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Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2014-2pp.172-180

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M.A. Grekov and A.A. Yazovskaya, "The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole," J. Appl. Math. Mech. 78 (2), 172-180 (2014)
Year 2014 Volume 78 Issue 2 Pages 172-180
Title The effect of surface elasticity and residual surface stress in an elastic body with an elliptic nanohole
Author(s) M.A. Grekov (St. Petersburg, Russia, magrekov@mail.ru)
A.A. Yazovskaya (St. Petersburg, Russia)
Abstract The deformation of an elastic plane with an elliptic hole in a uniform stress field is considered, taking into account the surface elasticity and the residual surface tension. The solution of the problem, based on the use of the linearized Gurtin-Murdoch surface elasticity relations and the complex Goursat-Kolosov potentials, is reduced to a singular integrodifferential equation. Using the example of a circular hole, for which an exact solution of the equation is obtained in closed form, the effect of the residual surface tension and the surface elasticity on the stress state close to and on the boundary of a nanohole is analysed for uniaxial tension. It is shown that the effect of the residual surface stress and the surface tension, due to deformation of the body, depends on the elastic properties of the surface, the value of the stretching load and the dimensions of the hole.
Received 03 July 2013
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