  We propose a novel mixed displacement-pressure formulation based on an energy
functional that takes into account the relation between the pressure and the
volumetric energy function. We demonstrate that the proposed two-field mixed
displacement-pressure formulation is not only applicable for nearly and truly
incompressible cases but also is consistent in the compressible regime.
Furthermore, we prove with analytical derivation and numerical results that the
proposed two-field formulation is a simplified and efficient alternative for
the three-field displacement-pressure-Jacobian formulation for hyperelastic
materials whose strain energy density functions are decomposed into deviatoric
and volumetric parts.
