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This material uses a strain-dependent permeability tensor that is orthotropic in the reference configuration, and accommodates strain-induced anisotropy [7]: $$\begin{equation} \mathbf{k}=k_{0}\mathbf{I}+\sum\limits _{a=1}^{3}k_{1}^{a}\mathbf{m}_{a}+k_{2}^{a}\left(\mathbf{m}_{a}\cdot\mathbf{b}+\mathbf{b}\cdot\mathbf{m}_{a}\right)\,,\label{eq505} \end{equation}$$ where, $$\begin{equation} \begin{aligned} & k_{0}=k_{0r}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{0}}}e^{M_{^{0}}\left(J^{2}-1\right)/2}\,,\\ & k_{1}^{a}=\frac{k_{1r}^{a}}{J^{2}}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{a}}}e^{M_{^{a}}\left(J^{2}-1\right)/2}\,,\\ & k_{2}^{a}=\frac{k_{2r}^{a}}{2J^{4}}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{a}}}e^{M_{a}\left(J^{2}-1\right)/2}\,. \end{aligned} \quad a=1,2,3\label{eq506} \end{equation}$$ Here, $\mathbf{m}_{a}$ are second order tensors representing the spatial structural tensors describing the orthogonal planes of symmetry, given by $$\begin{equation} \mathbf{m}_{a}=\mathbf{F}\cdot\left(\mathbf{V}_{a}\otimes\mathbf{V}_{a}\right)\cdot\mathbf{F}^{T},\quad a=1-3,\label{eq507} \end{equation}$$ where $\mathbf{V}_{a}$ are orthonormal vectors normal to the planes of symmetry. Note that the permeability in the reference state ($\mathbf{F}=\mathbf{I}$ ) is given by $\mathbf{k}=k_{0r}\mathbf{I}+\sum\limits _{a=1}^{3}\left(k_{1r}^{a}+k_{2r}^{a}\right)\mathbf{V}_{a}\otimes\mathbf{V}_{a}$ .