Analysis & PDE

  • Anal. PDE
  • Volume 12, Number 2 (2019), 417-447.

Fracture with healing: A first step towards a new view of cavitation

Gilles Francfort, Alessandro Giacomini, and Oscar Lopez-Pamies

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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.

Article information

Source
Anal. PDE, Volume 12, Number 2 (2019), 417-447.

Dates
Received: 2 October 2017
Revised: 20 April 2018
Accepted: 29 June 2018
First available in Project Euclid: 9 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1539050445

Digital Object Identifier
doi:10.2140/apde.2019.12.417

Mathematical Reviews number (MathSciNet)
MR3861896

Zentralblatt MATH identifier
06974518

Subjects
Primary: 74R10: Brittle fracture 35Q74: PDEs in connection with mechanics of deformable solids 49J45: Methods involving semicontinuity and convergence; relaxation 28A75: Length, area, volume, other geometric measure theory [See also 26B15, 49Q15] 47J35: Nonlinear evolution equations [See also 34G20, 35K90, 35L90, 35Qxx, 35R20, 37Kxx, 37Lxx, 47H20, 58D25]

Keywords
minimizing evolutions fracture free discontinuity problems

Citation

Francfort, Gilles; Giacomini, Alessandro; Lopez-Pamies, Oscar. Fracture with healing: A first step towards a new view of cavitation. Anal. PDE 12 (2019), no. 2, 417--447. doi:10.2140/apde.2019.12.417. https://projecteuclid.org/euclid.apde/1539050445


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