Convergence results for contact problems with memory term


In this paper, we consider two quasistatic contact problems. The material’s behavior is modelled with an elastic constitutive law for the first problem and a viscoplastic constitutive law for the second problem. The novelty arises in the fact that the contact is frictionless and is modelled with a condition which involves normal compliance and memory term. Moreover, for the second problem we consider a condition with unilateral constraint. For each problem we derive a variational formulation of the model and prove its unique solvability. Also, we analyze the dependence of the solution with respect to the data.


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

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


convergence result; memory term; history-dependent variational inequality; weak solution; Fréchet space; Gronwall inequality

Cite this paper as

F. Pătrulescu, A. Ramadan, Convergence results for contact problems with memory term, Math. Rep., vol. 17 (67), no. 1 (2015), pp. 24-41


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Publishing House of the Romanian Academy (Editura Academiei Române), Bucharest

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