Interacting continuous medium composed of an elastic solid and an incompressible newtonian fluid

Abstract

The constitutive equations for an interacting continuum composed of an elastic solid and an incompressible Newtonian fluid are developed. The condition of incompressibility alters the equations previously obtained by Green and Steel. The concept of thermodynamic pressure is introduced and the new equations are compared with those developed by previous investigators.Using these constitutive equations, methods of solution are presented in terms of displacements or a stress function for the steady state condition. The equations developed are shown to reduce to Darcy's law for flow of fluids through a rigid porous medium and Biot's equation of fluid flow through a linear elastic solid. One and two-dimensional steady-state problems are solved as examples.