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A dynamic elastic-visco-plastic unilateral contact problem with normal damped response and Coulomb friction
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SYSNO ASEP 0345046 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A dynamic elastic-visco-plastic unilateral contact problem with normal damped response and Coulomb friction Author(s) Eck, Ch. (DE)
Jarušek, Jiří (MU-W) RID, ORCID, SAI
Sofonea, M. (FR)Source Title European Journal of Applied Mathematics - ISSN 0956-7925
Roč. 21, č. 3 (2010), s. 229-251Number of pages 23 s. Language eng - English Country GB - United Kingdom Keywords elastic-vosco plastic material ; dynamic contact problem ; normal damped response ; unilateral constraint ; Coulomb friction ; weak solution ; penalitazion ; smoothing Subject RIV BA - General Mathematics R&D Projects IAA100750802 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000277939900002 EID SCOPUS 77955851459 DOI 10.1017/S0956792510000045 Annotation We consider a dynamic frictional contact problem between an elastic-visco-plastic body and a foundation. The contact is modelled with a normal damped response condition of such a type that the normal velocity is restricted with unilateral constraint, associated with the Coulomb law in which the coefficient of friction may depend on the velocity. We derive a variational formulation of the problem which has the form of a system coupling an integro differential equation for the stress field with an evolutionary variational inequality for the displacement field. This inequality is approximated by a variational equation using a smoothing of the friction and the penalty approximation of the unilateral condition. The existence of a weak solution to the variational equation is proved by the Galerkin method for an auxiliary problem with given viscoplastic part of the stress and a fixed point argument. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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