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Fracture with
healing: A first step towards a new view of cavitation
Gilles Francfort, Alessandro Giacomini and Oscar Lopez-Pamies |
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Vol. 12 (2019), No. 2, 417–447
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DOI: 10.2140/apde.2019.12.417
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 74R10, 35Q74, 49J45, 28A75, 47J35
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Milestones
Received: 2 October 2017
Revised: 20 April 2018
Accepted: 29 June 2018
Published: 14 August 2018
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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 |
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| Oscar Lopez-Pamies | |
| Department of Civil and
Environmental Engineering University of Illinois Urbana-Champaign Urbana, IL United States |
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