# Analysis of a contact problem with wear and unilateral constraint

## Abstract

This paper represents a continuation of our previous work, where a mathematical model which describes the equilibrium of an elastic body in frictional contact with a moving foundation was considered. An existence and uniqueness result was proved, together with a convergence result. The proofs were carried out by using arguments of elliptic variational inequalities. In this current paper, we complete our model by taking into account the wear of the foundation. This makes the problem evolutionary and leads to a new and nonstandard mathematical model, which couples a time-dependent variational inequality with an integral equation. We provide the unique weak solvability of the model by using a fixed point argument, among others. Then, we penalize the unilateral contact condition and prove that the penalized problem has a unique solution which converges to the solution of the original problem, as the penalization parameter converges to zero.

## Authors

Mircea Sofonea
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis,

Yahyeh Souleiman
(Laboratoire de Mathématiques et Physique, Université de Perpignan)

## Keywords

elastic material, frictional contact, normal compliance, unilateral constraint, wear, weak solution, penalization

## Cite this paper as

M. Sofonea, F. Pătrulescu, Y. Souleiman, Analysis of a contact problem with wear and unilateral constraint, Appl. Anal., vol. 95 no. 11 (2016), pp. 2590-2607,
DOI: 10.1080/00036811.2015.1102892

## PDF

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##### Publisher Name

Taylor & Francis, Abingdon, Oxfordshire

0003-6811

1563-504X

3546606

1349.74281