*EXPANSION

Keyword type: model definition, material

This option is used to define the thermal expansion coefficients of a material. They are interpreted as total expansion coefficients with respect to a reference temperature $T_{ref}$, i.e. the thermal strain $\epsilon_{th}$ of a material at a final temperature T and with initial temperature $T_{0}$ is determined by

$$\epsilon_{th}=\alpha(T)(T-T_{ref})-\alpha(T_o)(T_o-T_{ref}),$$ (168)

where $\alpha(T)$ is the thermal coefficient at a temperature T. There are two optional parameters TYPE and ZERO. Default for TYPE is TYPE=ISO, other values are TYPE=ORTHO for orthotropic materials and TYPE=ANISO for anisotropic materials. All constants may be temperature dependent. The parameter ZERO is used to determine the reference temperature, default is 0.

First line:

• *EXPANSION
• Enter the TYPE and ZERO parameters and their values, if needed

Following line for TYPE=ISO:

• $\alpha$.
• Temperature.

Repeat this line if needed to define complete temperature dependence.

Following line for TYPE=ORTHO:

• $\alpha_{11}$.
• $\alpha_{22}$.
• $\alpha_{33}$.
• Temperature.

Repeat this line if needed to define complete temperature dependence.

Following line for TYPE=ANISO:

• $\alpha_{11}$.
• $\alpha_{22}$.
• $\alpha_{33}$.
• $\alpha_{12}$.
• $\alpha_{13}$.
• $\alpha_{23}$.
• Temperature.

Repeat this line if needed to define complete temperature dependence.

Example:

*EXPANSION,ZERO=273.
12.E-6,373.
20.E-6,573.

tells you that the thermal strain in a body made of this material is $100. \times 12. \times 10^{-6}=12. \times 10^{-4}$ if heated from T=273 to T=373, and $300 \times 20 \times 10^{-6}=60 \times 10^{-4}$ if heated from T=273 to T=573.

Example files: beamt, beamt2.