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Subsubsection 4.1.2.4: Ellipsoidal Fiber Distribution Veronda-Westmann Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.6: Holzapfel-Gasser-Ogden

#### 4.1.2.5 Fung Orthotropic

The material type for orthotropic Fung elasticity [26, 27] is “Fung orthotropic”. The following material parameters must be defined:
 Young's modulus [P] Young's modulus [P] Young's modulus [P] shear modulus [P] shear modulus [P] shear modulus [P] Poisson's ratio [ ] Poisson's ratio [ ] Poisson's ratio [ ] coefficient [P] bulk modulus [P]
The hyperelastic strain energy function is given by [3], where, Here, and where defines the initial direction of material axis . See Section 4.1.1.2↑ on how to define the material axes for orthotropic materials. The Lamé constants ( and (, are related to Young's moduli , shear moduli and Poisson's ratios via The orthotropic Lamé parameters should produce a positive definite stiffness matrix.
Example:
<material id="3" type="Fung orthotropic">
<E1>124</E1>
<E2>124</E2>
<E3>36</E3>
<G12>67</G12>
<G23>40</G23>
<G31>40</G31>
<v12>-0.075</v12>
<v23>0.87</v23>
<v31>0.26</v31>
<c>1</c>
<k>120000</k>
</material>

Subsubsection 4.1.2.4: Ellipsoidal Fiber Distribution Veronda-Westmann Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.6: Holzapfel-Gasser-Ogden