Skip to content

perm-exp-iso

Module: biphasic

Category: materialprop

Type string: "perm-exp-iso"

Parameters

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

Description

The material type for exponential isotropic permeability is perm-exp-iso.

This isotropic material model has the general form

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

where \(J=\det\mathbf{F}\) is the determinant of the deformation gradient. For this material model,

\[ k\left(J\right)=k_{0}\exp\left(M\frac{J-1}{J-\varphi_{0}}\right)\,, \]

where \(\varphi_{0}\) is the referential solid volume fraction of the porous solid matrix. Pore closure occurs as \(J\) approaches \(\varphi_{0}\) from above, in which case the permeability reduces to zero,

\[ \lim_{J\to\varphi_{0}}k\left(J\right)=0\,. \]

Representative variations of \(k\left(J\right)/k_{0}\) are shown in the figure below.

FigPermExpIso.png

Figure 1. Exponential isotropic permeability, showing dependence of \(k\left(J\right)/k_{0}\) on material parameter \(M\), when \(\varphi_{0}=0.2\) and \(\varphi_{0}<J\le1.2\).

Example: 

<permeability name="Permeability" type="perm-exp-iso">
  <perm>0.001</perm>
  <M>1.5</M>
</permeability>