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

This material uses a strain-dependent diffusivity tensor that is orthotropic in the reference configuration and accommodates strain-induced anisotropy: $$\begin{equation} \mathbf{d}=d_{0}\mathbf{I}+\sum\limits _{a=1}^{3}d_{1}^{a}\mathbf{m}_{a}+d_{2}^{a}\left(\mathbf{m}_{a}\cdot\mathbf{b}+\mathbf{b}\cdot\mathbf{m}_{a}\right)\,,\label{eq513} \end{equation}$$ where $$\begin{equation} \begin{aligned}d_{0} & =d_{0r}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{0}}}e^{M_{^{0}}\left(J^{2}-1\right)/2}\,,\\ d_{1}^{a} & =\frac{d_{1r}^{a}}{J^{2}}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{a}}}e^{M_{^{a}}\left(J^{2}-1\right)/2}\,,\\ d_{2}^{a} & =\frac{d_{2r}^{a}}{2J^{4}}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha_{^{a}}}e^{M_{a}\left(J^{2}-1\right)/2}\,. \end{aligned} \quad a=1,2,3\label{eq514} \end{equation}$$ Here, $J$ is the Jacobian of the deformation, i.e. $J=\det\mathbf{F}$ where $\mathbf{F}$ is the deformation gradient. $\mathbf{m}_{a}$ are second order tensor representing the spatial structural tensors describing the orthogonal planes of symmetry, given by $$\begin{equation} \mathbf{m}_{a}=\mathbf{F}\cdot\left(\mathbf{V}_{a}\otimes\mathbf{V}_{a}\right)\cdot\mathbf{F}^{T},\quad a=1-3\,,\label{eq515} \end{equation}$$ 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 $\mathbf{k}=k_{0r}\mathbf{I}+\sum\limits _{a=1}^{3}\left(k_{1r}^{a}+k_{2r}^{a}\right)\mathbf{V}_{a}\otimes\mathbf{V}_{a}$ .