## Abstract

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.

## Authors

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

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

## Keywords

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

## About this paper

##### Journal

##### Publisher Name

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

##### Paper on the journal website

##### Print ISSN

1582-3067

##### Online ISSN

2285-3898/e

## MR

3342143

## ZBL

1374.74100

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