Boundary value problems in the theory of thermoporoelasticity for materials with double porosity

In this paper the linear quasi-static theory of thermoelasticity for solids with double porosity is considered. The system of equations of this theory is based on the equilibrium equations for solids with double porosity, conservation of fluid mass, constitutive equations, Darcy's law for materials with double porosity and Fourier's law for heat conduction. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness and existence theorems for classical solutions of the above mentioned BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)