====== EVP-GROB ======
===== Description =====
Elastic‑visco‑plastic constitutive law for solid elements at variable temperature

==== The model ====
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.
==== Files ====
Prepro: LGROB.F \\
Lagamine: GROB2E.F (2D), GROB3D.F (3D)
===== Availability =====
|Plane stress state| NO |
|Plane strain state| YES | 
|Axisymmetric state| NO |
|3D state| YES |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 45 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (I5) ^^
|NINTV| number of sub‑steps used to integrate numerically the constitutive equation in a time step.|

==== Real parameters ====
^ 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 ($b_K$)|
===== Stresses =====
==== Number of stresses ====
= 6 for 3-D 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 ====
=3
==== 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)|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 ($\bar{\varepsilon}^p$)|