Constitutive relations and internal equilibrium condition for fluid-saturated porous solids Linear description

Abstract

Using the nonlinear theory established in the paper [5], the constitutive relations for small deformations of the fluid-saturated porous solid are derived. It is assumed that the elastic properties of porous skeleton are non-isotropic while the skeleton pore structure is isotropic. Fluid filling pores is assumed to be barotropic. Such approach made it possible to construct the consistent linear description of elastic behaviour of porous medium in which all material constants are precisely defined and represent mechanical properties of individual constituents. It is shown that the pure elastic properties of fluid-filled anisotropic skeleton are characterized by 36 material constants and reduces to 7 constants for the isotropic case, and to 4 constants when the skeleton is isotropic and its material is incompressible. In each considered case, the only one material constant characterizes mechanical properties of the pore fluid whereas the remaining constants characterize elastic properties of porous skeleton.