====== EP1GDP ======
===== Description =====
Elasto-plastic constitutive law for solid elements at constant temperature \\
First gradient – plane deformation \\
→ for second gradient method from grenoble \\
\\
Implemented by: P. Besuelle, 2002

==== The model ====
This law is only  used for mechanical analysis of elastic isotropic solids undergoing large strains.
==== Files ====
Prepro: LEP1GDP.F \\
Lagamine: EP1GDP.F

===== Availability =====
|Plane stress state| NO |
|Plane strain state| YES |
|Axisymmetric state| NO |
|3D state| NO |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 581|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (1I5) ^^
|ISOL| = 0 : use of total stresses in the constitutive law|
|:::| $\neq$ 0 : use of effective stresses in the constitutive law. See [[appendices:a8|Appendix 8]] |
==== Real parameters ====
^ Line 1 (5G10.0 ) ^^
|K| K elastic modulus |
|G1| G1 elastic modulus |
|G2| G2 elastic modulus |
|ELIM| Peak deformation |
|RHO| Specific mass|
===== 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 ====
11
==== List of state variables ====
|Q(1)| = 1 in plane strain state |
|Q(2)| RHO actualised specific mass |
|Q(3)| $F_{11}$ deformation gradient |
|Q(4)| $F_{12}$ deformation gradient |
|Q(5)| $F_{21}$ deformation gradient |
|Q(6)| $F_{22}$ deformation gradient |
|Q(7)| ELIMP actualised peak deformation |
|Q(8)| Second deviatoric strain increment invariant |
|Q(9)| Second deviatoric strain invariant |
|Q(10)| IYIELD Plastic loading index |
|Q(11)| Second deviatoric stress invariant |