====== ANI3VH ======

===== Description =====

Anisotropic elasto-plastic law based on texture for solid elements at constant temperature.

==== The model ====

This law is used for mechanical analysis of elasto-plastic anisotropic solids undergoing large strains. Isotropic hardening is assumed.

==== Files ====

Prepro: LANIVH.F \\
Lagamine: ANI3VH.F

===== Availability =====

|Plane stress state| NO |
|Plane strain state| NO |
|Axisymmetric state| NO |
|3D state| YES |
|Generalized plane state| NO |

===== Input file =====

==== Parameters defining the type of constitutive law ====

^ Line 1 (2I5, 60A1)^^
|IL|Law number \\ Texture data being read as metallurgical data, this constitutive law MUST BE THE FIRST one (IL=1) |
|ITYPE| 500 FIXME 500 seems to be attributed to 2 different laws in LAWPRE.F|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|

==== Integer parameters ====

^ Line 1 (2I5) ^^
|NINTV| (Absolute) number of sub-steps used to integrate numerically the constitutive equation in a time step |
|:::| (Sign) indicator for analytical (+) or numerical (-) tangent matrix |
|METH| (Absolute) type of anisotropic yield surface to be used |
|:::| = ± 1 : Based on texture measurements (P. van Houtte), use MDPAM = -1 |
|:::| = ± 2 Hill, use MDPAM = -2 |
|:::| = ± 6 : Based on texture measurements (B. van Bael), use the correct MDPAM (< -5)|
|:::| < 0 : Use global axes |
|:::| > 0 : Use local axes |

==== Real parameters ====

^ Line 1 (7G10.0) ^^
|E| YOUNG's elastic modulus |
|ANU| POISSON's ratio |
|AK / AK| Hardening factor K (see below) |
|EPS0 / GAMMA0| Hardening deformation (see below) |
|AN| Hardening exponent (see below) |
|AM| Hardening rate exponent (not used) |
|TOL1| Tolerance (texture based yield surface) |
^ Line 2 (1G10.0) ^^
|TOLF| Idem |

__If METH=$\pm$2__ (Hill):
^ Line 1 (7G10.0) ^^
|E| YOUNG's elastic modulus |
|ANU| POISSON's ratio |
|AK / AK| Hardening factor K (see below) |
|EPS0 / GAMMA0| Hardening deformation (see below) |
|AN| Hardening exponent (see below) |
|AM| Hardening rate exponent (not used) |
|TOL1| Tolerance (texture based yield surface) |
^ Line 2 (7G10.0) ^^
|TOLF| Idem |
|HILL(1)| $\alpha_{23}$ |
|HILL(2)| $\alpha_{13}$ |
|HILL(3)| $\alpha_{12}$ |
|HILL(4)| $\alpha_{44}/2$ |
|HILL(5)| $\alpha_{55}/2$ |
|HILL(6)| $\alpha_{66}/2$ |

===== Stresses =====

==== Number of stresses ====

6 for 3D state

==== 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)|$\sigma_{yz}$|

===== State variables =====

==== Number of state variables ====

3

==== List of state variables ====

|Q(1)| Yield indicator |
|:::| = 0 : Current state is elastic |
|:::| = 1 : Current state is elasto-plastic |
|Q(2)| Equivalent plastic strain EPSEQ |
|Q(3)| Equivalent plastic strain rate |

==== Hardening form ====

  - If METH = ± 2 (HILL law): SIGMAY = AK*(EPS0+EPSEQ)^AN : \[\sigma=K(\varepsilon_0+\varepsilon_{eq})^N\]
  - If METH = ± 6 (law based on texture measurements): TAU=AK*(GAMMA0-GAMMA)^AN : \[\tau=K'(\Gamma^{\circ}+\Gamma)^N\]