Radial solutions for a dynamic debonding model in dimension two

TL;DR

This paper develops a mathematical model for dynamic debonding in a two-dimensional thin film, introducing a new energy release rate concept and proving existence of radial solutions using one-dimensional techniques.

Contribution

It introduces a general energy release rate definition for a 2D debonding model and proves existence of radial solutions employing representation formulas.

Findings

Well-posed energy release rate in radial case

Existence of radial solutions established

Representation formulas adapted from 1D models

Abstract

In this paper we deal with a debonding model for a thin film in dimension two, where the wave equation on a time-dependent domain is coupled with a flow rule (Griffith's principle) for the evolution of the domain. We propose a general definition of energy release rate, which is central in the formulation of Griffith's criterion. Next, by means of an existence result, we show that such definition is well posed in the special case of radial solutions, which allows us to employ representation formulas typical of one-dimensional models.