2.2.13 Temperature-dependent inelastic materials

Product: ABAQUS/Explicit

Elements tested

T2D2 T3D2 B21 B31 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 2.2.13–1, and the material properties are listed in Table 2.2.13–1.

Results and discussion

Figure 2.2.13–2 shows the history plot of Mises stress for the Mises plasticity model for all elements. We can see the material softening because the yield stress drops as the temperature increases. Figure 2.2.13–3 through Figure 2.2.13–11 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.

Input files

temp_plastic.inp

Input data used in this analysis.

temp_plastic_ef1.inp

External file referenced in this input.

Table

Table 2.2.13–1 Material properties.

Material	Properties	T=0	T=100
Mises plasticity (density=8032)	E	193.1 × 10⁹	160.1 × 10⁹
		0.3	0.3
		206893	186893
	H	206893	186893
Drucker plasticity (density=1000)	E	2.1 × 10⁷	1.9 × 10⁷
		0.3	0.3
		40000	36000
	H	40000	39000
		40	39
	K	1.0	0.9
		20.0	19.0
Hill's plasticity (density=2500)	E	1.0 × 10⁹	8.0 × 10⁸
		0.3	0.31
		1.0 × 10⁶	9.0 × 10⁵
	H	4.0 × 10⁵	3.7 × 10⁵
Crushable foam with volumetric hardening (density=500)	E	3.0 × 10⁶	2.0 × 10⁶
		0.0	0.0
	k	1.1	0.9
		0.1	0.1
Crushable foam with isotropic hardening (density=500)	E	3.0 × 10⁶	2.0 × 10⁶
		0.0	0.0
	k	1.1	0.9
		0.2983	0.10
Ductile failure (density=5800)	E	2.0 × 10⁸	1.8 × 10⁸
		0.3	0.3
		2.0 × 10⁵	1.8 × 10⁵
	H	4.0 × 10⁵	3.8 × 10⁵
Hill's plasticity (density=5850)	E	1.8 × 10⁸	2.0 × 10⁸
(rate dependent)		0.3	0.3
		1.8 × 10⁵	1.7 × 10⁵
	H	–8000	–8000
Mises plasticity (density=1500)	E	2.0 × 10⁹	1.8 × 10⁹
(rate dependent)		0.4	0.4
		6.0 × 10⁷	5.5 × 10⁷
	H	2.0 × 10⁷	3.5 × 10⁷
Drucker-Prager/Cap plasticity	E	30000	29000
(density= 2.4 × 10^–3)		0.3	0.29
	d	100	99
		37.67	36.67
	R	0.1	0.11
		0.0	0.0
		0.01	0.011
Porous metal plasticity	E	2.0 × 10¹¹	1.8 × 10¹¹
(density=7.7 × 10⁷)		0.33	0.33
		7.5 × 10⁸	7.5 × 10⁸
	H	0.0	0.0

Figures

Figure 2.2.13–1 Temperature-dependent material property test for inelastic materials.

Figure 2.2.13–2 Mises stress versus time for Mises plasticity.

Figure 2.2.13–3 Mises stress versus time for Drucker plasticity.

Figure 2.2.13–4 Mises stress versus time for Hill's plasticity.

Figure 2.2.13–5 Mises stress versus time for crushable foam plasticity with volumetric hardening.

Figure 2.2.13–6 Mises stress versus time for crushable foam plasticity with isotropic hardening.

Figure 2.2.13–7 Mises stress versus time for ductile failure plasticity.

Figure 2.2.13–8 Mises stress versus time for rate-dependent Hill's plasticity.

Figure 2.2.13–9 Mises stress versus time for rate-dependent Mises plasticity.

Figure 2.2.13–10 Mises stress versus time for Drucker-Prager/Cap plasticity.

Figure 2.2.13–11 Mises stress versus time for porous metal plasticity.