On the behaviour of the solution to a viscoplastic contact problem

Abstract

The present paper represents a continuation of [2]. There, a quasistatic contact problem for viscoplastic materials was considered, in which the contact was assumed to be frictionless and was described with normal compliance and unilateral constraint; the unique weak solvability of the problem was proved, a fully discrete scheme for the numerical approximation of the problem was described and numerical simulations were presented. In the present paper we analyse the dependence of the solution of the viscoplastic contact problem in [2] with respect to the data. We state and prove a convergence result, Theorem 3.1, then we illustrate its validity in the study of a two-dimensional numerical example.

Authors

Mikael Barboteu
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

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

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

Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Keywords

viscoplastic material; frictionless contact; normal compliance; unilateral constraint; weak-solution; convergence results; numerical simulations

Cite this paper as:

M. Barboteu, F. Pătrulescu, A. Ramadan, M. Sofonea, On the behaviour of the solution to a viscoplastic contact problem, in Advances in Mathematics, eds. L. Beznea, V. Brinzănescu, M. Iosifescu, G. Marinoschi, R. Purice, D. Timotin, pp. 75-88, The Publishing House of the Romanian Academy, 2013.

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About this paper

Title

Advances in Mathematics

Publisher Name

Editura Academiei Romane
(The Publishing House of the Romanian Academy)

Editors

L. Beznea, V. Brinzănescu, M. Iosifescu, G. Marinoschi, R. Purice, D. Timotin

Print ISSN
Online ISSN

MR

3203417

ZBL

?

References

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References

[1] Alart, A. Curnier, A mixed formulation for frictional contact problems prone to Newton like solution methods, Computer Methods in Applied Mechanics and Engineering, 92 (1991), 353–375.
[2] Barboteu, A. Matei, M. Sofonea, Analysis of quasistatic viscoplastic contact problems with normal compliance, Quarterly Jnl. of Mechanics and App. Maths. . ?????
[3] Cristescu, I. Suliciu, Viscoplasticity, Martinus Nijhoff Publishers, Editura Tehnica, Bucharest, (1982).
[4] Han, M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity, Studies in Advanced Mathematics, 30, American Mathematical Society–International Press, Sommerville, MA (2002).
[5] R. Ionescu, M.  Sofonea, Functional and Numerical Methods in Viscoplasticity, Oxford University Press, Oxford (1993).
[6] Jarusek, M. Sofonea, On the solvability of  dynamic elastic-visco-plastic contact problems, Zeitschrift fur Angewandte Matematik und Mechanik  (ZAMM), 88 (2008), 3-22.
[7] B. Khenous, P.  Laborde, Y. Renard, On the discretization of contact problems in elastodynamics, Lecture Notes in Applied Computational  Mechanics, 27 (2006), 31-38.
[8] B. Khenous, J.-C. Pommier, Y., Renard, Hybrid discretization of the Signorini problem with Coulomb friction. Theoretical aspects and comparison of some numerical solvers, Applied Numerical Mathematics, 56 (2006), 163-192.
[9] Laursen, Computational Contact and Impact Mechanics, Springer, Berlin (2002).
[10] Shillor, M. Sofonea, J.J. Telega, Models and Analysis of Quasistatic Contact, Lecture Notes in Physics, 655, Springer, Berlin (2004).
[11] Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.
[12] Sofonea, A. Matei, Mathematical Models in Contact Mechanics, London Mathematical Society Lecture Note Series, 398, Cambridge University Press, Cambridge (2012).
[13] Wriggers, Computational Contact Mechanics, Wiley, Chichester (2002).

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