An extension of the Hertz theory for three-dimensional coated bodies

S. B. Liu, A. Peyronnel, Q. J. Wang*, L. M. Keer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


This paper presents a work on extending the Hertz theory for circular and elliptical point contact problems involving coated bodies. The extended form of the Hertzian formulae are adopted to express maximum contact pressure, contact radius, and contact approach in terms of applied load, equivalent radius, and an extended equivalent modulus that properly considers the presence of a coating. The extended equivalent modulus is a function of Young's moduli and Poisson's ratios of the coating and the substrate, coating thickness, and a parameter, which is obtained through substantial numerical simulation. The extended Hertzian formulae are easy to use and give accurate predictions of contact characteristics.

Original languageEnglish (US)
Pages (from-to)303-314
Number of pages12
JournalTribology Letters
Issue number3
StatePublished - Mar 2005


  • Coating
  • Contact mechanics
  • Equivalent Young's modulus
  • Hertz theory

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Surfaces and Interfaces
  • Surfaces, Coatings and Films


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