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Subsubsection 4.1.3.13: Orthotropic CLE Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.15: Natural Neo-Hookean

#### 4.1.3.14 Osmotic Pressure from Virial Expansion

The material type for osmotic pressure from virial expansion is “osmotic virial expansion”. The following material parameters need to be defined:
 Fluid volume fraction in reference (strain-free) configuration, [ ] Concentration of interstitial solute causing the osmotic pressure (moles per volume of the mixture in the reference configuration), [n/L] First virial coefficient [FL/n] Second virial coefficient [FL/n] Third virial coefficient [FL/n]
The Cauchy stress for this material is where is the osmotic pressure, given by is the solute concentration in the current configuration, and is the relative volume.
This osmotic swelling pressure in the interstitial fluid of a porous material represents an entropic mechanism whose magnitude is independent of the external bath osmolarity. Typically, this material should be used in a solid mixture where the swelling pressure is resisted by a solid matrix in tension.
Example:
<Material>
<material id="1" type="solid mixture">
<solid type="osmotic virial expansion">
<phiw0>0.8</phiw0>
<cr lc="1">100</cr>
<c1>2.436e-6</c1>
<c2>0</c2>
<c3>0</c3>
</solid>
<solid type="spherical fiber distribution"/>
</material>
</Material>