A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH ADHESION FOR NONLINEAR ELASTIC MATERIALS

The aim of this paper is to study a quasistatic contact problem between a nonlinear elastic body and a foundation. The contact is adhesive and frictional and is modelled with a version of normal compliance condition and the associated Coulomb's law of dry friction. The evolution of the bonding field is described by a first order differential equation. We establish the variational formulation of the mechanical problem and prove an existence result of the weak solution if the coefficient of friction is sufficiently small by passing to the limit with respect to time. The proofs are based on arguments of time-discretization, compactness, lower semicontinuity and Banach fixed point.