Boundary Integral Equations Method in the Coupled Theory of Thermoelasticity for Porous Materials

This paper concerns with the coupled linear theory of thermoelasticity for porous materials and the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The system of governing equations based on the equations of motion, the constitutive equations, the equation of fluid mass conservation, Darcy’s law for porous materials, Fourier’s law of heat conduction and the heat transfer equation. The system of general governing equations is expressed in terms of the displacement vector field, the change of volume fraction of pores, the change of fluid pressure in pore network and the variation of temperature of porous material. The fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions and its basic properties are presented. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated and on the basis of Green’s identities the uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs of steady vibrations are proved by means of the boundary integral equations method (potential method) and the theory of singular integral equations.