The constitutive equations of finite strain poroelasticity in the light ofa micro-macro approach

After recalling the constitutive equations of finite strain poroelasticity formulated at the macroscopic level, we adopt a microscopic point of view w hich consists of describing the fluid-saturated porous medium at a space sc ale on which the fluid and solid phases are geometrically distinct. The con stitutive equations of poroelasticity are recovered from the analysis condu cted on a representative elementary volume of porous material open to fluid mass exchange. The procedure relies upon the solution of a boundary value problem defined on the solid domain of the representative volume undergoing large elastic strains. The macroscopic potential, computed as the integral of the free energy density over the solid domain, is shown to depend on th e macroscopic deformation gradient and the porous space volume as relevant variables. The corresponding stress-type variables obtained through the dif ferentiation of this potential turn out to be the macroscopic Boussinesq st ress tensor and the pore pressure. Furthermore, such a procedure makes it p ossible to establish the necessary and sufficient conditions to ensure the validity of an 'effective stress' formulation of the constitutive equations of finite strain poroelasticity. Such conditions are notably satisfied in the important case of an incompressible solid matrix. (C) Elsevier, Paris.