====== EVP-IRS ======
===== Description =====
Elastic‑visco‑plastic constitutive law for solid elements at constant 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 or recovery are included.
==== Files ====
Prepro: LIRSI.F \\
Lagamine: IRSI2S.F, IRSI2E.F, IRSI2A.F, IRSI3D.F
===== Availability =====
|Plane stress state| YES |
|Plane strain state| YES | 
|Axisymmetric state| YES |
|3D state| YES |
|Generalized plane state| YES |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 40 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (2I5) ^^
|NINTV| number of sub‑steps used to integrate numerically the constitutive equation in a time step.|
|ICRIFR|=  0 : nothing|
|:::|= 1 : fracture criterion is computed|
==== Real parameters ====
^ Line 1 (7G10.0) ^^
|E| YOUNG’s elastic modulus |
|ANU|POISSON’s ratio |
|AN|strain rate exponent ($n$)|
|B|strain rate coefficient ($B$)|
|AM|hardening exponent ($m$)|
|H1|hardening coefficient ($H_1$)|
|AQ|recovery exponent ($q$)|
^ Line 2 (4G10.0) ^^
|H2|recovery coefficient ($H_2$)|
|AKO|initial yield limit ($K_o$)|	 
|ANI|strain exponent $(\bar{\sigma} = C \bar{\varepsilon}^n)$ only for the criterion of fracture|
|RHO|specific mass|
===== 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 ====
= 24
==== 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 $K_o$|
|Q(3)|hydrostatic stress ($\sigma_m$)|
|Q(4)|equivalent inelastic strain ($\bar{\varepsilon}^p$)|
|Q(5)|plastic work per unit|
|Q(6)| total strain energy per unit volume|
|Q(8)$\rightarrow$Q(11)| failure criteria|
|Q(12)|equivalent stress ($\bar{\sigma}$)|
|Q(13)|localisation indicator (Vilotte) : increment of|
|Q(14)|cumulated $\varepsilon_{eq}$|
|Q(15)|$\varepsilon_{xx}$|
|Q(16)|$\varepsilon_{yy}$|
|Q(17)|$\varepsilon_{zz}$|
|Q(18)|$\varepsilon_{xy}$|
|Q(19)|$\dot{\varepsilon}_{eq}$|
|Q(24)|actualised specific mass|