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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 and Prikazchikov, Danila A. 2019. Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory. Mathematics and Mechanics of Solids 24 (5) , pp. 1405-1424. 10.1177/1081286518797378

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Engineering
Publisher: SAGE Publications
ISSN: 1081-2865
Date of First Compliant Deposit: 13 February 2019
Date of Acceptance: 1 August 2018
Last Modified: 03 Jul 2019 09:52
URI: http://orca-mwe.cf.ac.uk/id/eprint/119467

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