Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version)

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IssuesArchive of Issues2013-1pp.79-90

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Total articles in the database: 2048
In Russian (ΟΜΜ): 1249
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M.A. Grekov and S.A. Kostyrko, "A film coating on a rough surface of an elastic body," J. Appl. Math. Mech. 77 (1), 79-90 (2013)
Year 2013 Volume 77 Issue 1 Pages 79-90
Title A film coating on a rough surface of an elastic body
Author(s) M.A. Grekov (St Petersburg, Russia,
S.A. Kostyrko (St Petersburg, Russia,
Abstract A solution of the plane problem of the theory of elasticity for a film-substrate composite is solved by a perturbation method for a substrate with a rough surface. An algorithm for calculating any approximation, which ultimately leads to the solution of the same Fredholm equation of the second kind, is given. Formulae for calculating the right-hand side of this equation, which depends on all the preceding approximations, are derived. An exact solution of the integral equation in the form of Fourier series, whose coefficients are expressed in quadratures, is given in the case of a substrate with a periodically curved surface. The stresses on the flat surface of the film and on the interfacial surface are found in a first approximation as functions of the form of bending of the surface, the mean thickness of the film and the ratio of Young's moduli of the film and the substrate. It is shown, in particular, that the greatest stress concentration on the film surface occures on a protrusion of the softer substrate.
Received 02 October 2012
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