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 Subsection 4.1.3: Unconstrained Materials Up Subsection 4.1.3: Unconstrained Materials Subsubsection Cell Growth Carter-Hayes

The material type for a Carter-Hayes material is Carter-Hayes. The following parameters must be defined:
<E0> Young's modulus at reference density [P]
<rho0> reference density [M/L ]
<gamma> exponent of solid-bound molecule density for calculation of Young's modulus [ ]
<v> Poisson's ratio [ ]
<sbm> 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.
<material id="1" name="solid matrix" type="multiphasic">
  <solid_bound sbm="1">
  <solid type="Carter-Hayes">
  <permeability type="perm-const-iso">
  <osmotic_coefficient type="osm-coef-const">
  <reaction name="solid remodeling" type="mass-action-forward">
    <vP sbm="1">1</vP>
    <forward_rate type="Huiskes reaction rate">

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