====== ANI-DAM ======
===== Description =====
Elasto(-visco)-plastic damage law of anisotropic materials for solid elements at variable temperature 
==== The model ====
Mechanical analysis of thermo-elasto(-visco)-plastic-damage orthotropic solids undergoing large strains, plastic mixed hardening and damage isotropic hardening are assumed. 
==== Files ====
Prepro: LADAM.F \\
Lagamine: ADAM2S.F, ADAM2E.F, ADAM2A.F, ADAM3D.F
===== Availability =====
|Plane stress state|YES |
|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| 235|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing.|
==== Integer parameters ====
^ Line 1 (9I5) ^^
|NTEMP|number of temperature at which material data are given (one temperature is possible)|
|NINTV| number of sub-steps used to integrate numerically the constitutive equation in a time step|
|MTHER|1, for adiabatic case (uncoupled model) \\ others, for coupled model|
|IVISC| 1, for EVP law \\ others, for EP law|
|MMATE|1, for brittle material\\ others, for ductile material|
|NTRAN|0 always\\ It was the old **wrong** way to use material principal axes different from the global axes. In such a case, you must use local axes, see control parameters|
|MNINTV|Max. of number of sub-steps (0$\rightarrow$100)|
|MITERA|number of sub-iteration (0$\rightarrow$10)|
|MUTIP|number of multiplicator for sub-steps (0$\rightarrow$2)|


==== Real parameters ====
**__2D Case__**
^Line 1 (7G10.0)^^
|ECROU| 0 for isotropic hardening\\ 1 for kinematic hardening\\ [0,1] for mixed hardening|
|COEFQ|TAYLOR-QUINNEY's coefficient (q)|
|DNMAX| 0 for EP without damage\\ (0,1) $rightarrow$ Max. damage value at initial fracture \\ otherwise $\rightarrow$ 0.95 limit damage value|
|PROC|precision of iteration\\ (0 $\rightarrow$1.D-3)|
|TEMP0|initial temperature|
|ANGLE|Angle between the 1-2 principal axes of material and X-Y axes of co-ordinate. Only for 2D|
|THICK|thickness for plane state.|
**__3D Case__**
^Line 1 (7G10.0)^^
|ECROU| 0 for isotropic hardening\\ 1 for kinematic hardening\\ [0,1] for mixed hardening|
|COEFQ|TAYLOR-QUINNEY's coefficient (q)|
|DNMAX| 0 for EP without damage\\ (0,1) $rightarrow$ Max. damage value at initial fracture \\ otherwise $\rightarrow$ 0.95 limit damage value|
|PROC|precision of iteration\\ (0 $\rightarrow$1.D-3)|
|TEMP0|initial temperature|
|TRAN11|gradient of material principal direction in global coordinate|
|TRAN12|:::|
^Line 2 (7G10.0)^^
|TRAN13|gradient of material principal direction in global coordinate|
|TRAN21|:::|
|TRAN22|:::|
|TRAN23|:::|
|TRAN31|:::|
|TRAN32|:::|
|TRAN33|:::|

**__Both cases__**
^Line 1 (6G10.0)^^
|TEMP| temperature|
|ROC|heat capacity per unit volume (used when MTHER = 1)|
|VISCO|viscosity parameter (unit: time).|
|ALPHAT1|thermal expansion coefficient in 1 direction|
|ALPHAT2|thermal expansion coefficient in 2 direction|
|ALPHAT3|thermal expansion coefficient in 3 direction|
^Line 2 (6G10.0)^^
|E1|YOUNG's modulus in 1 direction|
|RP01|yield limit of uniaxial tension in 1 direction|
|ET1|elasto-plastic tangent modulus in 1 direction|
|ANU12|POISSON's ratio in 1-2 plane|
|RD01|initial damage limit in 1 direction|
|DT1|damage tangent modulus in 1 direction|
^Line 3 (6G10.0)^^
|E2|YOUNG's modulus in 2 direction|
|RP02|yield limit of uniaxial tension in 2 direction|
|ET2|elasto-plastic tangent modulus in 2 direction|
|ANU23|POISSON's ratio in 2-3 plane|
|RD02|initial damage limit in 2 direction|
|DT2|damage tangent modulus in 2 direction|
^Line 4 (6G10.0)^^
|E3|damage tangent modulus in 2 direction|
|RP03|yield limit of uniaxial tension in 3 direction|
|ET3|elasto-plastic tangent modulus in 3 direction|
|ANU13|POISSON's ratio in 1-3 plane|
|RD03|initial damage limit in 3 direction|
|DT3|damage tangent modulus in 3 direction|
^Line 5 (3G10.0)^^
|G12|shear elastic modulus in 1-2 plane|
|RP012|yield limit in 1-2 plane|
|GT12|elasto-plastic shear tangent modulus in 1-2 plane|
^Line 6 (3G10.0)^^
|G23|shear elastic modulus in 2-3 plane|
|RP023|yield limit in 2-3 plane|
|GT23|elasto-plastic shear tangent modulus in 2-3 plane|
^Line 7 (3G10.0)^^
|G13|shear elastic modulus in 1-3 plane|
|RP013|yield limit in 1-3 plane|
|GT13|elasto-plastic shear tangent modulus in 1-3 plane|














===== Stresses =====
==== Number of stresses ====
6 for the 3D state \\ 4 for the other cases
==== 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)|$\sigma_{YZ}$|
For the other cases:
|SIG(1)|$\sigma_{XX}$|
|SIG(2)|$\sigma_{YY}$|
|SIG(3)|$\sigma_{XY}$|
|SIG(4)|$\sigma_{ZZ}$|
===== State variables =====
==== Number of state variables ====
28 for the 3D state\\ 26 for the other cases
==== List of state variables ====
|Q(1)| element thickness (t) in plane stress state \\ 1 in plane strain state \\ circumferential strain rate $\dot{\varepsilon_\theta}$ in axisymmetric state \\ 0 in 3D state|
|Q(2)| 0  if the current state is elastic\\ 1  if the current state is elasto-plastic |
|Q(3)| 0  if the current state is not damage\\ 1  if the current state is damage |
|Q(4)| initial temperature|
|Q(5)| equivalent plastic strain ($\varepsilon_{eq}$) |
|Q(6)| equivalent damage ($d_{eq}$)|
|Q(7)| plastic hardening level (R)|
|Q(8)| damage hardening level (B)|
|Q(9)| damage in 1 direction of material ($D_{1}$)|
|Q(10)| damage in 2 direction of material ($D_{2}$)|
|Q(11)| damage in 3 direction of material ($D_{3}$)|
|Q(12)| equivalent stress ($\sigma_{eq}$)|
|Q(13)| plastic work per unit volume ($W_p$)|
|Q(14)| damage work per unit volume ($W_d$)|
|Q(15)| part of the dissipated power converted into heat ($\dot{Q}$)|
|Q(16)| total strain energy per unit volume ($W_t$)  (elastic + plastic + damage)|
|Q(17)| fracture criteria|
|Q(22)||
|Q(23)| back stresses for kinematic and mixed hardening|
|Q(N)| (N = 28 for 3-D state, = 26 for other cases)|