Contact problem for elastic spheres: Applicability of the Hertz theory to non-small contact areas

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40 Scopus citations

Abstract

The problem of normal contact of two identical elastic spheres is considered. The corresponding mixed boundary-value problem is formulated at the surface of the sphere, thereby relaxing the assumption of the Hertz theory about small size of the contact area compared to the sizes of the contacting bodies. A general solution in the form of Legendre series expansions is used to reduce the problem to dual series equations, and, subsequently, to a Fredholm integral equation of the second kind. Analysis of the contact stress and surface displacements of the sphere is carried out. Comparison of the results with the Hertz theory shows that the latter predicts contact stresses with high accuracy even for relatively large contact areas.

Original languageEnglish (US)
Pages (from-to)576-588
Number of pages13
JournalInternational Journal of Engineering Science
Volume49
Issue number7
DOIs
StatePublished - Jul 2011
Externally publishedYes

Keywords

  • Contact mechanics
  • Elastic sphere
  • Fredholm integral equation
  • General solution
  • Legendre polynomials

ASJC Scopus subject areas

  • General Materials Science
  • General Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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