O. Chau, J. R. Fernández, M. Shillor and M. Sofonea

A model for the adhesive, quasistatic and frictionless contact between
a viscoelastic body and a deformable foundation is described. The adhesion
process is modeled by a bonding field on the contact surface, and contact
is described by a modified normal compliance condition. The problem is
formulated as a coupled system of a variational equality for the displacements
and a differential equation for the bonding field. The existence of a unique weak
solution for the problem and its continuous dependence on the adhesion
parameters are established. Then, the numerical analysis of the problem
is conducted for the semi-discrete and fully-discrete approximations. The
convergence ofthe schemes is established and error estimates derived. Finally,
representative numerical simulations are presented, depicting the evolution of
the state of the system and, in particular, the evolution of the bonding field.