====== BODATH ======
===== Description =====
Bodner elastic-visco-plastic constitutive damage law with thermal effects for solid elements at variable temperature.
==== The model ====
Coupled thermo-mechanical analysis with damage of elastic-visco-plastic solids undergoing large strains.
==== Files ====
Prepro: LBODAT.F \\
Lagamine: BODC2E.F, BODC2A.F, BODC3D.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| 246|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing.|
==== Integer parameters ====
^ Line 1 (9I5) ^^
|NTEMP|number of temperatures at which material data are given|
|NINTV| number of sub-steps used to integrate numerically the constitutive equation in a time step|
|IFRAC|usefulness actually|
|ISDOT|>0\\ <0|

====  Real parameters independent of the temperature ====
^Line 1 (7G10.0)^^
|E|YOUNG's elastic modulus|
|ANU|POISSON's ratio|
|D0|assumed limiting plastic-shear strain rate|
|D1|maximum of directional hardness|
|RK1|maximum of istropic hardness|
|RM1|hardening exponent of isotropic hardness|
|RM2|hardening exponent of directional hardness|
^Line 2 (4G10.0)^^
|R1|recovery exponent of isotropic hardness|
|R2| recovery exponent of directional hardness|
|ALPHA| thermal expansion coefficient ($\alpha$)|
|COEF|TAYLOR QUINNEY's coefficient|
====Real parameters dependent of the temperature  ====
Repeat NTEMP times
^Line 1 (6G10.0)^^
|TEMPE| temperature|
|RKO|initial isotropic hardness ($K_o$) at temperature T|
|RK2|minimum or stable isotropic hardness ($K_o$) at temperature T|
|A1|recovery coefficient of isotropic hardness at temperature T|
|A2|recovery coefficient of directional hardness at temperature T|
|RN|strain rate sensitivity coefficient (n) at temperature T|
==== Real parameters related to the damage model====
^Line 1 (7G10.0)^^
|A|coefficient of stress function in the damage model (A)|
|S|exponent of stress function in the damage model (S)|
|THOLD|stress threshold for damage onset|
|R|exponent of equivalent plastic strain rate|
|TAUCO|ratio of deviatoric to volumetric damage|
|BETA|constant in the triaxial stress function|
|DSMAX|failure value of deviatoric damage|
===== 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 ====
25 for the 3D state\\ 23 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 \\ = element thickness (t) in generalized plane state |
|Q(2)| current equivalent stress in tension |
|Q(3)| current isotropic hardness, its initial value is KO|
|Q(4)| equivalent directional hardness |
|Q(5)-Q(N)| components of directional hardness (N = 10 for 3D state and N = 8 for other cases)|
|Q(N+1)| equivalent strain|
|Q(N+2)| deviatoric damage|
|Q(N+3)| volumetric damage|
|Q(N+4)|PUISB|
|Q(N+5)| PUISB*DELTAT (its final value is calculated in THNL2 or THNL3)|
|Q(N+6)| RHO * C (calculated in THNL2 or THNL3)|
|Q(N+7)-Q(N+12)| fracture criteria (not programmed)|
|Q(N+13)| NINTV|
|Q(N+14)| deviatoric damage rate|
|Q(N+15)| 0 if d < DSMAX\\ 1 if d > or = DSMAX|