Étude et analyse d’un problème antiplan électro-viscoélastique de contact avec frottement

Abstract

This thesis deals with methods for the weak solution of an antiplan electro viscoelastic contact problem with friction and with long-term memory. We present two variational formulations, noted PVviscoelastic and PVelectro−viscoelastic respectively, of the considered problem, where PVviscoelastic depends only on the displacement field u and PVelectro−viscoelastic depends on the displacement field u and on the electric potential ϕ. For the PVelectro−viscoelastic problem, we derive a variational formulation of the model which is given by a system coupling an evolutionary variational equality for the displacement fieldu, a time-dependent variational equation for the electric potential field ϕ(.) and a differential equation for the bonding field. We construct the variational formulation associated to this problem. Finally, we study the existence and uniqueness of the weak solution based on the Fixed-Point Theorem of Banach.