Feodor M. Borodich
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.
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.
Citation
Borodich, F. M., Galanov, B. A., Perepelkin, N. V., & Prikazchikov, D. A. (2019). Adhesive contact problems for a thin elastic layer: Asymptotic analysis and the JKR theory. Mathematics and Mechanics of Solids, 1405-1424. https://doi.org/10.1177/1081286518797378
Acceptance Date | Aug 1, 2018 |
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Publication Date | May 1, 2019 |
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 |
Files
BGPP_revised.pdf
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Publisher Licence URL
https://creativecommons.org/licenses/by-nc/4.0/
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