期刊
SIAM JOURNAL ON APPLIED MATHEMATICS
卷 76, 期 2, 页码 618-640出版社
SIAM PUBLICATIONS
DOI: 10.1137/15M1044096
关键词
surface tension; surface elasticity; contact problems; integral equations; microstructure
资金
- Simons Foundation through Collaboration Grant for Mathematicians
It has been shown that taking into account surface mechanics is extremely important for accurate modeling of many physical phenomena such as those arising in nanoscience, fracture propagation, and contact mechanics. This paper is dedicated to a contact problem of a rigid stamp indentation into an elastic isotropic semiplane with curvature-dependent surface tension acting on the boundary of the semiplane. Cases of both frictionless and adhesive contact of the stamp with the boundary of the semiplane are considered. Using the method of integral transforms, each problem is reduced to a system of singular integro-differential equations, which is further reduced to one or two weakly singular integral equations. It has been shown that the introduction of the curvature-dependent surface tension eliminates the classical singularities of the order 1/2 of the stresses and strains at the end-points of the contact interval. The numerical solution of the problem is obtained by approximation of unknown functions with Taylor polynomials.
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