ABAQUS Verification Manual  


2.2.5 Temperature-dependent elastic materials

Product: ABAQUS/Explicit  

Elements tested

T2D2    T3D2    B21    B31    SAX1    S4R    S4RS    S4RSW    C3D8R    CPE4R    CPS4R    CAX4R    M3D4R    C3D10M    CPS6M    CPE6M    CAX6M   

Features tested

Temperature-dependent material properties with predefined temperature fields are tested for the following elastic material models: isotropic elasticity, orthotropic elasticity, anisotropic elasticity, and lamina.

Problem description

This verification test consists of a set of single element models that include combinations of all the available element types with all the available material models. All 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 velocity is ramped from zero to 0.2. The temperature at all nodes increases from an initial value of 0° to a final value of 100°. The material properties are defined as a linear function of temperature, as shown in Table 2.2.5–1. The density for all the materials is 7850. For every material model, only those element types available for the model are used. The undeformed meshes are shown in Figure 2.2.5–1.

Results and discussion

Figure 2.2.5–2 shows the plot of vertical stress versus vertical strain for the isotropic elasticity model. The plots of vertical stress versus vertical strain for orthotropic elasticity (ENGINEERING CONSTANTS), orthotropic elasticity (ORTHOTROPIC), anisotropic elasticity, and lamina are shown in Figure 2.2.5–3, Figure 2.2.5–4, Figure 2.2.5–5, and Figure 2.2.5–6, respectively. The vertical stress and vertical strain are and for the truss, beam, and axisymmetric shell elements and and for the remaining elements.

Input files

temp_elastic.inp

Input data used in this analysis.

temp_elastic_ef1.inp

External file referenced in this analysis.

temp_elastic_simpson.inp

Explicit dynamics analysis using Simpson integration through the shell thickness.

temp_elastic_restart.inp

Restart data that completes 25 milliseconds of the response.

Table

Table 2.2.5–1 Material properties.

MaterialPropertiesT=0T=100
Isotropic elasticityE193.1 × 10997.0 × 109
 0.00.0
Orthotropic elasticity2.0 × 10111.0 × 1011
(ENGINEERING CONSTANTS)1.0 × 10115.0 × 1010
 1.0 × 10115.0 × 1010
 0.00.0
 0.00.0
 0.00.0
 7.69 × 10106.69 × 1010
 7.69 × 10106.69 × 1010
 9.0 × 1098.0 × 109
Orthotropic elasticity2.24 × 10111.00 × 1011
(ORTHOTROPIC)4.79 × 1054.59 × 105
 1.23 × 10110.5 × 1011
 4.21 × 1054.00 × 105
 4.74 × 1054.00 × 105
 1.21 × 10110.5 × 1011
 7.69 × 10107.00 × 1010
 7.69 × 10107.00 × 1010
 9.00 × 1098.00 × 109
Lamina2.0 × 10111.0 × 1011
 1.5 × 10110.7 × 1011
 0.00.0
 2.00 × 10101.80 × 1010
 9.00 × 1098.00 × 109
 8.50 × 1097.50 × 109
Anisotropic elasticity2.24 × 10111.00 × 1011
 4.79 × 1054.00 × 105
 1.23 × 10110.5 × 1011
 4.21 × 1054.00 × 105
 4.74 × 1054.00 × 105
 1.21 × 10110.5 × 1011
 1.00 × 1069.00 × 105
 2.00 × 1061.80 × 106
 3.00 × 1062.60 × 106
 7.69 × 10107.00 × 1010
 4.00 × 1063.60 × 106
 5.00 × 1064.60 × 106
 6.00 × 1065.60 × 106
 7.00 × 1066.60 × 106
 7.69 × 10107.00 × 1010
 8.00 × 1067.60 × 106
 9.00 × 1068.00 × 106
 1.00 × 1079.00 × 106
 1.10 × 1071.00 × 107
 1.20 × 1071.10 × 107
 9.00 × 1098.00 × 109


Figures

Figure 2.2.5–1 Temperature-dependent material property test for elastic materials.

Figure 2.2.5–2 Vertical stress versus vertical strain for isotropic elasticity.

Figure 2.2.5–3 Vertical stress versus vertical strain for orthotropic elasticity (ENGINEERING CONSTANTS).

Figure 2.2.5–4 Vertical stress versus vertical strain for orthotropic elasticity (ORTHOTROPIC).

Figure 2.2.5–5 Vertical stress versus vertical strain for anisotropic elasticity.

Figure 2.2.5–6 Vertical stress versus vertical strain for lamina.