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# Example30Material with Temperature-Dependent Anisotropic Coefficient of Expansion

General

• The material has the temperature-dependent anisotropic coefficient of expansion. The deformation under thermal load is analyzed.

• Multi-step thermal load analysis is performed. There are multiple reached temperatures. The stresses for each temperature are solved.

• Unless specified in the list below, the default conditions will be applied.

### Analysis Space

 Item Settings Analysis Space 3D Model unit mm

### Analysis Conditions

The temperature is applied evenly on the model.

Opt for the thermal load in the analysis condition, and set the reference temperature and the reached temperature.

There is no need to couple with the thermal analysis [Watt].

 Item Settings Solvers Mechanical Stress Analysis [Galileo] Analysis Type Static analysis Options Select “Thermal load”.

The Step/Thermal Load tab is set as follows.

In this setting, thermal load analysis is performed with 3 reached temperatures step by step.

Tab

Setting Item

Settings

Step Setting

Reference temperature

25[deg]

Step/Reached Temperature Setting

 Step Substeps Reached temperature [deg] 1 1 50 2 1 75 3 1 100

### Model

The model is a cubic solid body. The material has the temperature-dependent anisotropic coefficient of expansion. The outer boundary condition is

set with no displacement.

### Body Attributes and Materials

The material properties are set up as follows: The temperature dependency for the coefficient of expansion is set for the range of 25-50, 50-75, and 75-100 [deg].

For each temperature range, the anisotropy is set.

 Material Name Tab Properties Material_Property_001 Elasticity Material Type: Elastic/Isotropic Temperature Dependency: No Young’s modulus: 1×10^9[Pa] Poisson’s ratio: 0.3 Coefficient of Expansion Temperature Dependency: Select Anisotropy: Anisotropic   The temperature dependency of the coefficient of expansion is set as follows. alpha1, alpha2 and alpha3 are the coefficients for x,y and z directions.     * This is not the actual material’s property.

### Boundary Conditions

 Boundary Condition Name/Topology Tab Boundary Condition Type Settings Outer Boundary Condition Mechanical Displacement Select all X/Y/Z components. UX=0, UY=0, UZ=0

### Results

The figure below shows the principal stress at 50 deg.

From 25 to 50 deg, it is supposed to expand in X direction. However, as the outer boundary is fully fixed, the compressive stress is exhibited instead.

The figure below shows the principal stress at 75 deg.

From 50 to 75 deg, it is supposed to expand in Y direction. Again, as the outer boundary is fully fixed, the compressive stress in Y direction is exhibited instead, and added to that of X direction.

The figure below shows the principal stress at 100 deg.

From 75 to 100 deg, it is supposed to expand in Z direction. Again, as the outer boundary is fully fixed, the compressive stress in Z direction is exhibited instead, and added to those of X and Y directions.

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