This material uses a strain-dependent permeability tensor that accommodates strain-induced anisotropy: $$\mathbf{k}=\left(k_{0r}\mathbf{I}+\frac{k_{1r}}{J^{2}}\mathbf{b}+\frac{k_{2r}}{J^{4}}\mathbf{b}^{2}\right)\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)^{\alpha}e^{M\left(J^{2}-1\right)/2},$$ where $J$ is the Jacobian of the deformation, i.e. $J=\det\mathbf{F}$ where $\mathbf{F}$ is the deformation gradient, and $\mathbf{b}=\mathbf{F}\cdot\mathbf{F}^{T}$ is the left Cauchy-Green tensor. Note that the permeability in the reference state ($\mathbf{F}=\mathbf{I})$ is isotropic and given by $\mathbf{k}=\left(k_{0r}+k_{1r}+k_{2r}\right)\mathbf{I}$ .

Example:

<permeability name="Permeability" type="perm-ref-iso">
  <perm0>0.001</perm0>
  <perm1>0.005</perm1>
  <perm2>0.002</perm2>
  <M>1.5</M>
  <alpha>2</alpha>
</permeability>