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
(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
(Laboratoire de Mathématiques et Physique, Université de Perpignan)
viscoplastic material; frictionless contact; unilateral constraint; history-depdendent variational inequality; weak solution
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
Annals of the Academy of Romanian Scientists. Mathematics and its Applications
Publishing House of Romanian Scientists (Editura Academiei Oamenilor de Ştiinţă din România), Bucharest
 Shillor, M. Sofonea, J.J. Telega, Models and Analysis of Quasistatic Contact. Lect. Notes Phys., Springer, Berlin Heidelberg (2004).
 Sofonea, A. Matei. History-dependent quasivariational inequalities arising in Contact Mechanics, Eur. J. Appl. Math., 22 (2011), 471-491.