International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 7, Pages 411-437

Existence for viscoplastic contact with Coulomb friction problems

Amina Amassad and Caroline Fabre

Université de Nice-Sophia Antipolis, Laboratoire de Mathématiques J.A. Dieudonné, UMR 66 21 du CNRS, Parc Valrose, Nice Cedex 2 06108, France

Received 19 October 2001

Copyright © 2002 Amina Amassad and Caroline Fabre. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present existence results in the study of nonlinear problem of frictional contact between an elastic-viscoplastic body and a rigid obstacle. We model the frictional contact both by a Tresca's friction law and a regularized Coulomb's law. We assume, in a first part, that the contact is bilateral and that no separation takes place. In a second part, we consider the Signorini unilateral contact conditions. Proofs are based on a time-discretization method, Banach and Schauder fixed point theorems.