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 Farcaş
(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
Google Scholar
[2] Shillor, M. Sofonea, J.J. Telega, Models and Analysis of Quasistatic Contact. Lect. Notes Phys., Springer, Berlin Heidelberg (2004).
[3] Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.