A history-dependent contact problem with unilateral constraint


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


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)


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

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

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[3] Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.



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