The Elastic Field for Spherical Hertzian Contact of Isotropic Bodies Revisited: Some Alternative Expressions

[+] Author and Article Information
M. T. Hanson, T. Johnson

Department of Engineering Mechanics, University of Kentucky, Lexington, KY 40506-0046

J. Tribol 115(2), 327-332 (Apr 01, 1993) (6 pages) doi:10.1115/1.2921010 History: Received February 28, 1992; Revised September 01, 1992; Online June 05, 2008


Closed-form expressions in terms of elementary functions are derived for the elastic field resulting from spherical Hertz contact of isotropic bodies. Shear traction is also included using a Coulomb friction law; thus the shear stress in the contact region is equal to the contact pressure multiplied by a friction coefficient. This paper provides alternative expressions to those recently given by Hamilton (1983) and Sackfield and Hills (1983a). Two methods are outlined for obtaining the present solution and the complete solution for displacements and stresses are given for both normal and tangential loading in terms of just two distorted length parameters. The elastic field is written in a complex notation allowing the expressions to be put in a compact form. This also allows the expressions for sliding in two directions to be written as simply as for sliding in one direction.

Copyright © 1993 by The American Society of Mechanical Engineers
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