Calculus of Variations and Geometric Measure Theory

E. Bonetti - G. Bonfanti - R. Rossi

Analysis of a unilateral contact problem taking into account adhesion and friction

created by rossi on 18 Jun 2011


Submitted Paper

Inserted: 18 jun 2011

Year: 2011


In this paper, we investigate a contact problem between a viscoelastic body and a rigid foundation, when both the effects of the (irreversible) adhesion and of the friction are taken into account. We describe the adhesion phenomenon in terms of a damage surface parameter according to \textsc{Frémond}'s theory, and we model the unilateral contact by Signorini conditions and the friction by a {\it nonlocal} Coulomb law. All the constraints on the internal variables as well as the contact and the friction conditions are rendered by means of subdifferential operators, whence the highly nonlinear character of the resulting PDE system. Our main result states the existence of a global-in-time solution (to a suitable variational formulation) of the related Cauchy problem. It is proved by an approximation procedure combined with time discretization.