Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?

Patrick  Ballard

doi:10.3934/dcdss.2016001

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2016, Volume 9, Issue 2: 363-381. Doi: 10.3934/dcdss.2016001

This issue Previous Article Preface Next Article Parametric nonlinear PDEs with multiple solutions: A PGD approach

Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?

Patrick Ballard^1,

1.
CNRS and UMPC Université Paris 06, Institut Jean le Rond d'Alembert, UMR 7190, 75005 Paris

Received: March 2015

Revised: October 2015

Published: April 2016

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Abstract

The `stick-slip' phenomenon is the unsteady relative motion of two solids in frictional contact. Tentative explanations were given in the past by enriching the friction law (for example, introducing static and dynamic friction coefficients). In this article, we outline an approach for the analysis of the `stick-slip' phenomenon within the simple framework of the coupling of linear elasticity with the Coulomb dry friction law. Simple examples, both discrete and continuous, show that the solutions of the steady sliding frictional contact problem may exhibit bifurcations (loss of uniqueness) when the friction coefficient is taken as a control parameter. It is argued that such a bifurcation could account, in some cases, for the `stick-slip' phenomenon. The situations of a single point particle, of a linear elastic bounded body with homogeneous friction coefficient and of the elastic half-space with both homogenous and piecewise constant friction coefficient are analysed and compared.

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Mathematics Subject Classification: 74B05, 74M10, 74M15.

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References

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