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A Unified Approach to Dynamic Contact Problems in Viscoelasticity

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Institute of Computer Science, Jagiellonian University, Nawojki 11, PL-30072, Krakow, Poland

    Stanisław Migórski & Anna Ochal

Authors
  1. Stanisław Migórski
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  2. Anna Ochal
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Correspondence to Stanisław Migórski.

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*Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.

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Migórski, S., Ochal, A. A Unified Approach to Dynamic Contact Problems in Viscoelasticity. J Elasticity 83, 247–275 (2006). https://doi.org/10.1007/s10659-005-9034-0

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  • DOI: https://doi.org/10.1007/s10659-005-9034-0

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