# Convergence results for contact problems with memory term

## 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,

(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

1582-3067

2285-3898/e

3342143

1374.74100