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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>