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 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2008, Volume 8, Issue 2, Pages 105–129 (Mi vngu293)

Effective Thermoviscoelasticity of a Saturated Porous Ground

S. A. Sazhenkov

Novosibirsk State University

Abstract: The linearized model of reciprocal motion of an elastic porous body and a viscous compressible liquid in pores is considered, with the heat transfer effect being taken into account. It is assumed that the porous body has a periodic geometry and that the ratio of the pattern periodic cell and the diameter of the entire thermo-mechanical system is a small parameter in the model. The homogenization procedure, i.e. a limiting passage as the small parameter tends to zero, is fulfilled. As the result, we conclude that the limiting distributions of temperature and displacements of the media solve a well-posed initial-boundary value problem for the model of linear thermoviscoelasticity with memory of shape and heat. Moreover, coefficients of this newly constructed model arise from microstructure, more precisely; they are uniquely defined by data in the original model. Homogenization procedure is based on the method of two-scale convergence and is mathematically rigorously justified.

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Document Type: Article
UDC: 517.956.8; 517.958:[531.746.24+539.3(4)]

Citation: S. A. Sazhenkov, “Effective Thermoviscoelasticity of a Saturated Porous Ground”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 8:2 (2008), 105–129

Citation in format AMSBIB
\Bibitem{Saz08} \by S.~A.~Sazhenkov \paper Effective Thermoviscoelasticity of a Saturated Porous Ground \jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. \yr 2008 \vol 8 \issue 2 \pages 105--129 \mathnet{http://mi.mathnet.ru/vngu293}