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

Alexandre Charles 1 Patrick Ballard 2, *
* Corresponding author
2 M&S - Matériaux et Structures
LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
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 $C^\infty$. 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.
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Alexandre Charles, Patrick Ballard. Existence and uniqueness of solutions to dynamical unilateral contact problems with Coulomb friction: the case of a collection of points. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2014, 48 (1), pp.1-25. ⟨10.1051/m2an/2013092⟩. ⟨hal-00934944⟩

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