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BODAM
Description
Elastic-visco-plastic constitutive law for solid elements at constant temperature (Bodner model) with damage.
The model
This law is used for mechanical analysis of elastic-visco-plastic isotropic solids undergoing large strains. Strain rate effects and isotropic and directional hardening or recovery are included.
Files
Prepro: LBODAM.F
Lagamine: BODA2E.F, BODA2A.F, BODA3D.F
Availability
| Plane stress state | NO |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | YES |
Input file
Parameters defining the type of constitutive law
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 505 |
| COMMNT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (I5) | |
|---|---|
| NINTV | > 0 : Number of sub-steps used to integrate numerically the constitutive equation in a time step |
| = 0 : NINTV will be calculated in the law | |
Real parameters
Old versions (prior to 2019) of the code and the manual indicate Line 1 & Line 2 to be one single line, which is not possible considering the format (7G10.0); old data files may not be compatible with more recent versions of the code.
| Line 1 (7G10.0) | |
|---|---|
| E | YOUNG's elastic modulus |
| ANU | POISSON's ratio |
| D0 | Assumed limiting plastic-shear strain rate ($D_0$) |
| D1 | Directional hardening coefficient ($D_1$) |
| RK0 | Initial isotropic hardness ($K_0$) |
| RK1 | Maximum or limiting isotropic hardness ($K_1$) |
| RK2 | Minimum or stable isotropic hardness ($K_2$) |
| Line 2 (7G10.0) | |
| A1 | Recovery coefficient of isotropic hardness ($A_1$) |
| A2 | Recovery coefficient of directional hardness ($A_2$) |
| RM1 | Hardening exponent of isotropic hardness ($m_1$) |
| RM2 | Hardening exponent of directional hardness ($m_2$) |
| R1 | Recovery exponent of isotropic hardness ($r_1$) |
| R2 | Recovery exponent of directional hardness ($r_2$) |
| RN | Strain rate sensitivity coefficient ($n$) |
| Line 3 (7G10.0) | |
| A | Constant dividing the stress ($A$) |
| S | Exponent of the stress function ($s$) |
| THOLD | Threshold stress value ($\sigma_D$) |
| R | Exponent of equivalent plastic strain rate ($r$) |
| TAUCO | Ratio between deviatoric and isotropic damage ($\tau$) |
| BETA | Constant in the triaxial stress function ($\beta$) |
| DSMAX | Failure value of deviatoric damage |
Stresses
Number of stresses
6 for 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
= 22 for the 3D state
= 20 for the other cases
List of state variables
N = 10 for 3D state
N = 8 for other cases
| Q(1) | Element thickness ($t$) in plane stress state |
| = 1 : Plane strain state | |
| Circumferential strain rate ($\dot{\varepsilon}_{\theta}$) in axisymmetrical 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 $K_0$ |
| Q(4) | Equivalent directional hardness |
| Q(5)$\rightarrow$Q(N) | Components of directional hardness |
| Q(N+1) | Equivalent strain |
| Q(N+2) | Deviatoric damage |
| Q(N+3) | Bulk damage |
| Q(N+4$\rightarrow$N+9) | Fracture criteria (not programmed) |
| Q(N+10) | NINTV |
| Q(N+11) | $\dot{d}$ |
| Q(N+12) | = 0 if $d<d_{max}$ |
| = 1 if $d\geq d_{max}$ |
