====== Inelastic Potentials ======
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
$$
\mathbf{F}^e = \mathbf{F} \left(\mathbf{F}^{in}\right)^{-1} \hspace{.3cm} \text{and} \hspace{.3cm}  J^e = \frac{J}{J^{in}}
$$

===== IsotropicThermalExpansion =====

=== Description ===
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.

=== Parameters ===
^   Name                                                  ^  Metafor Code  ^ Dependency ^
|  Isotropic thermal expansion coefficient ($\alpha$)  |  ''HYPER_THERM_EXPANSION''  |  ''TO/TM''  |

===== OrthotropicThermalExpansion =====

=== Description ===
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!



=== Parameters ===
^   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''  |