 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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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, magrekov@mail.ru)
S.A. Kostyrko (St Petersburg, Russia, sergey.kostyrko@gmail.com) |
| 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 |
| Link to Fulltext |
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