A Paradox in Sliding Contact Problems With Friction

[+] Author and Article Information
G. G. Adams

Department of Mechanical Engineering,  Northeastern University, Boston, MA 02115 Fellow ASME

J. R. Barber

Department of Mechanical Engineering,  University of Michigan, Ann Arbor, MI 48109Mem. ASME

M. Ciavarella

Senior Resarcher,  CNR-ITC Str. Crocefisso 2∕B, 70126 Bari, Italy

J. R. Rice

Division of Engineering and Applied Sciences,  Harvard University, Cambridge, MA 02138Fellow ASME

This phenomenon leads to a paradoxical behavior of its own, i.e., the Craggs–Roberts paradox (5-6).

J. Appl. Mech 72(3), 450-452 (Oct 03, 2003) (3 pages) doi:10.1115/1.1867992 History: Received September 09, 2002; Revised October 03, 2003

In problems involving the relative sliding to two bodies, the frictional force is taken to oppose the direction of the local relative slip velocity. For a rigid flat punch sliding over a half-plane at any speed, it is shown that the velocities of the half-plane particles near the edges of the punch seem to grow without limit in the same direction as the punch motion. Thus the local relative slip velocity changes sign. This phenomenon leads to a paradox in friction, in the sense that the assumed direction of sliding used for Coulomb friction is opposite that of the resulting slip velocity in the region sufficiently close to each of the edges of the punch. This paradox is not restricted to the case of a rigid punch, as it is due to the deformations in the half-plane over which the pressure is moving. It would therefore occur for any punch shape and elastic constants (including an elastic wedge) for which the applied pressure, moving along the free surface of the half-plane, is singular. The paradox is resolved by using a finite strain analysis of the kinematics for the rigid punch problem and it is expected that finite strain theory would resolve the paradox for a more general contact problem.

Copyright © 2005 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

A flat rigid punch indenting an elastic half-plane




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In