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A unified approach to dynamic contact problems in viscoelasticity. (English) Zbl 1138.74375
Summary: In this paper we consider mathematical models describing dynamic viscoelastic contact problems with the Kelvin-Voigt constitutive law and subdifferential boundary conditions. We treat evolution hemivariational inequalities which are weak formulations of contact problems. We establish the existence of solutions to hemivariational inequalities with different types of non-monotone multivalued boundary relations. These results are consequences of an existence theorem for second order evolution inclusions. In a particular case we deliver sufficient conditions under which the solution to a hemivariational inequality is unique. Finally, applications to several unilateral and bilateral problems in contact mechanics are provided.

MSC:
74M15 Contact in solid mechanics
74D05 Linear constitutive equations for materials with memory
74M25 Micromechanics of solids
49J40 Variational inequalities
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