$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

This material model is a hyperelastic Mooney-Rivlin type with uncoupled deviatoric and volumetric behavior. The uncoupled strain energy W is given by: $$\begin{equation} W=c_{1}\left(\tilde{I}_{1}-3\right)+c_{2}\left(\tilde{I}_{2}-3\right)+\frac{1}{2}K\left(\ln J\right)^{2}\,.\label{eq449} \end{equation}$$ Here, $c_{1}$ and $c_{2}$ are the Mooney-Rivlin material coefficients, $\tilde{I}_{1}$ and $\tilde{I}_{2}$ are the invariants of the deviatoric part of the right Cauchy-Green deformation tensor, $\mathbf{\tilde{C}}=\mathbf{\tilde{F}}^{T}\cdot\mathbf{\tilde{F}}$ , where $\mathbf{\tilde{F}}=J^{-1/3}\mathbf{F}$ , $\mathbf{F}$ is the deformation gradient and $J=\det\mathbf{F}$ is the Jacobian of the deformation. When $c_{2}=0$ , this model reduces to an uncoupled version of the incompressible neo-Hookean constitutive model.