Analysis of a temperature-dependent model for adhesive contact with friction

TL;DR

This paper introduces a comprehensive model for adhesive contact involving thermal and frictional effects, proving the existence of global solutions using variational techniques, thus advancing the mathematical understanding of such complex interactions.

Contribution

It develops a new temperature-dependent model for adhesive contact with friction, including a surface damage parameter, and proves the existence of solutions.

Findings

Existence of global solutions to the model

Successful application of variational techniques

Inclusion of thermal and frictional effects in adhesion modeling

Abstract

We propose a model for unilateral contact with adhesion between a viscoelastic body and a rigid support, encompassing thermal and frictional effects. Following the approach by M. Fremond, adhesion is described in terms of a surface damage parameter. The main result of the paper states the existence of global solutions to the associated Cauchy problem. It is proved by passing to the limit in a carefully tailored approximate problem, via variational techniques.