Analytical solutions for inherently incremental, similar elastic contact problems with bulk stress

N. Sundaram, T. N. Farris

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Analytical solutions are obtained for a class of inherently incremental, similar elastic half-plane frictional contact problems which involve simultaneous application of a changing, remote bulk-stress during oblique loading. The method is based on Abel Integral Equations. The spatial gradient of the slip function is obtained uniquely by the conditions determining the existence of a bounded solution to the shear traction Cauchy SIE and global shear equilibrium, provided there is stick at all points in the contact throughout the loading. Solutions are obtained for both the cylindrical indenter and the flat punch with rounded edges. The method also lends itself easily to generalization to non-linear load paths and a number of such problems are considered. Problems involving the development of slip zones within the contact may be solved in some special cases.

Original languageEnglish (US)
Pages (from-to)2834-2841
Number of pages8
JournalInternational Journal of Solids and Structures
Issue number14-15
StatePublished - Jul 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


  • Analytical solution
  • Contact
  • Friction
  • Half-space
  • Integral equation
  • Singular integrals


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