Abstract: The problem of description of quasi-static behavior is studied for a planar thermoelastic body incorporating an inhomogeneity, which geometrically is a strip with a small cross-section. This problem contains a small positive parameter [Formula: see text] describing the thickness of the inhomogeneity, i.e., the size of the cross-section. Relying on the variational formulation of the problem, we investigate the behavior of solutions as [Formula: see text] tends to zero. As the result, by the version of the method of formal asymptotic expansions, we derive a closed limit model in which the inhomogeneity is thin (of zero width). After this, using the Galerkin method and the classical techniques of derivation of energy estimates, we prove existence, uniqueness, and stability of a weak solution to this model.

Cite: Fankina I.V. , Furtsev A.I. , Rudoy E.M. , Sazhenkov S.A.
A quasi-static model of a thermoelastic body reinforced by a thin thermoelastic inclusion
Mathematics and Mechanics of Solids. 2024. V.29. N4. P.796-817. DOI: 10.1177/10812865231217043 WOS Scopus РИНЦ OpenAlex

Dates:

Published online:

Jan 19, 2024

Identifiers:

Web of science:	WOS:001145594600001
Scopus:	2-s2.0-85182864189
Elibrary:	61454258
OpenAlex:	W4391052777

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OpenAlex	2
Scopus	1
Web of science	2

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