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

## TL;DR

This paper analyzes the quasistatic limit of a one-dimensional debonding model for a thin film, showing convergence of dynamic solutions to quasistatic ones as inertia and viscosity vanish, with a focus on initial discontinuities.

## Contribution

It provides a rigorous proof of the convergence of dynamic to quasistatic solutions in a debonding model, including characterization of initial jumps.

## Key findings

- Dynamic solutions converge to quasistatic solutions as inertia and viscosity tend to zero.
- Initial discontinuities in the solution can occur and are characterized asymptotically.
- The model incorporates friction and toughness assumptions affecting the debonding process.

## Abstract

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 friction 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.