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Potential Method in the Coupled Theory of Viscoelasticity of Porous Materials

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Abstract

This paper concerns with the coupled linear theory of viscoelasticity for porous materials. In this theory the coupled phenomenon of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions and its basic properties are presented. Green’s identities are obtained and the uniqueness theorems for the regular (classical) solutions of the BVPs of steady vibrations are proved. The surface and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs of steady vibrations are proved by means of the potential method and the theory of singular integral equations.

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Acknowledgements

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

The author is very grateful to the anonymous reviewers for their valuable comments concerning this work.

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  1. Faculty of Exact and Natural Sciences, Tbilisi State University, I. Chavchavadze Ave., 3, 0179, Tbilisi, Georgia

    Maia M. Svanadze

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Svanadze, M.M. Potential Method in the Coupled Theory of Viscoelasticity of Porous Materials. J Elast 144, 119–140 (2021). https://doi.org/10.1007/s10659-021-09830-y

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  • DOI: https://doi.org/10.1007/s10659-021-09830-y

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