Elastic‑visco‑plastic constitutive law for solid elements at variable temperature
This law is used for a mechanical analysis of elastic‑visco‑plastic isotropic solids undergoing large strains.
Strain‑rate effects and isotropic hardening are included.
The temperature dependence of the material parameters is taken into account.
Prepro: LGROB.F
Lagamine: GROB2E.F (2D), GROB3D.F (3D)
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | NO |
| 3D state | YES |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 45 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| Line 1 (I5) | |
|---|---|
| NINTV | number of sub‑steps used to integrate numerically the constitutive equation in a time step. |
| Line 1 (7G10.0/7G10.0) | |
|---|---|
| EO | reference YOUNG's elastic modulus ($E_o$) |
| BE | corresponding temperature coefficient ($b_E$) |
| ANUO | reference POISSON's ratio ($\nu$) |
| BNU | corresponding temperature coefficient ($b_{<}$) |
| ANO | reference strain rate exponent ($n_o$) |
| BO | reference strain rate coefficient ($B_o$) |
| Q | corresponding temperature coefficient ($Q$) |
| AMO | reference hardening exponent ($m_o$) |
| AKSO | reference hardening saturation coefficient ($K_{so}$) |
| GAMMAO | reference hardening parameter ($\gamma_o$) |
| TETAO | reference hardening coefficient ($\theta_o$) |
| BTETA | corresponding temperature coefficient ($b_{\theta}$) |
| AKOO | reference initial yield limit ($K_{oo}$) |
| BK | corresponding temperature coefficient ($b_K$) |
= 6 for 3-D 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) | $\sigma_{zz}$ |
=3
| 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) | current yield limit in tension; its initial value is $K_o\exp(-b_K T)$ where $T$ is the absolute temperature in $K$ |
| Q(3) | equivalent inelastic strain ($\bar{\varepsilon}^p$) |