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Subsection 4.1.3: Unconstrained Materials Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.2: Cell Growth

#### 4.1.3.1 Carter-Hayes

The material type for a Carter-Hayes material is Carter-Hayes. The following parameters must be defined:
 Young's modulus at reference density [P] reference density [M/L] exponent of solid-bound molecule density for calculation of Young's modulus [ ] Poisson's ratio [ ] index of solid bound molecule [ ]
This model describes an unconstrained neo-Hookean material [19] whose Young's modulus is a power-law function of the referential apparent density of a solid-bound molecule. It is derived from the following hyperelastic strain-energy function: Here, is the right Cauchy-Green deformation tensor and is the determinant of the deformation gradient tensor.
Young's modulus depends on according to a power law [20, 21], This type of material references a solid-bound molecule that belongs to a multiphasic mixture. Therefore this material may only be used as the solid (or a component of the solid) in a multiphasic mixture (Section 4.10↓). The solid-bound molecule must be defined in the <Globals> section (Section 3.4.3↑) and must be included in the multiphasic mixture using a <solid_bound> tag. The parameter sbm must refer to the global index of that solid-bound molecule. The value of is specified within the <solid_bound> tag. If a chemical reaction is defined within that multiphasic mixture that alters the value of , lower and upper bounds may be specified for this referential density within the <solid_bound> tag to prevent from reducing to zero or achieving excessively elevated values.
Example:
<material id="1" name="solid matrix" type="multiphasic">
<phi0>0</phi0>
<solid_bound sbm="1">
<rho0>1</rho0>
<rhomin>0.1</rhomin>
<rhomax>5</rhomax>
</solid_bound>
<fixed_charge_density>0</fixed_charge_density>
<solid type="Carter-Hayes">
<sbm>1</sbm>
<E0>10000</E0>
<rho0>1</rho0>
<gamma>2.0</gamma>
<v>0</v>
</solid>
<permeability type="perm-const-iso">
<perm>1</perm>
</permeability>
<osmotic_coefficient type="osm-coef-const">
<osmcoef>1</osmcoef>
</osmotic_coefficient>
<reaction name="solid remodeling" type="mass-action-forward">
<Vbar>0</Vbar>
<vP sbm="1">1</vP>
<forward_rate type="Huiskes reaction rate">
<B>1</B>
<psi0>0.01</psi0>
</forward_rate>
</reaction>
</material>


Subsection 4.1.3: Unconstrained Materials Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.2: Cell Growth