Lagamine

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====== EP-LEV ======
===== Description =====
An elasto-viscoplastic simplified law
==== The model ====
Mechanical analysis of visco-plastic isotropic solids undergoing large strains. \\ Isotropic hardening is assumed. 
==== Files ====
Prepro: LLEV.F  \\
===== Availability =====
|Plane stress state| YES |
|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| 65|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
**For IANA = 1 (plane stress state)**
|MLAW|the method used to calculate the increments of stress \\ = 0 $\rightarrow$  Backword Euler method \\ = 1 $\rightarrow$ Radial Return method \\ = 2 $\rightarrow$  Decomposed mode method |
|MANA|= 0 $\rightarrow$ The tangent matrix obtained by setting $\dot{\lambda} = 0$ \\ = 1 $\rightarrow$ The tangent matrix obtained by setting $\dot{\lambda}_{eq}$ $\Rightarrow$ $\dot{\sigma}_{eq}$ \\ = 2 $\rightarrow$  The tangent matrix obtained by setting $\dot{\lambda}_{eq}$ $\Rightarrow$ $\dot{\varepsilon}_{eq}$\\ = 3 The tangent matrix obtained by the consistent condition|
**Else (plane strain and axisymmetric state)**
|MLAW| the method used to calculate the increments of stress \\ 0 $\rightarrow$ Radial Return method \\ 1 $ \rightarrow$ Implicit integration method\\ 2 $\rightarrow$  Modified implicit integration method|
__If MLAW = 0 (Radial return method)__
|MANA|= 0 $\rightarrow$ The tangent matrix obtained by setting $\dot{\omega} = 0$ \\ = 1 $\rightarrow$ The tangent matrix obtained by setting $\dot{\sigma}_{eq}$ = $\dot{\sigma}_{eq}^{trial}$ \\ = 2 $\rightarrow$  The tangent matrix obtained by setting $\dot{\sigma}_{eq}$ $\Rightarrow$ $\dot{\varepsilon}_{eq}$|
__Else (other methods)__
|MANA|= 0 $\rightarrow$ The tangent matrix obtained by setting $\dot{\lambda}_{vp} = 0$ \\ = 1 $\rightarrow$ The tangent matrix obtained by setting $\dot{\lambda}_{vp}$ $\Rightarrow$ $\dot{\sigma}_{eq}$ \\ = 2 $\rightarrow$  The tangent matrix obtained by setting $\dot{\lambda}_{eq}$ $\Rightarrow$ $\dot{\varepsilon}_{eq}$|

==== Real parameters ====

^Line 1 (4G10.0)^^
|E| YOUNG's elastic modulus |
|$\nu$| POISSON's ratio. |
|AC|parameter for $\sigma - \varepsilon$ relation|
|AM|parameter for $\sigma - \varepsilon$ relation|

Where:
\[\hat{\sigma}_{eq}=AC*\hat{D}_{eq}^{AM}\]
|$\hat{\sigma}_{eq}$| the equivalent deviatoric stress|
|$\hat{D}_{eq}$| the equivalent deviatoric velocity of deformation|


===== Stresses =====
==== Number of stresses ====
4
==== 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 ====
4
==== List of state variables ====
|Q(1)| element thickness (t) in plane stress state and generalized plane state  \\ 1 in plane strain state \\ circumferential strain rate ($\dot{varepsilon}_{\theta}$) in axisymmetric state|
|Q(2)| current yield limit in tension, its initial value is $R_{eo}$|
|Q(3)| equivalent deviatoric strain $\hat{\varepsilon}_{eq}$|
|Q(4)| equivalent deviatoric stress $\sigma_{eq}$ |
|Q(5)|critères de fractures|
|Q(10)|:::|
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