Theory Manual Version 3.4
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Subsection 5.2.2: Orthotropic Elasticity Up Section 5.2: Compressible Materials Subsection 5.2.4: Natural Neo-Hookean

### 5.2.3 Neo-Hookean Hyperelasticity

This is a compressible neo-Hookean material. It is derived from the following hyperelastic strain energy function [23]: The parameters and are the Lamé parameters from linear elasticity. This model reduces to the isotropic linear elastic model for small strains and rotations.
The Cauchy stress is given by, and the spatial elasticity tensor is given by The neo-Hookean material is an extension of Hooke's law for the case of large deformations. It is useable for certain plastics and rubber-like substances. A generalization of this model is the Mooney-Rivlin material, which is often used to describe the elastic response of biological tissue.
In FEBio this constitutive model uses a standard displacement-based element formulation and a "coupled" strain energy, so care must be taken when modeling materials with nearly-incompressible material behavior to avoid element locking.
Subsection 5.2.2: Orthotropic Elasticity Up Section 5.2: Compressible Materials Subsection 5.2.4: Natural Neo-Hookean