The Modified Mixture Theory for Fluid-Filled Porous Materials: Theory

Abstract

The mixture theory by Green and Naghdi is modified and applied to the problems of flow-through porous materials. By introducing porosity, we make clear that two constituents occupying the same point in the original mixture theory are an equivalent homogeneous solid and an equivalent homogeneous fluid which, respectively, represent a porous solid and a porous fluid in the actual sample. The micro-mechanical response studied by Carroll and Katsube is introduced and detailed deformation and flow mechanisms are provided at each point of the mixture. The resulting theory is compared with Biot’s theory and in fact reduces to Biot’s theory when the fluid velocity gradient terms are ignored.