Problème viscoélasticoplastique de contact avec compliance normale et frottement non monotone

Abstract

The purpose of this thesis is the study of a viscoelastodynamic contact problem with normal compliance and nonmonotonic friction, for which we prove a result of existence and uniqueness of weak solution. This thesis is composed of two chapters. The second chapter models the behavior of a viscoelastic body in motion subjected to contact interactions with a rigid obstacle. Normal compliance means that contact can occur with a certain deformation in the normal direction, which is more realistic for many materials. Nonmonotonic friction, on the other hand, allows the modeling of complex friction behaviors, such as generalized Coulomb-type friction, stick-slip, or other nonlinear and nonmonotonic effects. The problem is formulated in a dynamic framework, which makes its mathematical analysis more difficult. It generally leads to variational inequalities. The objectives are often to show the existence and the uniqueness of the solution.