Rate-dependent Mises plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
- Plasticity
Hardening:
Yield stress | Plastic strain |
200. |
0.0000 |
220. |
0.0009 |
220. |
0.0029 |
Rate dependence parameter, D=40.0
Rate dependence parameter, p=5.0
The rate dependence parameters are as follows for the test that verifies the temperature dependencies:
D=30.0, p=3.0 at 10.0° |
D=50.0, p=7.0 at 20.0° |
The power law is entered as a piecewise linear relationship for the cases in which rate-dependent test data are specified directly. (The units are not important.)
Results and discussion
The results agree well with exact analytical or approximate solutions.
Adiabatic rate-dependent Mises plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=30.0E6
Poisson's ratio, =0.3
- Plasticity
Hardening:
Yield stress | Plastic strain | Temperature |
30.0E3 |
0.000 |
0.0 |
50.0E3 |
0.200 |
0.0 |
50.0E3 |
2.000 |
0.0 |
- Other properties
Density, =1000.0
Specific heat, c=0.4
Inelastic heat fraction = 0.5
Rate dependence parameter, D=40.0
Rate dependence parameter, p=5.0
The power law is entered as a piecewise linear relationship for the cases in which rate-dependent test data are specified directly. (The units are not important.)
Results and discussion
The results agree well with exact analytical or approximate solutions.
Rate-dependent Hill plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
- Plasticity
Hardening:
Yield stress | Plastic strain |
200. |
0.0000 |
220. |
0.0009 |
220. |
0.0029 |
Anisotropic yield ratios: 1.5, 1.2, 1.0, 1.0, 1.0, 1.0
Rate dependence parameter, D=40.0
Rate dependence parameter, p=5.0
The power law is entered as a piecewise linear relationship for the cases in which rate-dependent test data are specified directly. (The units are not important.)
Results and discussion
The results agree well with exact analytical or approximate solutions.
Rate-dependent Drucker-Prager plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=300.0E3
Poisson's ratio, =0.3
- Plasticity
The linear Drucker-Prager model is used in each case.
Angle of friction, =40.0
Dilation angle, =40.0
Rate dependence parameter, D=10.0
Rate dependence parameter, p=1.0
For the test that verifies the temperature dependencies, the rate dependence parameters are as follows:
D=9.0, p=0.9 at 10.0° |
D=11.0, p=1.1 at 20.0° |
Hardening curve:
Yield stress | Plastic strain |
6.0E3 |
0.000000 |
9.0E3 |
0.020000 |
11.0E3 |
0.063333 |
12.0E3 |
0.110000 |
12.0E3 |
1.000000 |
The power law is entered as a piecewise linear relationship for the cases in which rate-dependent test data are specified directly. (The units are not important.)
Results and discussion
The tests in this section are set up as cases of homogeneous deformation of a single element of unit dimensions. Consequently, the results are identical for all integration points within the element. The constitutive path is integrated with 20 increments of fixed size.
Rate-dependent crushable foam plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=3.0E6
Poisson's ratio, =0.2
- Plasticity
Initial yield stress in hydrostatic compression, =2.0E5
Strength in hydrostatic tension, =2.0E4
Initial yield stress in uniaxial compression, =2.2E5
Yield stress ratio, =1.1
Yield stress ratio, =0.1
Rate dependence parameter, D=10.0
Rate dependence parameter, p=1.0
Hardening curve (from uniaxial compression):
Yield stress | plastic strain |
2.200E5 |
0.0 |
2.465E5 |
0.1 |
2.729E5 |
0.2 |
2.990E5 |
0.3 |
3.245E5 |
0.4 |
3.493E5 |
0.5 |
3.733E5 |
0.6 |
3.962E5 |
0.7 |
4.180E5 |
0.8 |
4.387E5 |
0.9 |
4.583E5 |
1.0 |
4.938E5 |
1.2 |
5.248E5 |
1.4 |
5.515E5 |
1.6 |
5.743E5 |
1.8 |
5.936E5 |
2.0 |
6.294E5 |
2.5 |
6.520E5 |
3.0 |
6.833E5 |
5.0 |
6.883E5 |
10.0 |
For the test that verifies the temperature dependencies, the rate dependence parameters are as follows:
D=9.0, p=0.9 at 10.0° |
D=11.0, p=1.1 at 20.0° |
The power law is entered as a piecewise linear relationship for the cases in which rate-dependent test data are specified directly. (The units are not important.)
Results and discussion
The results agree well with exact analytical or approximate solutions.
Rate-dependent porous metal plasticity
Elements tested
Problem description
Material:
- Elasticity
Young's modulus, E=200.0E3
Poisson's ratio, =0.3
- Plasticity
Hardening curve:
Yield stress | Plastic strain |
200.0 |
0.0000 |
220.0 |
0.0009 |
220.0 |
0.0029 |
Rate dependence parameter, D=40.0
Rate dependence parameter, p=5.0
- Porous metal plasticity
===1.0
Initial relative density, =0.95 (=0.05).
(The units are not important.)
Results and discussion
The results agree well with exact analytical or approximate solutions.
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