N+4) | thermodynamic reaction conjugated to volumetric damage ($Y_{*}$) |
| Q(N+5) | plastic work per unit volume |
| Q(N+6) | damage work per unit volume |
| Q(N+7) | total strain energy per unit volume (elastic + plastic + damage) |
| Q(N+8) | part of the dissipated power converted into heat |
| Q(N+9) | current temperature |
| Q(N+10 | fracture criteria |
| Q(N+15) | |
Example of the error that might occur:
