On the static and dynamic behavior of fluid saturated composite porous solids: A homogenization approach

The macroscopic description of the dynamical behavior of a porous solid composed of two nonwelded solid phases saturated by a single-phase fluid is derived using two-space homogenization techniques for periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration. At the microscopic scale the two solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations, with appropriate boundary conditions at the solid–solid and solid–fluid interfaces. The nonwelded interface between the two solid phases is represented by displacement and/or velocity discontinuities proportional to the stresses across the interface, while the stresses are assumed to be continuous. After performing the homogenization procedure, constitutive relations, Darcy’s and Biot’s type dynamic equations for the saturated composite porous material are obtained.