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Subsubsection 4.1.3.9: Holmes-Mow Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.11: Isotropic Elastic

#### 4.1.3.10 Holzapfel-Gasser-Ogden Unconstrained

The material type for the unconstrained Holzapfel-Gasser-Ogden material [28] is HGO unconstrained. The following material parameters must be defined:
 Shear modulus of ground matrix [P] Fiber modulus [P] Fiber exponential coefficient [P] Fiber mean orientation angle [deg] Fiber dispersion [] Bulk modulus [P]
The strain-energy function is given by: The fiber strain is where and . The Macaulay brackets around indicate that this term is zero when and equal to when this strain is positive.
There are two fiber families along the vectors (), lying in the plane of the local material axes , making an angle with respect to . Each fiber family has a dispersion , where . When there is no fiber dispersion, implying that all the fibers in that family act along the angle ; the value represents an isotropic fiber dispersion. All other intermediate values of produce a periodic von Mises fiber distribution, as described in [28]. is the shear modulus of the ground matrix; is the fiber modulus and is the exponential coefficient.
Unlike the uncoupled Holzapfel-Gasser-Ogden material presented in Section 4.1.2.6↑, this unconstrained version does not enforce isochoric deformation. This unconstrained model may be used to describe the porous solid matrix of a biphasic or multiphasic tissue model, where pore volume may change in response to influx or efflux of interstitial fluid.
Example:
<material id="2" type="HGO unconstrained">
<c>7.64</c>
<k1>996.6</k1>
<k2>524.6</k2>
<gamma>49.98</gamma>
<kappa>0.226</kappa>
<k>7.64e3</k>
</material>


Subsubsection 4.1.3.9: Holmes-Mow Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.11: Isotropic Elastic