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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 3, 2015, pp. 251–275
DOI: 10.4171/ZAA/1538

Published online: 2015-07-08

Variational-Hemivariational Approach to a Quasistatic Viscoelastic Problem with Normal Compliance, Friction and Material Damage

Leszek Gasiński[1], Anna Ochal[2] and Meir Shillor[3]

(1) Jagiellonian University, Kraków, Poland
(2) Jagiellonian University, Kraków, Poland
(3) Oakland University, Rochester, USA

This work studies a model for quasistatic frictional contact between a viscoelastic body and a reactive foundation. The constitutive law is assumed to be nonlinear and contains damage e ects modeled by a parabolic di erential inclusion. Contact is described by the normal compliance condition and a subdi erential frictional condition. A variational-hemivariational formulation of the problem is provided and the existence and uniqueness of its solution is proved. The proof is based on a surjectivity result for pseudomonotone coercive operators and a xed point argument.

Keywords: Quasistatic contact, nonlinear viscoelastic material, normal compliance, subdifferential friction condition, damage, variational-hemivariational inequality

Gasiński Leszek, Ochal Anna, Shillor Meir: Variational-Hemivariational Approach to a Quasistatic Viscoelastic Problem with Normal Compliance, Friction and Material Damage. Z. Anal. Anwend. 34 (2015), 251-275. doi: 10.4171/ZAA/1538