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Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2011-4pp.476-488

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M.A. Grekov, "Two types of interface defects," J. Appl. Math. Mech. 75 (4), 476-488 (2011)
Year 2011 Volume 75 Issue 4 Pages 476-488
Title Two types of interface defects
Author(s) M.A. Grekov (St Petersburg, Russia,
Abstract The solution of a plane problem in the theory of elasticity for a two-component body with an interface, a finite part of which is either weakly distorted or is a weakly curved crack is constructed using the perturbation method. In the first case, it is assumed that the discontinuities in the forces and displacements at the interface are known, and, in the second case, the non-equilibrium nature of the load in the crack is taken into account. General quadrature formulae are derived for the complex potentials, which enable any approximation to be obtained in terms of elementary functions in many important practical cases. An algorithm is indicated for calculating each approximation. Families of defects are studied, the form of which is determined by power functions. The effect of the amplitude of the distortion and the shape of the interface crack on the Cherepanov-Rice integral as well as the shape of the distorted part of the interface on the stress concentration is investigated in the first approximation. An analysis of the applicability of the oscillating solution for a distorted interface crack is carried out. The results of the calculations are shown in the form of graphical relations.
Received 24 June 2010
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