# American Institute of Mathematical Sciences

April  2016, 9(2): 363-381. doi: 10.3934/dcdss.2016001

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

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

Received  March 2015 Revised  October 2015 Published  March 2016

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.
Citation: Patrick Ballard. Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 363-381. doi: 10.3934/dcdss.2016001
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