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The relation between load and penetration for a spherical punch

Published online by Cambridge University Press:  26 February 2010

C. M. Segedin
C. M. Segedin
Affiliation:
Auckland University College, Auckland, New Zealand.
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Extract

The indentation produced by an axially symmetrical punch bearing on the plane surface of an elastic half-space has been considered by Harding and Sneddon [1], who used Hankel transforms and a well-known pair of dual integral equations, and for the case of a spherical punch they took the indenting surface to be part of the approximating paraboloid of revolution. Chong [2], also using these dual integral equations has treated the case of a symmetrical punch of polynomial form and considers a two-termed expansion for a spherical punch. More recently, Payne [3] has given the exact solution for a spherical punch using either oblate spheroidal coordinates or toroidal coordinates.

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 156 - 161
Copyright
Copyright © University College London 1957

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References

1.Harding, J. W. and Sneddon, I. N., “Elastic stresses produced by the indentation of the plane surface of a semi-infinite elastic solid by a rigid punch”, Proc. Cambridge Phil. Soc., 041 (1945), 16–26.CrossRefGoogle Scholar
2.Chong, F., “Indentation of a semi-infinite medium by an axially symmetric rigid punch”, Iowa State College J. of Science, 026 (1952), 1–15.Google Scholar
3.Payne, L. E., “On axially symmetric punch, crack and torsion problems”, Journal Soc. Ind. and Applied Maths., 001 (1953), 53.CrossRefGoogle Scholar
4.Green, A. E. and Zerna, W., Theoretical Elasticity (Oxford, 1954), 171 et seq.Google Scholar
5.Jeans, J. H., Electricity and Magnetism (Cambridge U.P., 5th Edition), 249.Google Scholar