Existence and uniqueness for dynamical unilateral contact with coulomb friction : a model problem.

Patrick Ballard (1) , Stéphanie Basseville (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

A simple dynamical problem involving unilateral contact and dry friction of Coulomb type is considered as an archetype. We are concerned with the existence and uniqueness of solutions of the system with Cauchy data. In the frictionless case, it is known [Schatzman, Nonlinear Anal. Theory, Methods Appl.2 (1978) 355–373] that pathologies of non-uniqueness can exist, even if all the data are of class $\mathcal{C}^\infty$. However, uniqueness is recovered provided that the data are analytic [Ballard]. Under this analyticity hypothesis, we prove the existence and uniqueness of solutions for the dynamical problem with unilateral contact and Coulomb friction, extending [Ballard] to the case where Coulomb friction is added to unilateral contact.

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

Patrick Ballard, Stéphanie Basseville. Existence and uniqueness for dynamical unilateral contact with coulomb friction : a model problem.. ESAIM: Mathematical Modelling and Numerical Analysis, 2005, 39 (1), pp.59-78. ⟨hal-00461828⟩