The Cauchy stress is given by, $$\begin{equation} \boldsymbol{\sigma}=\frac{\mu}{J}\left(\mathbf{b}-\mathbf{I}\right)+\frac{\lambda}{J}\left(\ln J\right)\mathbf{I}\,,\label{eq423} \end{equation}$$ and the spatial elasticity tensor is given by $$\begin{equation} \boldsymbol{\mathcal{C}}=\frac{\lambda}{J}\mathbf{I}\otimes\mathbf{I}+\frac{2}{J}\left(\mu-\lambda\ln J\right)\mathbf{I}\,\overline{\underline{\otimes}}\,\mathbf{I}\,.\label{eq424} \end{equation}$$ 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.