© Hindawi Publishing Corp. EXISTENCE FOR VISCOPLASTIC CONTACT WITH COULOMB FRICTION PROBLEMS

We present existence results in the study of nonlinear problem of frictional contact be-tween 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 con-sider the Signorini unilateral contact conditions. Proofs are based on a time-discretization method, Banach and Schauder fixed point theorems. 2000 Mathematics Subject Classification: 74A55, 74B20, 35Q99, 49J40. 1. Introduction, notation, and main results. This paper deals with the analysis of nonlinear frictional contact problems between an elastic-viscoplastic body and a rigid obstacle. We present both cases of a bilateral contact between the two bodies and a unilateral contact (involving Signorini model) and we consider nonlinear friction law. Before stating the scientific context and our results, we first introduce some notatio