Calculus of Variations and Geometric Measure Theory
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F. Riva - L. Nardini

Existence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping

created by riva on 16 Jul 2018
modified on 15 Jan 2019

[BibTeX]

Submitted Paper

Inserted: 16 jul 2018
Last Updated: 15 jan 2019

Year: 2018

Abstract:

In this paper we analyse a one-dimensional debonding model for a thin film peeled from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffith's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffith's criterion.

Keywords: Thin films, Griffith's criterion, Dynamic debonding, Wave equation in time-dependent domains, Dynamic energy release rate, Energy-dissipation balance, Maximum dissipation principle, Duhamel's principle


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