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perm-Holmes-Mow

Module: biphasic

Category: materialprop

Type string: "perm-Holmes-Mow"

Parameters

Name Description Default Units
perm perm 1 [L^4/F.t]
M M 0 []
alpha alpha 0 []

Description

The material type for Holmes-Mow permeability is perm-Holmes-Mow.

This isotropic material is similar to the constant isotropic permeability material described above, except that it uses a strain-dependent permeability tensor 1:

\[ \mathbf{k}=k\left(J\right)\mathbf{I}, \]

where,

\[ k\left(J\right)=k_{0}\left(\frac{J-\varphi_{r}^{s}}{1-\varphi_{0}}\right)^{\alpha}e^{\frac{1}{2}M\left(J^{2}-1\right)}\,, \]

and \(J\) is the Jacobian of the deformation, i.e. \(J=\det\mathbf{F}\) where \(\mathbf{F}\) is the deformation gradient. Here, \(\varphi_{r}^{s}\) is the referential solid volume fraction in the current configuration and \(\varphi_{0}=\varphi_{r}^{s}\left(0\right)\) is its value in the reference configuration.

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>

  1. Holmes, M. H. and Mow, V. C., "The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration", J Biomech 23, 11 (1990), pp. 1145-56. ↩