The InelasticPotential material law regroups all the inelastic contributions $\mathbf{F}^{in}$ to the total deformation gradient $\mathbf{F}$. The law is responsible for the computation of the elastic part $\mathbf{F}^{in}$ of the total deformation gradient and associated elastic volume variation $J^e$ as
$$
\mathbf{F}^e = \mathbf{F} \left(\mathbf{F}^{in}\right)^{-1} \hspace{.3cm} \text{and} \hspace{.3cm} J^e = \frac{J}{J^{in}}
$$
Isotropic thermal expansion writes $$ \mathbf{F}^{in} = \mathbf{F}^{th} = \left( 1+\alpha \right) \mathbf{I} \hspace{.3cm} \text{and} \hspace{.3cm} J^{in}=\left( 1+\alpha \right)^3 $$ with $\alpha$ the isotropic thermal expansion coefficient.
| Name | Metafor Code | Dependency |
|---|---|---|
| Isotropic thermal expansion coefficient ($\alpha$) | HYPER_THERM_EXPANSION | TO/TM |
Orthotropic thermal expansion writes $$ \mathbf{F}^{in} = \mathbf{F}^{th} = \mathbf{I}+\boldsymbol{\alpha} \hspace{.3cm} = \left[ \begin{array}{c c c} 1+\alpha_1 & 0 & 0 \\ 0 & 1+\alpha_2 & 0 \\ 0 & 0 & 1+\alpha_3 \end{array} \right] \text{and} \hspace{.3cm} J^{in}=\left( 1+\alpha_1 \right)\left( 1+\alpha_2 \right)\left( 1+\alpha_3 \right) $$ with $\boldsymbol{\alpha}$ the orthotropic thermal expansion (diagonal) matrix expressed in the material axes!
| Name | Metafor Code | Dependency |
|---|---|---|
| Orthotropic thermal expansion coefficient ($\alpha_1$) | HYPER_THERM_EXPANSION_1 | TO/TM |
| Orthotropic thermal expansion coefficient ($\alpha_2$) | HYPER_THERM_EXPANSION_2 | TO/TM |
| Orthotropic thermal expansion coefficient ($\alpha_3$) | HYPER_THERM_EXPANSION_3 | TO/TM |