A unified approach to dynamic contact problems in viscoelasticity


S. Migórski, migorski(at)softlab.ii.uj.edu.pl
A. Ochal, ochal(at)softlab.ii.uj.edu.pl
       Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland

Pages: 23

Abstract: In this paper we consider the mathematical models describing the dynamic viscoelastic contact problems with the Kelvin-Voigt constitutive law and the subdifferential boundary conditions. We treat the evolution hemivariational inequalities which are the weak formulations of these contact problems. We establish the results on the existence of solutions to hemivariational inequalities with different types of nonmonotone multivalued boundary relations. These results are a consequence of an existence theorem for second order evolution inclusions. Finally, the applications to several unilateral and bilateral problems in contact mechanics are given.

Keywords: viscoelasticity, hemivariational inequality, subdifferential, pseudomonotone, contact problem, friction, inclusion.

Published: Journal of Elasticity, 83  (2006), 247-276.