====== HIL-JET ======
===== Description =====
Elasto isotrop-plastic anisotropic constitutive law for solid elements at constant temperature for element jet.
==== The model ====
Mechanical analysis of elasto isotropic-plastic anisotropic element undergone large deformation.  Isotropic hardening is assumed. 
==== Files ====
Prepro: LJTHIL.F \\
Lagamine: JT2HIL.F, JT3HIL.F
===== 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| 63|
|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 \\  -1 calcul automatique du NINTV |
|NPOINT| number of points to define the hardening law |
==== Real parameters ====
^ Line 1 (2G10.0) ^^
|E|Young modulus|
|ANU|Poisson ratio|
=== If NPOINT = 0 ===
^Line 1 (2G10.0)^^
|SY11|$\sigma_{11}^{y}$| 
|ET11|$E_{11}^{t}$|
^Line 2 (2G10.0)^^
|SY22|$\sigma_{22}^{y}$| `
|ET22|$E_{22}^{t}$|
^Line 3 (2G10.0)^^
|SY33|$\sigma_{33}^{y}$|
|ET33| $E_{33}^{t}$|
^Line 4 (2G10.0)^^
|SY12|$\sigma_{12}^{y}$|
|ET12|$E_{12}^{t}$|
For 3D analysis:
^Line 5 (2G10.0)^^
|SY13|$\sigma_{13}^{y}$|
|ET13|$E_{13}^{t}$|
^Line 6 (2G10.0)^^
|SY23|$\sigma_{23}^{y}$|
|ET23|$E_{23}^{t}$|

===If NPOINT > 0 ===
It needs at least 3 cards for this law (I7, NPOINT = 2) 
^Line 1 (7G10.0)^^ 
|SY11| $\sigma_{xx}^{y}$| 
|SY22|$\sigma_{yy}^{y}$|
|SY33| $\sigma_{zz}^{y}$| 
|SY12|$\sigma_{xy}^{y}$|
|SY13| $\sigma_{xz}^{y}$| 
|SY23|$\sigma_{zy}^{y}$|
^Line 2 (2G10.0) - Repeated NPOINT times^^
|EPS(I)|(equivalent $\sigma - \epsilon$ relation)|
| SIG(I)|:::|
With NPOINT > 0, the shape of the yield locus is constant ; only its size evolves. The normality rule is not completely fulfilled with this option. It is indeed defined as :\\
$\dot{\lambda}\frac{\partial f}{\partial \underline{\sigma}} = \underline{\dot{\varepsilon}^{p}} $ = $ \begin{pmatrix} \dot{\varepsilon_{11}^{p} }\\ \dot{\varepsilon_{22}^{p} }\\ \dot{\varepsilon_{33}^{p} }\\ \dot{\gamma_{12}^{p} } \\ \dot{\gamma_{13}^{p} } \\ \dot{\gamma_{23}^{p} }\end{pmatrix}$ instead of $ \begin{pmatrix} \dot{\varepsilon_{11}^{p} }\\ \dot{\varepsilon_{22}^{p} }\\ \dot{\varepsilon_{33}^{p} }\\ \dot{\varepsilon_{12}^{p} } \\ \dot{\varepsilon_{13}^{p} } \\ \dot{\varepsilon_{23}^{p} }\end{pmatrix}$
 ===== Stresses =====
==== Number of stresses ====
4 for 2D analysis \\ 6 for 3D analysis
==== Meaning ====
The stresses are the components of CAUCHY stress tensor in global (X,Y,Z) coordinates. \\
For the 2D analysis
|SIG(1)|$\sigma_{XX}$|
|SIG(2)|$\sigma_{YY}$|
|SIG(3)|$\sigma_{ZZ}$|
|SIG(4)|$\sigma_{XY}$|
For 3D analysis:
|SIG(1)|$\sigma_{XX}$|
|SIG(2)|$\sigma_{YY}$|
|SIG(3)|$\sigma_{ZZ}$|
|SIG(4)|$\sigma_{XY}$|
|SIG(5)|$\sigma_{XZ}$|
|SIG(6)|$\sigma_{YZ}$|


===== State variables =====
==== Number of state variables ====
31 for 2D analysis\\
24 for 3D analysis
==== List of state variables ====
|Q(1)| current yield limit in tension|
|Q(2)| equivalent plastic strain ($\epsilon$)|
|Q(3)| equivalent VM type stress for this element|
|Q(4)|$\sigma_{xx}$ in local axes of the element |
|Q(5)|$\sigma_{yy}$ in local axes of the element |
|Q(6)|$\sigma_{zz}$ in local axes of the element |
|Q(7)|$\sigma_{xy}$ in local axes of the element  |
|Q(8)|$\sigma_{1}$ anti-hourglass stress|
|Q(9)|$\sigma_{2}$ anti-hourglass stress|
|Q(10 to 13)|x  nodal coordinates in local axes of the element  |
|Q(14 to 17)|y  nodal coordinates in local axes of the element |
|Q(18)|0 in plane state \\ average radius (Xcoordinate) of the element in axisymmetric state|
|Q(19)| area of the element in the XY plane |
|Q(20)| area of the no deformed element |
|Q(21)| X(4) - X(2) in initial structure |
|Q(22)| X(3) - X(1) in initial structure |
|Q(23)| Y(4) - Y(2) in initial structure  |
|Q(24)| Y(4) - Y(2) in initial structure |
|Q(25)|$A_{11}$ parameter of anisotropy|
|Q(26)| $A_{12}$ parameter of anisotropy |
|Q(27)| $A_{13}$ parameter of anisotropy |
|Q(28)| $A_{22}$ parameter of anisotropy |
|Q(29)| $A_{23}$ parameter of anisotropy |
|Q(30)| $A_{33}$ parameter of anisotropy |
|Q(31)| $A_{44}$ parameter of anisotropy |
For 3D analysis:
|Q(1)| current yield limit tension |
|Q(2)| equivalent plastic strain ($\overline{\varepsilon}^{p}$)|
|Q(3)| equivalent VM type stress for this element |
|Q(4)|$\sigma_{11}$ anti-hourglass stress |
|Q(5)| $\sigma_{12}$ anti-hourglass stress |
|Q(6)| $\sigma_{13}$ anti-hourglass stress |
|Q(7)| $\sigma_{21}$ anti-hourglass stress |
|Q(8)| $\sigma_{22}$ anti-hourglass stress |
|Q(9)| $\sigma_{23}$ anti-hourglass stress |
|Q(10)| $\sigma_{31}$ anti-hourglass stress |
|Q(11)| $\sigma_{32}$ anti-hourglass stress |
|Q(12)| $\sigma_{33}$ anti-hourglass stress |
|Q(13)| $\sigma_{41}$ anti-hourglass stress |
|Q(14)| $\sigma_{42}$ anti-hourglass stress |
|Q(15)| $\sigma_{43}$ anti-hourglass stress |
|Q(16)| $A_{11}$ parameter of anisotropy |
|Q(17)| $A_{12}$ parameter of anisotropy |
|Q(18)| $A_{13}$ parameter of anisotropy |
|Q(19)| $A_{22}$ parameter of anisotropy |
|Q(20)| $A_{23}$ parameter of anisotropy |
|Q(21)| $A_{33}$ parameter of anisotropy |
|Q(22)| $A_{44}$ parameter of anisotropy |
|Q(23)| $A_{55}$ parameter of anisotropy |
|Q(24)| $A_{66}$ parameter of anisotropy |