Mathematical analysis of thermo-elasto-viscoplastic contact problems with time-fractional derivatives

Abstract

This thesis is devoted to the mathematical modeling of contact problems for thermo-elastic viscoplastic materials, with particular emphasis on the incorporation of Caputo fractional-order derivatives into their constitutive laws. The primary objective of this work is to establish the existence and uniqueness of weak solutions to these models, by means of Gronwall-type lemmas and results from nonlinear analysis. The thesis is structured in two parts: The first part recalls various contact mechanical model and presents the necessary mathematical tools. The second part focuses on the modeling and mathematical analysis of the considered contact problems