A history-dependent contact problem with unilateral constraint

Abstract

We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The contact is frictionless and is modelled with a new and nonstandard condition which involves both normal compliance, unilateral constraint and memory effects. We derive a variational formulation of the problem then we prove its unique weak solvability. The proof is based on arguments on history-dependent variational inequalities

Authors

Anca Farcaş
(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis,
Romanian Academy)

Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Keywords

viscoplastic material; frictionless contact; unilateral constraint; history-depdendent variational inequality; weak solution

Cite this paper as

A. Farcaş, F. Pătrulescu, M. Sofonea, A history-dependent contact problem with unilateral constraint, Ann. Acad. Rom. Sci. Ser. Math. Appl., vol 4, no. 1 (2012), pp. 90-96

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About this paper

Journal

Annals of the Academy of Romanian Scientists. Mathematics and its Applications

Publisher Name

Publishing House of Romanian Scientists (Editura Academiei Oamenilor de Ştiinţă din România), Bucharest

Print ISSN

2066-5997

Online ISSN

2066-6594

MR

2959899

ZBL

1284.74088

Google Scholar

References

Paper in html format

References

[1] Jarusek, M. Sofonea, On the solvability of  dynamic elastic-visco-plastic contact problems, Zeitschrift fur Angewandte Matematik und Mechanik  (ZAMM), 88 (2008), 3-22.
[2] Shillor, M. Sofonea,  J.J. Telega, Models and Analysis of Quasistatic Contact. Lect. Notes Phys., Springer, Berlin Heidelberg (2004).
[3] Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.

 

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