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Initial deformation about convex surfaces formed from identical, rough elastic-plastic bodies which approach along their normal at first contact

Published online by Cambridge University Press:  17 February 2009

Graham Weir
Graham Weir
Affiliation:
Applied Mathematics, IRL, Wellington, New Zealand; e-mail: g.weir@irl.cri.nz.
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Abstract

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The low-velocity impact of two convex surfaces comprised of identical material, which approach each other along the direction of the normal at first contact, and obey a J2 = k2 plastic yield condition, is shown for very early times to satisfy the following conditions: the interior surface which separates the two bodies is equivalent to either the locus of points formed by the intersecting curves resulting from moving the two bodies towards each other along their normal; or to the locus of points formed from the level surfaces (suitably parametrized) drawn about each body at the time of first contact. This separating surface lies midway between the geometrical overlap of the two approaching surfaces for times sufficiently short for inertial effects not to significantly affect the approaching velocities.

Keywords

identical particlesseparating surfacerigid-plastic impactslevel surfacesdeformation
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 4 , April 2007 , pp. 449 - 459
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Courant, R., Differential and Integral Calculus, Volume 2 (Blackie and Son, London, 1962).Google Scholar
[2]Crook, A. W., “A study of some impacts between metal bodies by a piezo-electric method”, Proc. Roy. Soc. 212 (1952) 377–390.Google Scholar
[3]Goldsmith, W., Impact (Edward Arnold, London, 1960).Google Scholar
[4]Goldstein, H., Classical Mechanics (Addison-Wesley Press, Inc., Cambridge, Mass., 1968).Google Scholar
[5]Hill, R., The Mathematical Theory of Plasticity, 1st ed. (Clarendon, Oxford, 1983).Google Scholar
[6]Iyanaga, S. and Kawada, Y. (eds.), Encyclopedic Dictionary of Mathematics (Math. Soc. Japan, The MIT Press, London, 1980).Google Scholar
[7]Jaeger, J. C. and Cook, N. G. W., Fundamentals of Rock Mechanics, 1st ed. (Methuen, London, 1969).Google Scholar
[8]Johnson, K. L., Contact Mechanics (Cambridge University Press, Cambridge, 1985).CrossRefGoogle Scholar
[9]Nadai, A., Theory of flow and fracture in solids, 2nd ed. (McGraw-Hill, New York, 1950).Google Scholar
[10]Thornton, C. and Ning, Z., “A theoretical model for the stick/bounce behaviour of adhesive, elastic-plastic spheres”, Powder Technology 99 (1998) 154–162.CrossRefGoogle Scholar
[11]Weir, G. J., “The shape of dented elastic-plastic ellipses and ellipsoids”, New Zealand J. Mathematics, in press.Google Scholar
[12]Weir, G. J. and Tallon, S. P., “The coefficient of restitution for normal, low velocity impacts”, Chem. Eng. Sci. 60 (2005) 3637–3647.CrossRefGoogle Scholar