It is well known that the conventional Coulomb friction condition can lead to non-uniqueness of solution in elastostatic solutions if the friction coefficient is sufficiently high. Interest in this field has centered on discrete formulations, particularly with reference to the finite element method. More recently Hild has demonstrated the existence of a multiplicity of non-unique solutions to a simple problem in two-dimensional continuum elasticity and showed how to determine the conditions for such states to exist by formulating an eigenvalue problem. Both the discrete and continuum examples of non-uniqueness seem to be related to the well known physical phenomenon whereby a frictional system can become locked or ‘wedged’ in a state of stress even when no external loads are applied (the homogeneous problem), but the equivalence is not complete because of the influence of unilateral inequalities in the physical problem. We shall discuss the relations between these concepts in the context of simple continuum and discrete problems in two-dimensional linear elasticity.
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ASME/STLE 2004 International Joint Tribology Conference
October 24–27, 2004
Long Beach, California, USA
Conference Sponsors:
- Tribology Division
ISBN:
0-7918-4181-2
PROCEEDINGS PAPER
Non-Uniqueness, Eigenvalue Solutions and Wedged Configurations Involving Coulomb Friction
J. R. Barber,
J. R. Barber
University of Michigan, Ann Arbor, MI
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P. Hild
P. Hild
Universite´ de Franche-Comte´, Besanc¸on, France
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J. R. Barber
University of Michigan, Ann Arbor, MI
P. Hild
Universite´ de Franche-Comte´, Besanc¸on, France
Paper No:
TRIB2004-64368, pp. 127-132; 6 pages
Published Online:
December 22, 2008
Citation
Barber, JR, & Hild, P. "Non-Uniqueness, Eigenvalue Solutions and Wedged Configurations Involving Coulomb Friction." Proceedings of the ASME/STLE 2004 International Joint Tribology Conference. ASME/STLE 2004 International Joint Tribology Conference, Parts A and B. Long Beach, California, USA. October 24–27, 2004. pp. 127-132. ASME. https://doi.org/10.1115/TRIB2004-64368
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