Variational principles developed for and applied to porous-elastic solids

Abstract

A dual variational principle is formulated for a general porous-elastic material in Laplace transform space. The material may be anisotropic and spatially inhomogeneous. As an application of the theory, we consider two problems of a crack in an infinite strip of inhomogeneous rock. In the first we bound the Stress Intensity Factor in both the transform and real time domains. For the second, we place bounds on a function of the poroelastic Stress Intensity Factor and pore pressure gradient coefficient, in transform space. The bounds are compared with an effective medium solution in both cases. We discuss the significance of the method with regard to bounding effective properties in non-static problems. We obtain, in implicit form, bounds on effective permeability for a rigid porous solid in transform space. These suggest the effective property is history dependent. Asymptotic methods are used to obtain large and small time results.