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Subsubsection 4.1.3.1: Carter-Hayes Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.3: Cubic CLE

4.1.3.2 Cell Growth

The material type for cell growth is “cell growth[8]. The following material parameters need to be defined:
 intracellular solid volume fraction in reference (strain-free) configuration, [ ] intracellular molar content of membrane-impermeant solute (moles per volume of the cell in the reference configuration), [n/L] extracellular osmolarity, [n/L]
The Cauchy stress for this material is where is the osmotic pressure, given by where is the relative volume. The values of the universal gas constant and absolute temperature must be specified as global constants.
Cell growth may be modeled by simply increasing the mass of the intracellular solid matrix and membrane-impermeant solute. This is achieved by allowing the parameters and to increase over time as a result of growth, by associating them with user-defined load curves. Since cell growth is often accompanied by cell division, and since daughter cells typically achieve the same solid and solute content as their parent, it may be convenient to assume that and increase proportionally, though this is not an obligatory relationship. To ensure that the initial configuration is a stress-free reference configuration, let in the initial state prior to growth.
Example (using units of mm, N, s, nmol, K):
<Globals>
<Constants>
<T>298</T>
<R>8.314e-06</R>
<Fc>0</Fc>
</Constants>
</Globals>
<Material>
<material id="1" name="Cell" type="cell growth">
<phir lc="1">1</phir>
<cr lc="2">1</cr>
<ce>300</ce>
</material>
</Material>