A CAUCHY-LIPSCHITZ METHOD FOR EXISTENCE AND EULER METHOD FOR NUMERICAL APPROACH IN QUASISTATIC CONTACT PROBLEMS IN RATE-TYPE VISCOPLASTICITY

Abdelbaki Merouani (Algeria) and Sedik Djabi (Algeria)

Received September 28, 2006

Abstract

In this paper, we study two initial and boundary value problems describing the quasistatic evolution of rate-type viscoplastic materials with and without internal state variables submitted to contact boundary condition. Variational formulations are given and, using a Cauchy-Lipschitz technique, the existence and uniqueness results are obtained. Finally, the numerical approach of the solution is studied and a concrete algorithm based on an Euler method is proposed. The theoretical results presented here are completed by two numerical examples and the advantages of these new proofs respect to the ones cited in the paper are commented.

Keywords and phrases: viscoplastic, existence and uniqueness, monotone operator.