Towards constitutive equations for the deep Earth

A new formulation of constitutive equations for states of high compression is introduced for isotropic media, exploiting a separation between hydrostatic and deviatoric components in strain energy. The strain energy is represented as functions of strain invariants, with one purely volumetric component and the other which vanishes for purely hydrostatic deformation. This approach preserves the form of familiar equations of state through the volumetric component, but allows the addition of volume and pressure dependence of the shear modulus from the deviatoric term. A suitable shear modulus representation to accompany a Keane equation of state is demonstrated.