Borodich, FM, Galanov, BA, Perepelkin, NV and Prikazchikov, D (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. ISSN 1081-2865

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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
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Sage Publications at - please refer to any applicable terms of use of the publisher.
Uncontrolled Keywords: thin elastic layer, asymptotics, JKR theory, adhesive contact, Winkler–Fuss foundation
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 22 Oct 2018 14:38
Last Modified: 20 May 2019 09:29

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