ABSTRACT
The problem studied in this chapter includes friction and material damage. Contact is modeled with the normal compliance condition and friction with a general version of Coulomb’s law. The process is assumed to be quasistatic and the material’s behavior is described by a viscoelastic constitutive law with damage. We derive the variational formulation of the problem and prove the existence and uniqueness of the weak solution using arguments for elliptic and parabolic variational inequalities and the Banach fixed-point theorem. We then consider numerical approximations of the model problem. We introduce fully discrete schemes in which the spatial domain is discretized by the finite element method. We show the existence of the unique approximate solution and, under suitable assumptions on the regularity of the solution, we derive optimal error estimates.
