This material uses a porosity and concentration-dependent diffusivity tensor that remains isotropic with deformation: $$\mathbf{d}=d_{0}\exp\left(-\alpha_{D}\frac{1-\varphi^{w}}{\varphi^{w}}-\frac{c}{c_{D}}\right)\mathbf{I},$$ where $c_{D}^{-1}=1/c_{D}$ and the porosity $\varphi^{w}$ varies with deformation according to the kinematic constraint $$\varphi^{w}=1-\frac{\varphi_{r}^{s}}{J}\,.$$ $J$ is the Jacobian of the deformation, i.e. $J=\det\mathbf{F}$ where $\mathbf{F}$ is the deformation gradient and $\varphi_{r}^{s}$ is the referential solid volume fraction. Here, $c$ represents the actual concentration of the solute whose diffusivity is given by $\mathbf{d}$ . This constitutive relation is based on the experimental findings reported by Albro et al. [1].

Example:

<solute sol="1">
  <diffusivity type="diff-Albro-iso">
    <free_diff>123e-6</free_diff>
    <alphad>18</alphad>
    <cdinv>0.0625</cdinv>
  </diffusivity>
  <solubility type="solub-const">
    <solub>1</solub>
  </solubility>
</solute>