Elasto-viscoplastic constitutive law with thermal effects for solid elements at variable temperature
Coupled thermo-mechanical analysis of elasto-viscoplastic isotropic element undergoing large strains.
Prepro: LLEVT.F
Lagamine: LEVT2D.F,
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 230 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing. |
| Line 1 (3I5) | |
|---|---|
| NTEMP | number of temperature at which material data are given |
| IALG | 0 if $\alpha$ is given 1 if $\int{\alpha dT}$ is given |
| METK | 0 $\dot{\lambda}$ function $\hat{D}_{eq}$ and analytical compliance matrix 1 compliance matrix computed by perturbation |
if NTEMP $\neq$ 0
| Line 1 (7G10.0) - Repeat NTEMP times | |
|---|---|
| T | temperature |
| E | YOUNG's elastic modulus at temperature T |
| ANU | POISSON's ratio at temperature T |
| ALPHA | thermal expansion coefficient ($\alpha$) or $\int{\alpha dT}$ at temperature (see IALG) |
| $A_{c}$ | parameter for $\sigma- \dot{\varepsilon}_{\theta}$ relation at temperature T |
| $A_{m}$ | parameter for $\sigma- \dot{\varepsilon}_{\theta}$ relation at temperature T $\hat{\sigma}_{eq} = A_{c} \hat{D}_{eq}^{A_{m}}$ |
| CTQ | Taylor-Qinney's coefficient (q) at temperature T if NTEMP = 0. |
if NTEMP = 0
| Line 1 (5G10.0) | |
|---|---|
| $E_{0}$ | E = $E_{0}(1-exp(-B_{E}*T))$ |
| $\nu_{0}$ | $\nu= \nu_{0}exp(B_{\nu}*T)$ |
| $\alpha_{0}$ | $\alpha= \alpha_{0}exp(B_{\alpha}/T)$ |
| $A_{c0}$ | $A_{c}= A_{c0}exp(B_{A_{c}}/T)$ |
| $A_{m0}$ | $A_{m}= A_{m0}(1-exp(-B_{A_{m}}*T))$ |
| Line 2 (5G10.0) | |
| $B_{E}$ | To check before use (June 91 A-M.HABRAKEN) |
| $B_{\nu}$ | |
| $B_{\alpha}$ | |
| $B_{A_{c}}$ | |
| $B_{A_{m}}$ | |
4 (for plane state)
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates.
| SIG(1) | $\sigma_{XX}$ |
| SIG(2) | $\sigma_{YY}$ |
| SIG(3) | $\sigma_{XY}$ |
| SIG(4) | $\sigma_{ZZ}$ |
7
| Q(1) | circumferential strain rate $\dot{\varepsilon_\theta}$ in axisymmetric state 1 in plane strain state |
| Q(2) | current yield limit in tension |
| Q(3) | 0 if the current state is elastic 1 if the current state is elasto-plastic |
| Q(4) | equivalent plastic strain $\overline{\varepsilon}^{p}$ |
| Q(5) | plastic work per unit volume |
| Q(6) | part of the dissipated power converted into heat |
| Q(7) | initial temperature |