====== EVP-BONZ ======
FIXME This page does not match the code. The law corresponding to ITYPE = 36 is law KOLYM; in addition, LBONZ.F does not exist in Prepro.
===== Description =====
Elastic-visco-plastic constitutive law for solid elements at constant temperature (Bodner model)
==== The model ====
This law is used for a mechanical analysis of elastic‑visco‑plastic isotropic solids undergoing large strains. \\
Strain‑rate effects and isotropic and directional hardening or recovery are included.
==== Files ====
Prepro: LBONZ.F \\
Lagamine:  
===== Availability =====
|Plane stress state| NO |
|Plane strain state| YES | 
|Axisymmetric state| YES |
|3D state| YES |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 36 |
|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) ^^
|E| YOUNG’s elastic modulus |
|ANU|POISSON’s ratio |
|D0|assumed limiting plastic-shear strain rate ($D_0$)|
|D1|directional hardening coefficient ($D_1$)|
|RK0|initial isotropic hardness ($K_0$)|
|RK1|maximum or limiting isotropic hardness ($K_1$)|
|RK2|minimum or stable isotropic hardness ($K_2$)|
^ Line 2 (7G10.0) ^^
|A1|recovery coefficient of isotropic hardness ($A_1$)|
|A2|recovery coefficient of directional hardness ($A_2$)|
|RM1|hardening exponent of isotropic hardness ($m_1$)|
|RM2|hardening exponent of directional hardness ($m_2$)|
|R1|recovery exponent of isotropic hardness ($r_1$)|
|R2|recovery exponent of directional hardness ($r_2$)|
|RN|strain rate sensitivity coefficient ($n$)|
===== 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 ====
= 17 for 3-D state \\ 
= 15 for the other cases
==== 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 equivalent stress in tension|
|Q(3)|current isotropic hardness; its initial value is $K_0$|
|Q(4)| equivalent directional hardness|
|Q(5)$\rightarrow$Q(N)| components of directional hardness (N=10 for 3-D state, N=8 for other cases)|
|Q(N+1)| equivalent strain|
|Q(N+2$\rightarrow$N+7)| failure criteria|