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

This material uses a strain-dependent permeability tensor that accommodates strain-induced anisotropy [7]: $$\begin{equation} \mathbf{k}=\left(k_{0r}\mathbf{I}+\frac{k_{1r}}{J^{2}}\mathbf{b}+\frac{k_{2r}}{J^{4}}\mathbf{b}^{2}\right)\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)e^{M\left(J^{2}-1\right)/2}\,,\label{eq504} \end{equation}$$ Note that the permeability in the reference state ($\mathbf{F}=\mathbf{I})$ is isotropic and given by $\mathbf{k}=\left(k_{0r}+k_{1r}+k_{2r}\right)\mathbf{I}$ .