A dynamic unilateral contact problem with adhesion and friction in viscoelasticity

Marius Cocou (1, 2) , Mathieu Schryve (2) , Michel Raous (2)

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

The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented.

Mots clés: viscoelasticity; dynamic problems; friction; healing; adhesion; unilateral contact

Domaines: Mécanique des solides [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Marius Cocou, Mathieu Schryve, Michel Raous. A dynamic unilateral contact problem with adhesion and friction in viscoelasticity. Zeitschrift für Angewandte Mathematik und Physik, 2010, 61 (4), pp.721 - 743. ⟨10.1007/s00033-009-0027-x⟩. ⟨hal-00461928⟩