Abstract
A solution is given for the frictionless indentation of an elastic half-space by a flat-ended cylindrical punch with a central circular recess, when the load is large enough to establish a circular region of contact in the recess. The problem is reduced to two simultaneous Fredholm equations using the method of complex potentials due to Green and Collins. Results are presented for the relationship between load, contact radius and penetration for various punch geometries.
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References
Barber JR (1983) The solution of elasticity problems for the half-space by the method of Green and Collins. App Sci Res 40: 135–157
Collins WD (1963) On the solution of some axisymmetric boundary-value problems by means of integral equations: IV. Potential problems for a circular annuals. Proc Edinburgh Math Soc 13:235–246
Shibuya T, Koizumi T and Nakahara I (1974) An elastic contact problem for a half-space indented by a flat annular rigid stamp. Int J Engrg Sci 12:759–771
Gladwell GML (1980) Contact problems in the classical theory of elasticity. Sijthoff & Noordhoff, Alphen aan den Rijn, 518–526
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Barber, J.R. A four-part boundary value problem in elasticity — indentation by a discontinuously concave punch. Appl. Sci. Res. 40, 159–167 (1983). https://doi.org/10.1007/BF00386217
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DOI: https://doi.org/10.1007/BF00386217