Elasto-plastic isotropic constitutive law with damage for solid elements at constant temperature endochronic
This law is used for mechanical analysis of elasto‑plastic isotropic solids undergoing large strains, taking account of internal damage generated by plastic strains. Plastic isotropic hardening is assumed.
Prepro: LEPDAM.F
Lagamine: ENDO2A.F
| Plane stress state | NO |
| Plane strain state | NO |
| Axisymmetric state | YES |
| 3D state | NO |
| Generalized plane state | NO |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 220 |
| 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) | |
|---|---|
| E | YOUNG’s elastic modulus |
| ANU | Poisson ratio |
| TAU | ratio of volumetric damage to deviatoric damage $(=\tau)$ |
| AG | rate of deviatoric damage $(=a_G)$ |
| RE | initial yield limit $(=R_e)$ |
| AK | hardening coefficient $(=k)$ |
| AN | hardening exponent $(=n)$ |
= 6 for the 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) | $\sigma_{zz}$ |
= 9
| Q(1) | = element thickness (t) in plane stress state |
| = 1 in plane strain state | |
| = circumferential strain rate ($\dot{\varepsilon_{\theta}}$) in axisymmetrical 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) | equivalent plastic strain $(\varepsilon_p)$ |
| Q(4) | amount of deviatoric damage (= d) |
| Q(5) | amount of volumetric damage (= `U) |
| Q(6) | thermodynamic reaction conjugated to deviatoric damage $(=Y_d)$ |
| Q(7) | thermodynamic reaction conjugated to deviatoric damage $(=Y_{\delta})$ |
| Q(8) | hardening level (R) |
| Q(9) | damage level (B) |