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 Subsubsection Holmes-Mow Up Subsection 4.1.3: Unconstrained Materials Subsubsection Isotropic Elastic 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:
<c> Shear modulus of ground matrix [P]
<k1> Fiber modulus [P]
<k2> Fiber exponential coefficient [P]
<gamma> Fiber mean orientation angle [deg]
<kappa> Fiber dispersion []
<k> 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↑, 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.
<material id="2" type="HGO unconstrained">

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