Debond dynamics of an elastic strip, II: Simple transient motion

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

“…Analytical models of dynamic debonding involving a single spatial dimension have been developed in the last fifty years as a simplified but still meaningful version of dynamic crack growth based on Griffith's criterion. Starting from the works of Hellan [6,7] and Burridge & Keller [2] (see also the books of Freund [5] and Hellan [8]) it is highlighted how in this field they are one of the few models for which a mathematical formulation provides an exhaustive description of the involved physical processes. Nevertheless they still possess all the relevant features and difficulties of general Fracture Dynamics, such as the time dependence of the domain of the wave equation and the presence of an energy criterion governing the evolution of the system.…”

On the Approximation of Quasistatic Evolutions for the Debonding of a Thin Film via Vanishing Inertia and Viscosity

“…We refer to [5], [11], [12], [13], [14] for an introduction to one-dimensional debonding models from an engineering point of view; a first analysis on the quasistatic limit in these kind of models is instead developed in [10], [15]. The rigorous mathematical formulation we will follow throughout the paper has been introduced in [7], used in [16], [17], [18] for the undamped case, and adopted in [23] and [24] for well-posedness results in the damped case.…”

A Continuous Dependence Result for a Dynamic Debonding Model in Dimension One

“…The interest of the physical and engineering community on dynamic debonding models involving one spatial dimension originates in the '70s from the works of Hellan [9,10,11], Burridge & Keller [2] and carries on in the '90s with the ones of Freund collected in [8]. The importance of this kind of models relies on the fact that they possess deep similarities to the theory of dynamic crack growth based on Griffith's criterion, but at the same time they are much easier to treat, allowing an exhaustive comprehension of the involved physical processes.…”