diff-ref-iso

Module: solute

Category: materialprop

Type string: "diff-ref-iso"

Parameters

Name	Description	Default	Units
free_diff	free diffusivity	1	[L^2/t]
diff0	diff0	1	[L^2/t]
diff1	diff1	0	[L^2/t]
diff2	diff2	0	[L^2/t]
M	M	0	[]
alpha	alpha	0	[]

Description

The material type for a strain-dependent diffusivity tensor which is isotropic in the reference configuration is diff-ref-iso.

This material uses a strain-dependent diffusivity tensor that accommodates strain-induced anisotropy:

\[ \mathbf{d}=\left(d_{0r}\mathbf{I}+\frac{d_{1r}}{J^{2}}\mathbf{b}+\frac{d_{2r}}{J^{4}}\mathbf{b}^{2}\right)\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{r}^{s}}\right)e^{M\left(J^{2}-1\right)/2}, \]

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 diffusivity in the reference state \((\mathbf{F}=\mathbf{I})\) is isotropic and given by \(\mathbf{d}=\left(d_{0r}+d_{1r}+d_{2r}\right)\mathbf{I}\).

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>