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126.96.36.199 Natural Neo-Hookean
The material type for a natural Neo-Hookean material is natural neo-Hookean. The following parameters must be defined:
This model describes an unconstrained Neo-Hookean material using the natural strain tensor . 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 188.8.131.52↑.
<material id="1" type="natural neo-Hookean"> <G>500.0</G> <k>333.3</k> </material>