Linear elastic constitutive relation for multiphase porous media using microstructure superposition: Dry media

A constitutive relation for multiphase porous media containing a phase-change constituent is developed based on a periodic representative unit cell, microstructure superposition technique, and homogenization scheme. Multiphase porous mediae, consisting of different solid phases, fluid phases, and phase-change constituents, play an important role in variety engineering applications. A microstructure superposition method, stemmed from linear superposition theory, is devised such that the constitutive relation of the media can be obtained in an analytical form and the derivation is straightforward and tractable. The original microstructure of the media is firstly divided into several simple microstructure configurations. The microscopic stresses and strains are obtained for each individual microstructure configuration based on its own equilibrium and equivalent equations, and complex Fourier series expansion of strains. The microscopic strains are then superposed together to obtain the constitutive relation of the multiphase porous media using homogenization scheme. The derived constitutive relation can be applied to study the mechanical behavior of porous media consisting of two solid phases with one being able to change phase between solid and liquid and one liquid phase. As a particular application of the derived constitutive relation, the mechanical behavior of porous media with a single solid phase under dry condition was studied and the results were consistent with other models and agreed well with available experimental data.