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Subsubsection 4.1.3.14: Osmotic Pressure from Virial Expansion Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.16: Neo-Hookean

4.1.3.15 Natural Neo-Hookean

The material type for a natural Neo-Hookean material is natural neo-Hookean. The following parameters must be defined:
 shear modulus [P] bulk modulus [P]
This model describes an unconstrained Neo-Hookean material using the natural strain tensor [24]. 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 left natural (Hencky) strain tensor where is the left stretch tensor in the polar decomposition .
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="natural neo-Hookean">
<G>500.0</G>
<k>333.3</k>
</material>


Subsubsection 4.1.3.14: Osmotic Pressure from Virial Expansion Up Subsection 4.1.3: Unconstrained Materials Subsubsection 4.1.3.16: Neo-Hookean