Adhesive Frictionless Contact Between an Elastic Isotropic Half-Space and a Rigid Axi-Symmetric Punch |
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Authors: | Haneesh Kesari Adrian J Lew |
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Institution: | 1.Department of Mechanical Engineering,Stanford University,Stanford,USA |
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Abstract: | In this paper we consider the problem of adhesive frictionless contact of an elastic half-space by an axi-symmetric punch.
We obtain integral equations that define the tractions and displacements normal to the surface of the half-space, as well
as the size of the contact regions, for the cases of circular and annular contact regions. The novelty of our approach resides
in the use of Betti’s reciprocity theorem to impose equilibrium, and of Abel transforms to either solve or substantially simplify
the resulting integral equations. Additionally, the radii that define the annular or circular contact region are defined as
local minimizers of the function obtained by evaluating the potential energy at the equilibrium solutions for each pair of
radii. With this approach, we rather easily recover Sneddon’s formulas (Sneddon, Int. J. Eng. Sci., 3(1):47–57, 1965) for circular contact regions. For the annular contact region, we obtain a new integral equation that defines the inverse
Abel transform of the surface normal displacement. We solve this equation numerically for two particular punches: a flat annular
punch, and a concave punch. |
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