This article is cited in 3 papers

Mathematics

On the hierarchy of thin delaminated inclusions in elastic bodies

A. M. Khludnev^ab, T. S. Popova<sup>c

a</sup> Lavrentiev Institute of Hydrodynamics SBRAS, Acad. Lavrentiev ave, 15, Novosibirsk 630090, Russia;
^b Novosibirsk State University, Pirogova st., 2, Novosibirsk 630090, Russia
^c M. K. Ammosov North-Eastern Federal University, Belinskogo st., 58, Yakutsk 677000, Russia

Abstract: We consider models of thin delaminated inclusions in elastic bodies. The delamination means a presence of a crack between the inclusion and the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. This approach leads to free boundary problem formulations. Connections between different mathematical models are discussed. Passages to limits with respect to inclusion rigidity parameters are analyzed.

Keywords: thin inclusion, elastic body, crack, non-linear boundary conditions, rigidity parameter, limiting models.

UDC: 539.3+517.958

Received: 19.02.2016

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