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This isotropic material has a permeability that varies as a function of the determinant $J$ of the deformation gradient. Its general form is $$\begin{equation} \mathbf{k}=k\left(J\right)\mathbf{I}\,,\label{eq:isotropic-permeability} \end{equation}$$ where, $$\begin{equation} k\left(J\right)=k_{0}\exp\left(M\frac{J-1}{J-\varphi_{0}}\right)\,.\label{eq:perm-exp-iso} \end{equation}$$ Pore closure occurs as $J$ approaches $\varphi_{0}$ from above, in which case the permeability reduces to zero, $$\begin{equation} \lim_{J\to\varphi_{0}}k\left(J\right)=0\,.\label{eq:perm-pore-closure} \end{equation}$$ In the special case when $M=0$ , the permeability becomes constant. In the limit of infinitesimal strains, the permeability has the form $$\begin{equation} k\left(J\right)=k_{0}\left(1+\frac{M}{1-\varphi_{0}}\left(J-1\right)+\mathcal{O}\left(\left(J-1\right)^{2}\right)\right)\,.\label{eq:perm-expiso-Taylor} \end{equation}$$