This article is cited in 1 paper

Differentical equations, dynamical systems and optimal control

On crack propagations in elastic bodies with thin inclusions

A. M. Khludnev^ab, T. S. Popova<sup>c

a</sup> Lavrentyev Institute of Hydrodynamics, pr. Lavrent'eva, 15, 630090, Novosibirsk, Russia
^b Novosibirsk State University, pr. Lavrentieva, 15, 630090, Novosibirsk, Russia
^c North-Eastern Federal University, ul. Kulakovskogo, 48, 677000, Yakutsk, Russia

Abstract: The paper concerns an analysis of a crack propagation phenomena for an elastic body with thin inclusions and cracks. In the frame of free boundary approach, we investigate a dependence of the solutions on a rigidity parameter of the inclusion. A passage to the limit is justified as the parameter goes to infinity. Derivatives of the energy functionals are found with respect to the crack length for the models considered with different rigidity parameters. The Griffith criterion is used to describe a crack propagation. In so doing, an optimal control problem is investigated with a rigidity parameter being a control function. A cost functional coincides with a derivative of the energy functional with respect to the crack length. A solution existence is proved.

Keywords: thin elastic inclusion, Timoshenko beam, semirigid inclusion, crack, delamination, nonpenetration boundary condition, optimal control.

UDC: 517.958, 539.3

MSC: 35Q74, 35Q93

Received April 10, 2017, published July 5, 2017

Language: English

DOI: 10.17377/semi.2017.14.050

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