The Variational Approach to Fracture

In this tract, we offer a panorama of the variational approach to brittle fracture that has developed in the past eight years or so. The key concept dates back to Griffith and consists in viewing crack growth as the result of a competition between bulk and surface energy. We revisit Griffith's insig...

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Bibliographic Details
Published inJournal of elasticity Vol. 91; no. 1-3; pp. 5 - 148
Main Authors Bourdin, Blaise, Francfort, Gilles A., Marigo, Jean-Jacques
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2008
Springer Nature B.V
Springer Verlag
Subjects
Automotive Engineering
Classical Mechanics
Engineering Sciences
Mechanics
Physics
Physics and Astronomy
Solid mechanics
Functions of bounded variations
26A45
Quasi-static
Fracture
Griffith
74R10
Cohesive energies
Variational formulation
Relaxation
47J30
49J40
Evolution
Global minimizers
Local minimizers
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Summary:In this tract, we offer a panorama of the variational approach to brittle fracture that has developed in the past eight years or so. The key concept dates back to Griffith and consists in viewing crack growth as the result of a competition between bulk and surface energy. We revisit Griffith's insight in the light of the contemporary tools of the Calculus of Variations. We also import Barenblatt's contributions and always strive to gauge the respective merits of both types of surface energy. The advocated variational approach provides an incisive picture of initiation and propagation whose features are detailed. The material is mathematical in nature, but not overly preoccupied with technicalities. An effort is being made to connect the approach with more classical treatments of fracture, and to illustrate the results in simple test settings, or through relevant numerical simulations.
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-007-9107-3