Convergence results for contact problems with memory term

Abstract

In this paper, we consider two quasistatic contact problems. The material’s behavior is modelled with an elastic constitutive law for the first problem and a viscoplastic constitutive law for the second problem. The novelty arises in the fact that the contact is frictionless and is modelled with a condition which involves normal compliance and memory term. Moreover, for the second problem we consider a condition with unilateral constraint. For each problem we derive a variational formulation of the model and prove its unique solvability. Also, we analyze the dependence of the solution with respect to the data.

Authors

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

Ahmad Ramadan
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Keywords

convergence result; memory term; history-dependent variational inequality; weak solution; Fréchet space; Gronwall inequality

Cite this paper as

F. Pătrulescu, A. Ramadan, Convergence results for contact problems with memory term, Math. Rep., vol. 17 (67), no. 1 (2015), pp. 24-41

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About this paper

Publisher Name

Publishing House of the Romanian Academy (Editura Academiei Române), Bucharest

Print ISSN

1582-3067

Online ISSN

2285-3898/e

MR

3342143

ZBL

1374.74100

Google Scholar

References

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References

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[3] M. Barboteu, F. Patrulescu, A. Ramadan,M. Sofonea, History-dependent contact models for viscoplastic materials, IMA J. Appl. Math., 79, no. 6 (2014), 1180-1200.
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[5] J.J. Massera, J.J. Schaffer, Linear Differential Equations and Function Spaces, Academic Press, New York-London (1966).
[6] M. Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.
[7] M. Sofonea, A. Matei, Mathematical Models in Contact Mechanics, London Mathematical Society Lecture Note Series, 398, Cambridge University Press, Cambridge (2012).
[8] M. Sofonea, F. Patrulescu, Analysis of a history-dependent frictionless contact problem, Math. and Mech. of Solids,18 (2013), 409-430.

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