A New Class of History-Dependent Evolutionary Variational-Hemivariational Inequalities with Unilateral Constraints

摘要

In this paper we study a new abstract evolutionary variational-hemivariational inequality which involves unilateral constraints and history-dependent operators. First, we prove the existence and uniqueness of solution by using a mixed equilibrium formulation with suitable selected functions together with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a dynamic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity combined with the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.