## 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 **Farca****ş**

(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

## 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

##### Paper on journal website

##### Print ISSN

2066-5997

##### Online ISSN

2066-6594

## MR

2959899

## ZBL

1284.74088

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