Quadriphasic mechanics of swelling incompressible porous media

A chemo-electro-mechanical formulation of quasi-static finite deformation of swelling incompressible porous media is derived from mixture theory. The model consists of an electrically charged porous solid saturated with a monovalent ionic solution. Incompressible and isothermal deformation is assumed. Hydration forces are neglected. The mixture as a whole is assumed locally electroneutral. Four phases following different kinematic paths are defined: solid, fluid, anions and cations. Balance laws are derived for each phase and for the mixture as a whole. A Lagrangian form of the second law of thermodynamics is derived for incompressible porous media and is used to derive the constitutive relationships of the medium. It is shown that the theory is consistent with Biot's theory for the limiting case without ionic effects and with Staverman's results for the limiting case without deformation.