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 Subsubsection 4.9.3.2: Constant Orthotropic Diffusivity Up Subsection 4.9.3: Diffusivity Materials Subsubsection 4.9.3.4: Referentially Orthotropic Diffusivity 

4.9.3.3 Referentially Isotropic Diffusivity

The material type for a strain-dependent diffusivity tensor which is isotropic in the reference configuration is “diff-ref-iso”. The following material parameters need to be defined:
<free_diff> free diffusivity [L /t]
<diff0> diffusivity [L /t]
<diff1> diffusivity [L /t]
<diff2> diffusivity [L /t]
<M> exponential strain-dependence coefficient ( ) [ ]
<alpha> power-law exponent ( ) [ ]
This material uses a strain-dependent diffusivity tensor that accommodates strain-induced anisotropy: where is the jacobian of the deformation, i.e. where is the deformation gradient, and is the left Cauchy-Green tensor. Note that the diffusivity in the reference state ( is isotropic and given by .
Example:
<diffusivity name="Diffusivity" type="diff-ref-iso">
  <phi0>0.2</phi0>
  <free_diff>0.005</free_diff>
  <diff0>0.001</diff0>
  <diff1>0.005</diff1>
  <diff2>0.002</diff2>
  <M>1.5</M>
  <alpha>2</alpha>
</diffusivity>


 Subsubsection 4.9.3.2: Constant Orthotropic Diffusivity Up Subsection 4.9.3: Diffusivity Materials Subsubsection 4.9.3.4: Referentially Orthotropic Diffusivity