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Existence and uniqueness of solutions to dynamical unilateral contact problems with coulomb friction: the case of a collection of points

Published online by Cambridge University Press:  11 October 2013

Alexandre Charles  and
Patrick Ballard
Alexandre Charles
Affiliation:
Laboratoire de Mécanique et d’Acoustique, CNRS, 31, chemin Joseph Aiguier, 13402 Marseille Cedex 20, France. [email protected]
Patrick Ballard
Affiliation:
Laboratoire de Mécanique et d’Acoustique, CNRS, 31, chemin Joseph Aiguier, 13402 Marseille Cedex 20, France. [email protected]
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Abstract

This study deals with the existence and uniqueness of solutions to dynamical problems of finite freedom involving unilateral contact and Coulomb friction. In the frictionless case, it has been established [P. Ballard, Arch. Rational Mech. Anal. 154 (2000) 199–274] that the existence and uniqueness of a solution to the Cauchy problem can be proved under the assumption that the data are analytic, but not if they are assumed to be only of class C∞. Some years ago, this finding was extended [P. Ballard and S. Basseville, Math. Model. Numer. Anal. 39 (2005) 59–77] to the case where Coulomb friction is included in a model problem involving a single point particle. In the present paper, the existence and uniqueness of a solution to the Cauchy problem is proved in the case of a finite collection of particles in (possibly non-linear) interactions.

Keywords

Unilateral dynamics with frictionfrictional dynamical contact problemsexistence and uniqueness
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 1 , January 2014 , pp. 1 - 25
Copyright
© EDP Sciences, SMAI, 2013

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