A general approach to isothermal hyperelastic modelling of saturated porous media at finite strains with compressible solid constituents

A general approach is proposed for defining the macroscopic free-energy function of a saturated porous medium subjected to finite deformations, under isothermal conditions, in the case of compressible fluid and solid constituents. Reference is made to an elementary volume treated as an 'open system', moving with the solid skeleton. The strain-like variables are characterized by a suitable strain measure and the variation of fluid-mass content. Although the free energy is obtained by assembling the contributions of the single constituents, the resulting free energy is not the simple sum of the free energies of the single constituents. It is shown that the simplified approaches previously proposed in the literature are recovered as particular cases of the more general framework proposed in the present article and, in addition, new simplified constitutive frameworks are investigated. The proposed approach paves the way to the consistent hyperelastic-plastic and thermo-elastic modelling of saturated porous media with compressible fluid and solid constituents.