Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

History-dependent hemivariational inequalities with applications to Contact Mechanics

In this paper we survey some of our recent results on the existence and uniqueness of solutions to nonconvex and nonsmooth problems which arise in Contact Mechanics. The approach is based on operator subdifferential inclusions and hemivariational inequalities, and focuses on three aspects. First, we report on results on the second order history-dependent subdifferential inclusions and hemivaria...

A Class of Variational-Hemivariational Inequalities with Applications to Frictional Contact Problems

A class of variational-hemivariational inequalities is studied in this paper. An inequality in the class involves two nonlinear operators and two nondifferentiable functionals, of which at least one is convex. An existence and uniqueness result is proved for a solution of the inequality. Continuous dependence of the solution on the data is shown. Convergence is established rigorously for finite...

Dynamic Frictional Contact of a Viscoelastic Beam

Abstract. In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The beam is assumed to be situated horizontally and to move, in both horizontal and tangential directions, by the effect of applied forces. The left end of the beam is clamped and the right one is free. Its horizontal displacement is constrained because of the presence of a deform...

Optimal control for a class of mechanical thermoviscoelastic frictional contact problems

Abstract: We study optimal control of systems governed by a coupled system of hemivariational inequalities, modeling a dynamic thermoviscoelastic problem, which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt viscoelastic law, include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. We consider...

Covariant description for frictional contact problems