Electron. J. Math. Phys. Sci., 2002, 1,1, 47-71

 

ON THE ANALYSIS OF A VISCOPLASTIC CONTACT PROBLEM WITH TIME DEPENDENT TRESCA'S FRICTION LAW

 

Amina Amassad ^* and Caroline Fabre ^#

de Nice-Sophia Antipolis, Laboratoire J.-A. Dieudonné

UMR-CNRS 6621, Parc Valrose, F-06108 Nice, France

E-mail: ^* amassad@math.unice.fr and ^# cfabre@math.unice.fr

Received: 26 May 2002/ Accepted: 27 July 2002/ Published: 22 August 2002

Abstract: This paper deals with the study of a nonlinear problem of frictional contact between an elastic-viscoplastic body and a rigid obstacle. We model the frictional contact by a version of Tresca's friction law where the friction bound depends on time. Firstly, we obtain an existence and uniqueness result in a weak sense for a model including the bilateral contact. To this end we use a time discretization method and the Banach fixed-point theorem. Secondly, we show an existence result for a mechanical problem with the unilateral contact conditions (Signorini's contact) using an iterative method

 

Keywords: Quasistatic frictional contact, bilateral contact, unilateral contact, Tresca's friction law, fixed point, discretization

AMS Mathematical Subject Classification: 74D10, 74A55, 49B40

 

© 2002 by EJMAPS (http://www.ejmaps.org). Reproduction for noncommercial purposes permitted