Table of Contents
EVP-BONZ
This page does not match the code. The law corresponding to ITYPE = 36 is law KOLYM; in addition, LBONZ.F does not exist in Prepro.
Description
Elastic-visco-plastic constitutive law for solid elements at constant temperature (Bodner model)
The model
This law is used for a 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: LBONZ.F
Lagamine:
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 | 36 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
Integer parameters
| Line 1 (I5) | |
|---|---|
| NINTV | number of sub‑steps used to integrate numerically the constitutive equation in a time step. |
Real parameters
| 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 ($n$) |
Stresses
Number of stresses
= 6 for 3-D 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
= 17 for 3-D state
= 15 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 3-D 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 (N=10 for 3-D state, N=8 for other cases) |
| Q(N+1) | equivalent strain |
| Q(N+2$\rightarrow$N+7) | failure criteria |