Thermal effects in adhesive contact: modelling and analysis

TL;DR

This paper models the thermal effects in adhesive contact between a viscoelastic body and a rigid support, proving the existence of global solutions to the complex PDE system that includes entropy and temperature evolution.

Contribution

It introduces a comprehensive PDE model incorporating thermal effects and adhesion, and proves the existence of global solutions for this complex system.

Findings

Existence of global in time solutions established

Model includes entropy balance equations for temperature evolution

Framework applicable to viscoelastic adhesive contact problems

Abstract

In this paper, we consider a contact problem with adhesion between a viscoelastic body and a rigid support, taking thermal effects into account. The PDE system we deal with is derived within the modelling approach proposed by M. Fremond and, in particular, includes the entropy balance equations, describing the evolution of the temperatures of the body and of the adhesive material. Our main result consists in showing the existence of global in time solutions (to a suitable variational formulation) of the related initial and boundary value problem.