# A penalized viscoplastic contact problem with unilateral constraints

## Abstract

In this paper we study 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 present a penalization method in the study of this problem. We start by introducing the penalized problem, then we prove its unique solvability as well as the convergence of its solution to the solution of the original problem, as the penalization parameter converges to zero

## Authors

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

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

(Laboratoire de Mathématiques et Physique, Université de Perpignan)

## Keywords

viscoplastic material; frictionless contact; unilateral constraint; weak solution

## Cite this paper as:

F. Pătrulescu, A. Farcaş, A Ramadan, A penalized viscoplastic contact problem with unilateral constraints, Annals of the University of Bucharest – mathematical series, vol. 4 (LXII), no. 1 (2013), pp. 213-227

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##### Publisher Name

Editura Universitatii din Bucuresti, Bucuresti

2067-9009

3093541

1324.74023