ABSTRACT
In this chapter we study a dynamic contact problem between a viscoelastic body and an obstacle. The contact is with adhesion, the evolution of which is described by an ordinary differential equation. As in the previous chapter, we use a nonlinear Kelvin-Voigt viscoelastic constitutive law to model the material behavior and a modified normal compliance contact condition, involving a truncation operator, to model the contact. We derive a variational formulation of the contact problem and prove the existence and uniqueness of its solution. The proof is based on the construction of two intermediate problems and the use of the Banach fixed-point theorem. We introduce a fully discrete scheme for the numerical approximations of the dynamic adhesive contact problem and derive error estimates on the solutions.
