### Abstract

Original language | English |
---|---|

Pages (from-to) | 79-90 |

Journal | Journal of Applied Mathematics and Mechanics |

Volume | 77 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2013 |

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**A film coating on a rough surface of an elastic body.** / Grekov, M.A.; Kostyrko, S.A.

Research output

TY - JOUR

T1 - A film coating on a rough surface of an elastic body

AU - Grekov, M.A.

AU - Kostyrko, S.A.

PY - 2013

Y1 - 2013

N2 - 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 occurs on a protrusion of the softer substrate.

AB - 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 occurs on a protrusion of the softer substrate.

U2 - 10.1016/j.jappmathmech.2013.04.010

DO - 10.1016/j.jappmathmech.2013.04.010

M3 - Article

VL - 77

SP - 79

EP - 90

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 1

ER -