A quasistatic contact problem with adhesion and friction for viscoelastic materials
We consider a mathematical model which describes the contact between a deformable body and a foundation. The contact is frictional and is modelled by a version of normal compliance condition and the associated Coulomb's law of dry friction in which adhesion of contact surfaces is taken into account. The evolution of the bonding field is described by a first order differential equation and the material's behaviour is modelled by a nonlinear viscoelastic constitutive law. We derive a variational formulation of the mechanical problem and prove the existence and uniqueness of a weak solution if the friction coefficient is sufficiently small. The proof is based on time-dependent variational inequalities, differential equations and the Banach fixed point theorem.