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Subsubsection 4.9.3.4: Referentially Orthotropic Diffusivity Up Subsection 4.9.3: Diffusivity Materials Subsection 4.9.4: Solubility Materials

4.9.3.5 Albro Isotropic Diffusivity

The material type for a porosity and concentration-dependent diffusivity which is isotropic is “diff-Albro-iso”. The following material parameters need to be defined:
 free diffusivity [L/t] inverse of characteristic concentration for concentration-dependence [L/n] coefficient of porosity-dependence [ ]
This material uses a porosity and concentration-dependent diffusivity tensor that remains isotropic with deformation: where and the porosity varies with deformation according to the kinematic constraint is the Jacobian of the deformation, i.e. where is the deformation gradient and is the referential solid volume fraction. Here, represents the actual concentration of the solute whose diffusivity is given by . 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>