Contributions to the study of various boundary value problems arising in contact mechanics.

This thesis focuses on the variational investigation of contact issues between a deformable body and a foundation , with or without friction. We examine dynamic processes for viscoplastic and thermo-viscoelastic materials assuming minor deformations. The obtained results pertain to the existence and uniqueness of a weak solution for the studied problems. The thesis is structured into three parts. The first part provides a review of the necessary mathematical tools and various mechanical contact models studied. The second part focuses on the study of thermo-viscoelastic contact problems with friction, damage and wear. The third part is dedicated to the analysis of frictionless viscoplastic problems with adhesion