This article is cited in 3 papers

The junction problem for two weakly curved inclusions in an elastic body

A. M. Khludnev^ab, T. S. Popova<sup>c

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^c North-Eastern Federal University named after M. K. Ammosov

Abstract: Under study are the boundary value problems that describe the equilibria of two-dimensional elastic bodies with thin weakly curved inclusions in the presence of delamination, which means that there is a crack between the inclusions and an elastic body. Some inequality-type nonlinear boundary conditions are imposed on the crack faces that exclude mutual penetration. This puts the problems into the class of those with unknown contact area. We assume that the inclusions have a contact point, find boundary conditions at the junction point, and justify passage to infinity with respect to the rigidity parameter of the thin inclusion. In particular, we obtain and analyze limit models.

Keywords: boundary value problem, elastic body, inclusion, crack, junction conditions.

UDC: 517.958

MSC: 35R30

Received: 04.12.2019
Revised: 17.12.2019
Accepted: 25.12.2019

DOI: 10.33048/smzh.2020.61.414

 English version: Siberian Mathematical Journal, 2020, 61:4, 743–754

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