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: $$W=\frac{\kappa}{2}K_{1}^{2}+\mu K_{2}^{2}.$$ Here, $K_{1}$ and $K_{2}$ are the first and second invariants of the left natural (Hencky) strain tensor $\boldsymbol{\eta}=\ln\mathbf{V}$ where $\mathbf{V}$ is the left stretch tensor in the polar decomposition $\mathbf{F}=\mathbf{V}\cdot\mathbf{R}$ .

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>