Analysis of a history-dependent frictionless contact problem

Abstract

We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and an obstacle, the so-called foundation. The contact is frictionless and is modeled with a new and nonstandard condition which involves both normal compliance, unilateral constraint and memory effects. We derive a variational formulation of the problem which is the form of a history-dependent variational inequality for the displacement field.

Then, using a recent result obtained by Sofonea and Matei, we prove the unique weak solvability of the problem. Next, we study the continuous dependence of the weak solution with respect the data and prove a first convergence result. Finally, we prove that the weak solution of the problem represents the limit of the weak solution of a contact problem with normal compliance and memory term, as the stiffness coefficient of the foundation converges to infinity.

Authors

Mircea Sofonea
Laboratoire de Mathématiques et Physique, Université de Perpignan

Flavius Patrulescu
Tiberiu Popoviciu Institute of Numerical Analysis,
Romanian Academy

Keywords

viscoelastic material; frictionless contact; unilateral constraint; memory term; history-dependent variational inequality; weak solution

Cite this paper as:

M. Sofonea, F. Pătrulescu, Analysis of a history-dependent frictionless contact problem, Math. Mech. Solids, 18 (2013) no.4, pp. 409-430.

PDF

About this paper

Journal

Mathematics and Mechanics of Solids

Publisher Name

SAGE Publications, Thousand Oaks, CA

Print ISSN

1081-2865

Online ISSN

1741-3028

MR

3179460

ZBL

?

References

Paper in html format

Related Posts

Leave a Reply

Your email address will not be published. Required fields are marked *

Fill out this field
Fill out this field
Please enter a valid email address.

Menu