Mixture theory for a thermoelasto-plastic porous solid considering fluid flow and internal mass exchange

A thermoelastic–plastic body consisting of two phases, a solid and a fluid, each comprising two constituents is considered where one constituent in one phase is allowed to exchange mass with another constituent (of the same substance) in the other phase. A large strain setting is adopted and the formulation applies to general anisotropy and the existence of residual stresses. Generalized forms of Fourier’s, Fick’s and Darcy’s laws are derived and also the stresses on the constituent, phase and mixture level are established; in addition, the evolution law for general plasticity is given. Finally, and in particular, a general evolution law for the rate of deformation tensor related to mass exchange is proposed and this leads to general absorption and desorption evolution laws for mass exchange between two constituents (of the same substance), one belonging to the solid phase and the other to the fluid phase. Equilibrium curves for absorption and desorption also emerge from the theory.

► We develop the mixture theory consisting phases and constituents.
► Kinematics accounts for plasticity, growth/swelling and residual stresses.
► A general evolution law for kinematics related to mass exchange is proposed.
► General absorption and desorption evolution laws for mass exchange is derived.
► Equilibrium curves for absorption and desorption emerge from the theory.