A theoretical treatment on the mechanics of interfaces in deformable porous media

Abstract The presence of interfaces (such as cracks, membranes and bi-material boundaries) in hydrated porous media may have a significant effect on the nature of their deformation and interstitial fluid flow. In this context, the present paper introduces a mathematical framework to describe the mechanical behavior of interfaces in an elastic porous media filled with an inviscid fluid. While bulk deformation and flow are characterized by displacement gradient and variations in the fluid chemical potential, their counterpart in the interface are derived by defining adequate projections of strains and flow onto the plane of the interface. This operation results in the definition of three interface deformation and stress measures describing decohesion, mean tangential strain and relative tangential strain, as well as three interface fluid driving forces and flux representing normal flux, mean tangential flux and relative tangential flux. Consistent with this macroscopic description of interface behavior, a set of governing equations are then introduced by considering the conservation of mass and the balance of momentum in the mixture. In particular, we show that the coupled mechanisms of interface deformation and fluid flow are described by six differential equations for fluid flow and three equations for solid deformation. It is also shown that a simpler set of governing equation can be derived when incompressible constituents are considered. The behavior of the mixture is finally specified through a general linear constitutive relation that relies on the definition of quadratic strain energy and dissipation functions. While an large number of material constants are needed in the general case, we show that under simplifying assumptions, the behavior of the interface can be written in terms of only eight material constants. A summary and discussion is then provided on the proposed formulation and potential applications are suggested.