Abstract
We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modelled with a rate-type constitutive law with internal state variable. The contact is frictionless and is modelled with normal compliance, unilateral constraint and memory term.
We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove its unique weak solvability. The proof is based on arguments of history-dependent quasivariational inequalities.
We also study the dependence of the solution with respect to the data and prove a convergence result.
Authors
Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)
Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)
Anca Farcaş
(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)
Keywords
Cite this paper as:
M. Sofonea, F. Pătrulescu, A. Farcaş, A viscoplastic contact problem with normal compliance, unilateral constraint and memory term, Appl. Math. Opt., vol. 62 (2014), pp. 175-198
About this paper
Journal
Applied Mathematics and Optimization
Publisher Name
Springer US, New York, NY
Print ISSN
0095-4616
Online ISSN
1432-0606
MR
3175193
ZBL
1297.74086
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