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.
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A Paradox in Sliding Contact Problems With Friction
G. G. Adams,
G. G. Adams
Department of Mechanical Engineering,
Northeastern University
, Boston, MA 02115 Fellow ASME
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J. R. Barber,
J. R. Barber
Department of Mechanical Engineering,
University of Michigan
, Ann Arbor, MI 48109Mem. ASME
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M. Ciavarella,
M. Ciavarella
Senior Resarcher
,
CNR-ITC
Str. Crocefisso 2∕B, 70126 Bari, Italy
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J. R. Rice
J. R. Rice
Division of Engineering and Applied Sciences,
Harvard University
, Cambridge, MA 02138 Fellow ASME
Search for other works by this author on:
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 02138 Fellow ASMEJ. Appl. Mech. May 2005, 72(3): 450-452 (3 pages)
Published Online: October 3, 2003
Article history
Received:
September 9, 2002
Revised:
October 3, 2003
Citation
Adams, G. G., Barber, J. R., Ciavarella, M., and Rice, J. R. (October 3, 2003). "A Paradox in Sliding Contact Problems With Friction." ASME. J. Appl. Mech. May 2005; 72(3): 450–452. https://doi.org/10.1115/1.1867992
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