Radial solutions for a dynamic debonding model in dimension two. (June 2022)

• Record Type: Journal Article
• Authors: Lazzaroni, Giuliano; Molinarolo, Riccardo; Solombrino, Francesco
• Is Part Of: Nonlinear analysis. Volume 219(2022)
• Publication Date: 2022-06
• Subjects: 35L85 -- 35Q74 -- 35R35 -- 74H20 -- 74K35; Thin films -- Dynamic debonding -- Wave equation in time-dependent domains -- Dynamic energy release rate -- Energy-dissipation balance -- Maximum dissipation principle -- Griffith's criterion -- Dynamic fracture; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112822
• Languages: English
• ISSNs: 0362-546X

Abstract

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.