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)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 M&S - Matériaux et Structures

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.

Mots clés: Unilateral dynamics with friction; Frictional dynamical contact problems; Existence and uniqueness

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

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, 2014, 48 (1), pp.1-25. ⟨10.1051/m2an/2013092⟩. ⟨hal-00934944⟩