The JKR-type adhesive contact problems for transversely isotropic elastic solids

Feodor M. Borodich*, Boris A. Galanov, Leon M. Keer, Maria M. Suarez-Alvarez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


The JKR (Johnson, Kendall, and Roberts) and Boussinesq-Kendall models describe adhesive frictionless contact between two isotropic elastic spheres or between a flat end punch and an elastic isotropic half-space. Here adhesive contact is studied for transversely isotropic materials in the framework of the JKR theory. The theory is extended to much more general shapes of contacting axisymmetric solids, namely the distance between the solids is described by a monomial (power-law) function of an arbitrary degree d≥1. The classic JKR and Boussinesq-Kendall models can be considered as two particular cases of these problems, when the degree of the punch d is equal to two or it goes to infinity, respectively. It is shown that the formulae for extended JKR contact model for transversely isotropic materials have the same mathematical form as the corresponding formulae for isotropic materials; however the effective elastic contact moduli have different expression for different materials. The dimensionless relations between the actual force, displacements and contact radius are given in explicit form. Connections of the problems to nanoindentation of transversely isotropic materials are discussed.

Original languageEnglish (US)
Pages (from-to)34-44
Number of pages11
JournalMechanics of Materials
StatePublished - Aug 2014


  • Adhesive contact
  • JKR theory
  • No-slip
  • Power-law punches
  • Transversely isotropic solids

ASJC Scopus subject areas

  • Materials Science(all)
  • Instrumentation
  • Mechanics of Materials


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