A general material model requires equations that relate stress to deformation and internal energy (or temperature). In most cases, the stress tensor may be separated into a uniform hydrostatic pressure (all three normal stresses equal) and a stress deviatoric tensor associated with the resistance of the material to shear distortion.
Then the relation between the hydrostatic pressure, the local density (or specific volume) and local specific energy (or temperature) is known as an equation of state.
Hooke's law is the simplest form of an equation of state and is implicitly assumed when you use linear elastic material properties. Hooke's law is energy independent and is only valid if the material being modeled undergoes relatively small changes in volume (less than approximately 2%). One of the alternative equation of state properties should be used if the material is expected to experience high volume changes during an analysis.
Before looking at the various equations of state available, it is good to understand some of the fundamental physics behind their formulations. Details are provided in Explicit Dynamics Analysis Guide (to be published).