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 Subsubsection 4.1.3.6: Ellipsoidal Fiber Distribution Neo-Hookean Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.8: Fung Orthotropic Compressible 

4.1.3.7 Ellipsoidal Fiber Distribution with Donnan Equilibrium Swelling

The material type for a swelling pressure combined with an ellipsoidal continuous fiber distribution is “EFD Donnan equilibrium”. The swelling pressure is described by the equations for ideal Donnan equilibrium, assuming that the material is porous, with a charged solid matrix, and the external bathing environment consists of a salt solution of monovalent counter-ions. The following material parameters need to be defined:
<phiw0> gel porosity (fluid volume fraction) in reference (strain-free) configuration, [ ]
<cF0> fixed-charge density in reference (strain-free) configuration, [n/L ]
<bosm> external bath osmolarity, [n/L ]
<beta> parameters [ ]
<ksi> parameters [P]
The Cauchy stress for this material is given by, is the stress contribution from the fibers, as described in Section 4.1.1↑. is the stress from the Donnan equilibrium response, as described in Section 4.1.3.4↑
Example (using units of mm, N, s, nmol, K):
<material id="1" type="EFD Donnan equilibrium">
  <phiw0>0.8</phiw0>
  <cF0 lc="1">1</cF0>
  <bosm>300</bosm>
  <beta>3,3,3</beta>
  <ksi>0.01,0.01,0.01</ksi>
  <mat_axis type="local">0,0,0</mat_axis>
</material>
<LoadData>
  <loadcurve id="1">
    <loadpoint>0,0</loadpoint>
    <loadpoint>1,150</loadpoint>
  </loadcurve>
</LoadData>
<Globals>
  <Constants>
    <R>8.314e-6</R>
    <T>310</T>
  </Constants>
</Globals>


 Subsubsection 4.1.3.6: Ellipsoidal Fiber Distribution Neo-Hookean Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.8: Fung Orthotropic Compressible