====== LEV-T ======
===== Description =====
Elasto-viscoplastic constitutive law with thermal effects for solid elements at variable temperature
==== The model ====
Coupled thermo-mechanical analysis of elasto-viscoplastic isotropic element undergoing large strains. 
 ==== Files ====
Prepro: LLEVT.F \\
Lagamine: LEVT2D.F, 
===== Availability =====
|Plane stress state|NO |
|Plane strain state| YES|
|Axisymmetric state| YES |
|3D state| NO|
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 230|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing.|
==== Integer parameters ====
^ Line 1 (3I5) ^^
|NTEMP|number of temperature at which material data are given|
|IALG|0 if $\alpha$ is given \\ 1 if $\int{\alpha dT}$ is given|
|METK| 0 $\dot{\lambda}$ function $\hat{D}_{eq}$ and analytical compliance matrix \\ 1 compliance matrix computed by perturbation|

==== Real parameters ====
**if NTEMP $\neq$ 0**

^Line 1 (7G10.0) - Repeat NTEMP times^^
|T| temperature|
|E|YOUNG's elastic modulus at temperature T|
|ANU|POISSON's ratio at temperature T|
|ALPHA|thermal expansion coefficient ($\alpha$) or $\int{\alpha dT}$ at temperature (see IALG)|
|$A_{c}$| parameter for $\sigma- \dot{\varepsilon}_{\theta}$ relation at temperature T|
|$A_{m}$| parameter for $\sigma- \dot{\varepsilon}_{\theta}$ relation at temperature T\\ $\hat{\sigma}_{eq} = A_{c} \hat{D}_{eq}^{A_{m}}$|
|CTQ| Taylor-Qinney's coefficient (q) at temperature T if NTEMP = 0.|
**if NTEMP = 0**
^Line 1 (5G10.0)^^
|$E_{0}$|E = $E_{0}(1-exp(-B_{E}*T))$|
|$\nu_{0}$|$\nu= \nu_{0}exp(B_{\nu}*T)$|
|$\alpha_{0}$|$\alpha= \alpha_{0}exp(B_{\alpha}/T)$|
|$A_{c0}$|$A_{c}= A_{c0}exp(B_{A_{c}}/T)$|
|$A_{m0}$|$A_{m}= A_{m0}(1-exp(-B_{A_{m}}*T))$|
^Line 	2 (5G10.0)^^
|$B_{E}$|To check before use (June 91 A-M.HABRAKEN) |
|$B_{\nu}$|:::|
|$B_{\alpha}$|:::|
|$B_{A_{c}}$|:::|
|$B_{A_{m}}$|:::|



===== Stresses =====
==== Number of stresses ====
 4 (for plane state)
==== Meaning ====
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates. \\
|SIG(1)|$\sigma_{XX}$|
|SIG(2)|$\sigma_{YY}$|
|SIG(3)|$\sigma_{XY}$|
|SIG(4)|$\sigma_{ZZ}$|
===== State variables =====
==== Number of state variables ====
7
==== List of state variables ====
|Q(1)| circumferential strain rate $\dot{\varepsilon_\theta}$ in axisymmetric state \\ 1 in plane strain state|
|Q(2)| current yield limit in tension|
|Q(3)| 0  if the current state is elastic\\ 1  if the current state is elasto-plastic |
|Q(4)| equivalent plastic strain $\overline{\varepsilon}^{p}$ |
|Q(5)| plastic work per unit volume |
|Q(6)| part of the dissipated power converted into heat |
|Q(7)| initial temperature|