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Subsubsection 4.8.2.5: Referentially Orthotropic Permeability Up Subsection 4.8.2: Permeability Materials Subsection 4.8.3: Fluid Supply Materials

#### 4.8.2.6 Referentially Transversely Isotropic Permeability

The material type for a biphasic material with strain-dependent permeability which is transversely isotropic in the reference configuration is “perm-ref-trans-iso”. The following material parameters need to be defined:
 isotropic hydraulic permeability [L/Ft] axial hydraulic permeability [L/Ft] axial hydraulic permeability [L/Ft] transverse hydraulic permeability [L/Ft] transverse hydraulic permeability [L/Ft] isotropic exponential strain-dependence coefficient () [ ] axial exponential strain-dependence coefficient () [ ] transverse exponential strain-dependence coefficient () [ ] isotropic power-law exponent () [ ] axial power-law exponent () [ ] transverse power-law exponent () [ ]
This material uses a strain-dependent permeability 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. is a second order tensor representing the spatial structural tensor describing the axial direction, given by where is a unit vector along the axial direction (defined as described in Section 4.1.1↑). Note that the permeability in the reference state ( is given by,
Example:
<permeability name="Permeability" type="perm-ref-trans-iso">
<perm0>0.002</perm0>
<perm1A>0.01</perm1A>
<perm2A>0.01</perm2A>
<perm1T>0.001</perm1T>
<perm2T>0.05</perm2T>
<M0>1.0</M0>
<MA>0.5</MA>
<MT>1.5</MT>
<alpha0>1.0</alpha0>
<alphaA>0.5</alphaA>
<alphaT>2.0</alphaT>
</permeability>


Subsubsection 4.8.2.5: Referentially Orthotropic Permeability Up Subsection 4.8.2: Permeability Materials Subsection 4.8.3: Fluid Supply Materials