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 Subsubsection Fung Orthotropic Up Subsection 4.1.2: Uncoupled Materials Subsubsection Mooney-Rivlin Holzapfel-Gasser-Ogden

The material type for the uncoupled Holzapfel-Gasser-Ogden material [28] is Holzapfel-Gasser-Ogden. 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]
This material model uncouples deviatoric and volumetric behaviors. The deviatoric strain-energy function is given by: where and the default volumetric strain energy function is 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.
<material id="2" type="Holzapfel-Gasser-Ogden">

 Subsubsection Fung Orthotropic Up Subsection 4.1.2: Uncoupled Materials Subsubsection Mooney-Rivlin