The contact of a simply connected axisymmetric punch with an elastic half-space is examined. The problem is mathematically formulated by using potential theory and complex variable analysis. The final solution of these equations is obtained by assuming a polynomial punch profile. The conditions for complete contact and incomplete contact are also derived. The solutions give the pressure profile at the punch–elastic half-space interface for any polynomial punch profile, even for noninteger power polynomials, as long as the contact region is simply connected. The results show that some classic solutions in linear elasticity are special cases of the derived solution and determine the range of validity for those solutions.
Issue Section:
Technical Papers
1.
Hay
, J. C.
, Bolshakov
, A.
, and Pharr
, G. M.
, 1999
, “Critical Examination of the Fundamental Relations Used in the Analysis of Nanoindentation Data
,” J. Mater. Res.
, 14
, pp. 2296
–2305
.2.
Komanduri
, R.
, Lucca
, D. A.
, and Tani
, Y.
, 1997
, “Technological Advances in Fine Abrasive Processes
,” Ann. CIRP
, 46
, No. 2
, pp. 545
–596
.3.
Fu
, G.
, and Chandra
, A.
, 2001
, “A Model for Wafer Scale Variation of Material Removal Rate in Chemical Mechanical Polishing Based on Elastic Pad Deformation
,” J. Electron. Mater.
, 30
, pp. 400
–408
.4.
Shield
, T. W.
, and Bogy
, D. B.
, 1989
, “Some Axisymmetric Problem for Layered Elastic Media: Part I—Multiple Region Contact Solutions for Simple-Connected Indenters
,” ASME J. Appl. Mech.
, 56
, pp. 798
–806
.5.
Gladwell, G. M. L., 1980, Contact Problems in the Classical Theory of Elasticity, Sijthoff & Noordhoof, Alphen aan den Rijn, The Netherland.
6.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
7.
Love
, A. E. H.
, 1939
, “Boussinesq’s Problem for a Rigid Cone,”
Quarterly J. Math.
10
, pp. 161
–175
.8.
Sneddon
, I. N.
, 1948
, “Boussinesq’s Problem for a Rigid Cone
,” Proc. Cambridge Philos. Soc.
44
, pp. 492
–507
.9.
Collins
, W. D.
, 1963
, “Potential Problems for a Circular Annulus
,” Proc. Edinburgh Math. Soc.
, 13
, pp. 235
–246
.10.
Popov
, G. Ia.
, 1962
, “The Contact Problem of the Theory of Elasticity for the Case of a Circular Area of Contact
,” J. Appl. Math. Mech., (English translation of PMM)
, 26
, pp. 207
–225
.11.
Green, A. E., and Zerna, W., 1954, Theoretical Elasticity, Oxford University Press, London.
12.
Wolfram, S., 1991, Mathematica–A System for Doing Mathematica by Computer, Addison-Wesley, Reading, MA.
Copyright © 2002
by ASME
You do not currently have access to this content.
