J. R. Fernández, O. Chau, 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 is stated.
Then, the numerical analysis of the problem is provided for a fully-discrete
approximation. The convergence of the scheme is established and error estimates
derived. Finally, a representative numerical simulation is presented, depicting the
evolution of the state of the system and, in particular, the evolution of the bonding field.