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Subsubsection 4.1.2.5: Fung Orthotropic Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.7: Mooney-Rivlin

#### 4.1.2.6 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:
 Shear modulus of ground matrix [P] Fiber modulus [P] Fiber exponential coefficient [P] Fiber mean orientation angle [deg] Fiber dispersion [] 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.
Example:
<material id="2" type="Holzapfel-Gasser-Ogden">
<c>7.64</c>
<k1>996.6</k1>
<k2>524.6</k2>
<gamma>49.98</gamma>
<kappa>0.226</kappa>
<k>1e5</k>
</material>


Subsubsection 4.1.2.5: Fung Orthotropic Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.7: Mooney-Rivlin