Analyse variationnelle et numérique de quelques problèmes viscoélastiques

Abstract

The purpose of this work is to study some problems in contact mechanics involving piezoelectric, elasto-viscoplastic, and thermo-electro-viscoelastic constitutive laws with long- term memory. The obtained results concern the existence and uniqueness of a weak solution to the studied problems. The thesis is structured in two parts: The first part recalls various contact mechanical models and presents the necessary Mathematical tools. The second part focuses on the modeling and mathematical analysis of the considered contact problems. A numerical approach is also carried out for two problems using a finite element scheme with implicit time discretization