Link Search Menu Expand Document
Converted document
 Subsubsection 4.1.2.4: Ellipsoidal Fiber Distribution Veronda-Westmann Up Subsection 4.1.2: Uncoupled Materials Subsubsection 4.1.2.6: Gent Material 

4.1.2.5 Fung Orthotropic

The material type for orthotropic Fung elasticity [31, 32] is “Fung orthotropic”. The following material parameters must be defined:
<E1> Young's modulus [P]
<E2> Young's modulus [P]
<E3> Young's modulus [P]
<G12> shear modulus [P]
<G23> shear modulus [P]
<G31> shear modulus [P]
<v12> Poisson's ratio [ ]
<v23> Poisson's ratio [ ]
<v31> Poisson's ratio [ ]
<c> coefficient [P]
<k> bulk modulus [P]
The hyperelastic strain energy function is given by [4], 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: Gent Material