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Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory

Borodich, Feodor M.; Galanov, Boris A.; Perepelkin, Nikolay V.; Prikazchikov, Danila A.

Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory Thumbnail


Authors

Feodor M. Borodich

Boris A. Galanov

Nikolay V. Perepelkin



Abstract

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius.

Acceptance Date Aug 1, 2018
Publication Date May 1, 2019
Publicly Available Date Mar 28, 2024
Journal Mathematics and Mechanics of Solids
Print ISSN 1081-2865
Publisher SAGE Publications
Pages 1405-1424
DOI https://doi.org/10.1177/1081286518797378
Keywords thin elastic layer, asymptotics, JKR theory, adhesive contact, Winkler–Fuss foundation
Publisher URL http://doi.org/10.1177/1081286518797378

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