This article is cited in 3 papers

Asymptotics of anisotropic weakly curved inclusions in an elastic body

A. M. Khludnev<sup>ab

a</sup> Lavrentyev Institute of Hydrodynamics SB RAS, Acad. Lavrentyev ave., 15, 630090 Novosibirsk
^b Novosibirsk State University, Pirogov str., 2, 630090 Novosibirsk

Abstract: We study boundary value problems that describeg the equilibrium for two-dimensional elastic bodies with thin weakly curved anisotropic inclusions. The presence of an inclusion means the existence of a crack between the inclusion and the elastic matrix. Nonlinear boundary conditions in the form of inequalities are imposed on the crack faces to prevent their mutual penetration, which leads to formulating the problems as problems with unknown contact domain. Limit passages are investigated over the rigidity parameters of the thin inclusions. In particular, we construct the models obtained by letting the rigidity parameters tend to infinity and analyze their properties.

Keywords: thin inclusion, elastic body, crack, nonlinear boundary condition, limit model.

UDC: 539.3+517.958

Received: 20.01.2016

DOI: 10.17377/sibjim.2017.20.110

 English version: Journal of Applied and Industrial Mathematics, 2017, 11:1, 88–98

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