## 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)

Ahmad **Ramadan**

(Laboratoire de Mathématiques et Physique, Université de Perpignan)

## Keywords

## 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

## About this paper

##### Publisher Name

Editura Universitatii din Bucuresti, Bucuresti

##### Paper on journal website

##### Print ISSN

2067-9009

##### Online ISSN

## MR

3093541

## ZBL

1324.74023

[1] Barboteu, A. Matei, M. Sofonea, *Analysis of quasistatic **viscoplastic contact problems with normal compliance*, *Quarterly **Jnl. of Mechanics and App. Maths*. . ?????

[2] Barboteu,F. Patrulescu, A. Ramadan, M. Sofonea, *History-dependent contact models for viscoplastic materials*, IMA J. Appl. Math., 79, no. 6 (2014), 1180-1200

[3] Barboteu, A. Ramadan, M. Sofonea, F. Patrulescu, *An elastic contact problem with normal compliance and memory term*, Machine Dynamics Research, 36, no. 1 (2012), 15-[4] Corduneanu,*Problemes globaux dans la theorie des equations **integrales de Volterra*, Ann. Math. Pure Appl., 67 (1965), 349-363.

[5] Farcas, F. Patrulescu,M. Sofonea,* A history-dependent contact problem with unilateral constraint*, Ann. Acad. Rom. Sci. Ser. Math. Appl., 4, no. 1 (2012), 90-96.

[6] Han, M. Sofonea, *Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, Studies in Advanced Mathematics*, 30, American Mathematical Society–International Press, Sommerville, MA (2002).

[7] Jarusek, M. Sofonea, *On the solvability of dynamic **elastic-visco-plastic contact problems*, Zeitschrift fur Angewandte Matematik und Mechanik (ZAMM), 88 (2008), 3-22.

[8] J. Massera, J.J. Schaffer, *Linear Differential Equations and Function Spaces*, Academic Press, New York-London (1966).

[9] Shillor, M. Sofonea, J.J. Telega, *Models and Analysis of Quasistatic Contact*, Lecture Notes in Physics, 655, Springer, Berlin (2004).

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

[11] Sofonea, A. Matei,* Mathematical Models in Contact Mechanics*, London Mathematical Society Lecture Note Series, 398, Cambridge University Press, Cambridge (2012).

[12] Sofonea, F. Patrulescu, *Analysis of a history-dependent frictionless contact problem*, Mathematics and Mechanics of Solids, 18, no.4 (2013), 409-430.

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