This isotropic material is similar to the constant isotropic permeability material described above, except that it uses a strain-dependent permeability tensor [32]: $$\mathbf{k}=k\left(J\right)\mathbf{I},$$ where, $$k\left(J\right)=k_{0}\left(\frac{J-\varphi_{0}}{1-\varphi_{0}}\right)^{\alpha}e^{\frac{1}{2}M\left(J^{2}-1\right)}\,,$$ and $J$ is the Jacobian of the deformation, i.e. $J=\det\mathbf{F}$ where $\mathbf{F}$ is the deformation gradient.

Example:

This example defines a permeability material of the Holmes-Mow type.

<permeability type="perm-Holmes-Mow">
  <perm>0.001</perm>
  <M>1.5</M>
  <alpha>2</alpha>
</permeability>