ANALYSIS OF A VISCOELASTIC FRICTIONLESS CONTACT PROBLEM WITH ADHESION

We consider a quasistatic frictionless contact problem for viscoelastic bodies with long memory. The contact is modelled with normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. The adhesion between contact surfaces is taken into account and the evolution of the bonding field is described by a first order differential equation. We derive a variational formulation of the mechanical problem and we establish an existence and uniqueness result by using arguments of time-dependent variational inequalities, differential equations and Banach fixed point theorem. Moreover, using compactness properties we study a regularized problem which has a unique solution and we obtain the solution of the original model by passing to the limit as the regularization parameter converges to zero.