Abstract
A macroscopic continuum theory of two-phase saturated porous media is derived by a purely variational deduction based on the least Action principle. The proposed theory proceeds from the consideration of a minimal set of kinematic descriptors and keeps a specific focus on the derivation of most general medium-independent governing equations, which have a form independent from the particular constitutive relations and thermodynamic constraints characterizing a specific medium. The kinematics of the microstructured continuum theory herein presented employs an intrinsic/extrinsic split of volumetric strains and adopts, as an additional descriptor, the intrinsic scalar volumetric strain which corresponds to the ratio between solid true densities before and after deformation. The present theory integrates the framework of the Variational Macroscopic Theory of Porous Media (VMTPM) which, in previous works, was limited to the variational treatment of the momentum balances of the solid phase alone. Herein, the derivation of the complete set momentum balances inclusive of the momentum balance of the fluid phase is attained on a purely variational basis. Attention is also focused on showing that the singular conditions, in which either the solid or the fluid phase are vanishing, are consistently addressed by the present theory, included conditions over free solid-fluid surfaces.
