Vol. 12, No. 2, 2019

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Fracture with healing: A first step towards a new view of cavitation

Gilles Francfort, Alessandro Giacomini and Oscar Lopez-Pamies

Vol. 12 (2019), No. 2, 417–447
DOI: 10.2140/apde.2019.12.417
Abstract

Recent experimental evidence on rubber has revealed that the internal cracks that arise out of the process, often referred to as cavitation, can actually heal.

We demonstrate that crack healing can be incorporated into the variational framework for quasistatic brittle fracture evolution that has been developed in the last twenty years. This will be achieved for two-dimensional linearized elasticity in a topological setting, that is, when the putative cracks are closed sets with a preset maximum number of connected components.

Other important features of cavitation in rubber, such as near incompressibility and the evolution of the fracture toughness as a function of the cumulative history of fracture and healing, have yet to be addressed even in the proposed topological setting.

Keywords
minimizing evolutions, fracture, free discontinuity problems
Mathematical Subject Classification 2010
Primary: 74R10, 35Q74, 49J45, 28A75, 47J35
Milestones
Received: 2 October 2017
Revised: 20 April 2018
Accepted: 29 June 2018
Published: 14 August 2018
Authors
Gilles Francfort
Laboratoire Analyse, Géométrie et Applications
Université Paris-Nord
Villetaneuse
France
Courant Institute of Mathematical Sciences
New York, NY
USA
Alessandro Giacomini
DICATAM, Sezione di Matematica
Università degli Studi di Brescia
Brescia
Italy
Oscar Lopez-Pamies
Department of Civil and Environmental Engineering
University of Illinois Urbana-Champaign
Urbana, IL
United States