Calculus of Variations and Geometric Measure Theory

F. Riva

On the approximation of quasistatic evolutions for the debonding of a thin film via vanishing inertia and viscosity

created by riva on 24 Jun 2019
modified on 12 May 2020


Published Paper

Inserted: 24 jun 2019
Last Updated: 12 may 2020

Journal: Journal of Nonlinear Science
Volume: 30
Number: 3
Pages: 903-951
Year: 2020
Doi: 10.1007/s00332-019-09595-8

ArXiv: 1906.09800 PDF
Links: Online version


In this paper we contribute to studying the issue of quasistatic limit in the context of Griffith's theory by investigating a one-dimensional debonding model. It describes the evolution of a thin film partially glued to a rigid substrate and subjected to a vertical loading. Taking viscosity into account and under suitable assumptions on the toughness of the glue, we prove that, in contrast to what happens in the undamped case, dynamic solutions converge to the quasistatic one when inertia and viscosity go to zero, except for a possible discontinuity at the initial time. We then characterise the size of the jump by means of an asymptotic analysis of the debonding front.

Keywords: Thin films, Griffith's criterion, Dynamic debonding, vanishing inertia and viscosity limit, quasistatic limit, Quasistatic debonding