The interaction of frictional slip and adhesion for a stiff sphere on a compliant substrate

R. M. McMeeking, M. Ciavarella, Gabriele Cricrì, Kyung-Suk Kim

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24 Citations (Scopus)


How friction affects adhesion is addressed. The problem is considered in the context of a very stiff sphere adhering to a compliant, isotropic, linear elastic substrate, and experiencing adhesion and frictional slip relative to each other. The adhesion is considered to be driven by very large attractive tractions between the sphere and the substrate that can act only at very small distances between them. As a consequence, the adhesion behavior can be represented by the Johnson-Kendall-Roberts model, and this is assumed to prevail also when frictional slip is occurring. Frictional slip is considered to be resisted by a uniform, constant shear traction at the slipping interface, a model that is considered to be valid for small asperities and for compliant elastomers in contact with stiff material. A model for the interaction of friction and adhesion, known to agree with some experimental data, is utilized. This model is due to Johnson, and its adhesion-friction interaction is assumed to stem, upon shrinkage of the contact area, from a postulated reversible energy release associated with frictional slip. This behavior is considered to arise from surface microstructures generated or eliminated by frictional slip, where these microstructures store some elastic strain energy in a reversible manner. The associated reversible energy release rate is derived from the energy exchanges that occur in the system. The Johnson model, and an asymptotic analysis of it for small amounts of frictional slip, is shown to be consistent with the reversible energy release rate that we identify.
Original languageEnglish
Article number031016
Number of pages7
JournalJournal of Applied Mechanics
Issue number3
Early online date13 Jan 2020
Publication statusPublished - 1 Mar 2020

Bibliographical note

Copyright © 2020 by ASME

R.M.M. acknowledges the support of an Alumni Award given by the Alexander von Humboldt Foundation, and a Leibniz Chair at the Leibniz Institute for New Materials, Saarbrücken, Germany. K.S.K. acknowledges the support of NSF award CMMI-1563591. This article is dedicated to John Hutchinson on the occasion of his 80th birthday.


  • energy release rate and delamination
  • mixed-mode fracture
  • stress analysis
  • Adhesion
  • Shear (Mechanics)
  • Traction


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