Calculus of Variations and Geometric Measure Theory

G. Bonfanti - M. Colturato - R. Rossi

Global existence for a highly nonlinear temperature-dependent system modeling nonlocal adhesive contact

created by michele on 10 Mar 2022


Published Paper

Inserted: 10 mar 2022
Last Updated: 10 mar 2022

Journal: Nonlinear Anal. Real World Appl.
Volume: 66
Pages: 64
Year: 2022
Doi: 10.1016/j.nonrwa.2022.103511


In this paper we analyze a new temperature-dependent model for adhesive contact that encompasses nonlocal adhesive forces and damage effects, as well as nonlocal heat flux contributions on the contact surface. The related PDE system combines heat equations, in the bulk domain and on the contact surface, with mechanical force balances, including micro-forces, that result in the equation for the displacements and in the flow rule for the damage-type internal variable describing the state of the adhesive bonds. Nonlocal effects are accounted for by terms featuring integral operators on the contact surface. The analysis of this system poses several difficulties due to its overall highly nonlinear character, and in particular to the presence of quadratic terms, in the rates of the strain tensor and of the internal variable, that appear in the bulk and surface heat equations. Another major challenge is related to proving strict positivity for the bulk and surface temperatures. We tackle these issues by very careful estimates that enable us to prove the existence of global-in-time solutions and could be useful in other contexts. All calculations are rigorously rendered on an accurately devised time discretization scheme in which the limit passage is carried out via variational techniques.

Keywords: adhesive contact, Global-in-time existence, Weak solvability, Nonlocal effects, Time discretization, Temperature