THE MECHANICAL BEHAVIOR OF A POROELASTIC MEDIUM SATURATED WITH A NEWTONIAN FLUID
Zhangxin Chen, Stephen Lincoln Lyons, Guan Qin · 2004
In this paper we systematically derive, via the theory of homoge- nization, the macroscopic equations for the mechanical behavior of a deformable porous medium saturated with a Newtonian ∞uid. The derivation is flrst based on the equations of linear elasticity in the solid, the Stokes equations for the ∞uid, and suitable conditions at the ∞uid-solid interface. A detailed comparison between the equations derived here and those by Biot is given. The homog- enization approach determines the form of the macroscopic constitutive rela- tionships between variables and shows how to compute the coe-cients in these relationships. The derivation is then extended to the nonlinear Navier-Stokes equations for the ∞uid in the deformable porous medium for the flrst time. A generalized Forchheimer law is obtained to take into account the nonlinear in- ertial efiects on the ∞ow of the Newtonian ∞uid through such a medium. Both quasi-static and transient ∞ows are considered in this paper. The properties of the macroscopic coe-cients are studied. The computational results show that the macroscopic equations predict well the behavior of the microscopic equations in certain reasonable test cases.