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Subsubsection 4.1.3.15: Natural Neo-Hookean Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.17: Coupled Mooney-Rivlin

4.1.3.16 Neo-Hookean

The material type for a Neo-Hookean material is neo-Hookean. The following parameters must be defined:
 Young's modulus [P] Poisson's ratio [ ]
This model describes an unconstrained Neo-Hookean material [19]. It has a non-linear stress-strain behavior, but reduces to the classical linear elasticity model for small strains and small rotations. It is derived from the following hyperelastic strain-energy function: Here, and are the first and second invariants of the right Cauchy-Green deformation tensor and is the determinant of the deformation gradient tensor. The relationship between the material parameters, E, and v, and the parameters used in the strain-energy function, is as follows.
This material model uses a standard displacement-based element formulation, so care must be taken when modeling materials with nearly-incompressible material behavior to avoid element locking. For this case, use the Mooney-Rivlin material described in Section 4.1.2.7↑.
Example:
<material id="1" type="neo-Hookean">
<E>1000.0</E>
<v>0.45</v>
</material>


Subsubsection 4.1.3.15: Natural Neo-Hookean Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.17: Coupled Mooney-Rivlin