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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 935–948
DOI: https://doi.org/10.33048/semi.2022.19.078 (Mi semr1551) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differentical equations, dynamical systems and optimal control

Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion

I. V. Fankinaab, A. I. Furtsevab, E. M. Rudoyab, S. A. Sazhenkovb

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Lavrentyev Institute of Hydrodynamics, pr. Lavrentyeva, 15, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.078
Abstract: Within the framework of two-dimensional elasticity theory, a heterogeneous body with a narrow inclusion lying strictly inside the body is considered. It is assumed that the elastic properties of inclusion and its width depend on the small parameter $\delta>0$. Moreover, we assume that the inclusion has a curvilinear rough boundary. We show that there exist three type of limiting problem as $\delta\to0$: $p>1$ – body with crack without interaction of its faces; $p=1$ – body with crack with adhesive interaction of its faces; $p\in[0,1)$ – homogeneous body (no crack).
Keywords: asymptotic analysis, inhomogeneous elastic body, narrow inclusion, curvilinear crack, interface conditions.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1613
This work was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.
Received September 14, 2022, published December 10, 2022
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 74K20
Language: English
Citation: I. V. Fankina, A. I. Furtsev, E. M. Rudoy, S. A. Sazhenkov, “Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 935–948
Citation in format AMSBIB
\Bibitem{FanFurRud22}
\by I.~V.~Fankina, A.~I.~Furtsev, E.~M.~Rudoy, S.~A.~Sazhenkov
\paper Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 935--948
\mathnet{http://mi.mathnet.ru/semr1551}
\crossref{https://doi.org/10.33048/semi.2022.19.078}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4518799}
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    • This publication is cited in the following 1 articles:
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