Temperature-dependent inelastic materials

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Explicit

Elements tested

T2D2

T3D2

B21

B31

PIPE21

PIPE31

SAX1

S4R

S4RS

S4RSW

C3D8R

CPE4R

CPS4R

CAX4R

M3D4R

Features tested

Temperature-dependent material properties with predefined field variables are tested for the following inelastic material models: Mises plasticity, Drucker plasticity, Hill's potential plasticity, crushable foam plasticity with volumetric hardening, crushable foam plasticity with isotropic hardening, ductile failure plasticity, rate-dependent Hill's potential plasticity, rate-dependent Mises plasticity, Drucker-Prager/Cap plasticity, and porous metal plasticity.

Problem description

This verification test consists of a set of single-element models that include combinations of all of the available element types with all of the available material models. All of the elements are loaded with a tensile load defined by specifying the vertical velocity at the top nodes of each element with the bottom nodes fixed. The temperature at all nodes of each element increases from an initial value of 0° to a final value of 100°. The material properties are defined as a linear function of temperature. For every material model only those element types available for the model are used. The undeformed meshes are shown in Figure 1, and the material properties are listed in Table 1.

Results and discussion

Figure 2 shows the history plot of Mises stress for the Mises plasticity model for all elements, except for pipe elements, which are consistent with beams. We can see the material softening because the yield stress drops as the temperature increases. Figure 3 through Figure 11 show the history plots of Mises stress for the other material models.

This problem tests the features listed but does not provide independent verification of them.

Tables

Table 1. Material properties.
Material Properties T=0 T=100
Mises plasticity (density=8032) E 193.1 × 109160.1 × 109
  ν0.3 0.3
  σ0206893 186893
  H 206893 186893
Drucker plasticity (density=1000) E 2.1 × 1071.9 × 107
  ν0.3 0.3
  σ040000 36000
  H  40000 39000
  β40 39
  K 1.0 0.9
  ψ20.0 19.0
Hill's plasticity (density=2500) E 1.0 × 1098.0 × 108
  ν0.3 0.31
  σ01.0 × 1069.0 × 105
  H 4.0 × 1053.7 × 105
Crushable foam with volumetric hardening (density=500) E 3.0 × 1062.0 × 106
  ν0.0 0.0
  k1.1 0.9
  kt0.1 0.1
Crushable foam with isotropic hardening (density=500) E 3.0 × 1062.0 × 106
  ν0.0 0.0
  k1.1 0.9
  νp0.2983 0.10
Ductile failure (density=5800) E 2.0 × 1081.8 × 108
  ν0.3 0.3
  σ02.0 × 1051.8 × 105
  H 4.0 × 1053.8 × 105
Hill's plasticity (density=5850) E 1.8 × 1082.0 × 108
(rate dependent) ν0.3 0.3
  σ01.8 × 1051.7 × 105
  H −8000 −8000
Mises plasticity (density=1500) E 2.0 × 1091.8 × 109
(rate dependent) ν0.4 0.4
  σ06.0 × 1075.5 × 107
  H 2.0 × 1073.5 × 107
Drucker-Prager/Cap plasticity E 30000 29000
(density= 2.4 × 10−3) ν0.3 0.29
  d 100 99
  β37.67 36.67
  R 0.1 0.11
  ϵv⁢o⁢lp⁢l0.0 0.0
  α0.01 0.011
Porous metal plasticity E 2.0 × 10111.8 × 1011
(density=7.7 × 107) ν0.33 0.33
  σ07.5 × 1087.5 × 108
  H 0.0 0.0

Figures

Figure 1. Temperature-dependent material property test for inelastic materials.

Figure 2. Mises stress versus time for Mises plasticity.

Figure 3. Mises stress versus time for Drucker plasticity.

Figure 4. Mises stress versus time for Hill's plasticity.

Figure 5. Mises stress versus time for crushable foam plasticity with volumetric hardening.

Figure 6. Mises stress versus time for crushable foam plasticity with isotropic hardening.

Figure 7. Mises stress versus time for ductile failure plasticity.

Figure 8. Mises stress versus time for rate-dependent Hill's plasticity.

Figure 9. Mises stress versus time for rate-dependent Mises plasticity.

Figure 10. Mises stress versus time for Drucker-Prager/Cap plasticity.

Figure 11. Mises stress versus time for porous metal plasticity.