A viscoplastic contact problem with normal compliance, unilateral constraint and memory term


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.


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)


viscoplastic material; frictionless contact; normal compliance; unilateral constraint; memory term; history-dependent variational inequality, weak solution; Fréchet space

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


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Applied Mathematics and Optimization

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Springer US, New York, NY

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