Variational theories of two-phase continuum poroelastic mixtures: A short survey

A comprehensive survey is presented on two-phase and multi-phase continuum poroelasticity theories whose governing equations at a macroscopic level are based, to different extents, either on the application of classical variational principles or on variants of Hamilton’s least Action principle. As a focal discussion, the ‘closure problem’ is recalled, since it is widespread opinion in the multiphase poroelasticity community that even the simpler two-phase purely-mechanical problem of poroelasticity has to be regarded as a still-open problem of applied continuum mechanics. This contribution integrates a previous review by Bedford and Drumheller, and covers the period from the early use of variational concepts by Biot, together with the originary employment of porosity-enriched kinematics by Cowin and co-workers, up to variational theories of multiphase poroelasticity proposed in the most recent years.