On the coupled theory of thermoelastic double-porosity materials

Abstract

In this paper, the linear model of thermoelastic double-porosity materials is proposed in which the coupled phenomenon of the concepts of Darcy’s law and the volume fractions is considered. The basic systems of governing equations of motion and steady vibrations are obtained. Then, the boundary value problems of steady vibrations are investigated by means of the potential method (boundary integral equation method) and the theory of singular integral equations. Namely, on the basis of Green’s identities and the surface and volume potentials the existence and uniqueness theorems for the classical solutions of the internal and external basic boundary value problems of the considered theory are proved.

Keywords:

• Double-porosity materials
• potential method
• steady vibrations
• thermoelasticity
• uniqueness and existence theorems

Mathematics subject classification:

• 74F10
• 74G25
• 74G30
• 35E05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shota Rustaveli National Science Foundation of Georgia (SRNSFG) [Project # FR-19-4790].