Étude et analyse des problèmes électro-élastiques avec frottement.

Abstract

In second is electro-viscoelastic problem which modeling the antiplane shear deformation of a cylinder in frictional contact with a foundation. The process this thesis, we study two problems, the first is electro-elastic and the are static and quasi-static respectively, and the friction is modeled with Tresca’s law. The problem leads to a new system coupling an evolutionary variational inequality for the displacement field u(.), a time-dependent variational equation for the electric potential field ϕ(.). First, we present in chapters 2 and 3 two variationals formulations, noted P2electro−elastic and P2electro−viscoelastic of the considered problems P1electro−elastic and P1electro−viscoelastic. In the second setp, we construct the product space X = V ×W. Finally, we study the existence and uniqueness of the weak solution based on the theory of evolutionary variational inequalities.