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The variational approach to fracture

This volume offers 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. Griffitha (TM)s insight in the light of the contemporary tools of the Calculus of Variations is revisited. Also, Barenblatta (TM)s contributions are imported and there is a continuous striving 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 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. Reprinted from Journal of Elasticity Vol. 90(1).

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  • "This volume offers 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. Griffitha (TM)s insight in the light of the contemporary tools of the Calculus of Variations is revisited. Also, Barenblatta (TM)s contributions are imported and there is a continuous striving 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 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. Reprinted from Journal of Elasticity Vol. 90(1)."@en
  • "One of the goals of the Journal of Elasticity: The Physical and Ma- ematical Science of Solids is to identify and to bring to the attention of the research community in the physical and mathematical sciences extensive expositions which contain creative ideas, new approaches and currentdevelopmentsinmodellingthebehaviourofmaterials. Fracture has enjoyed a long and fruitful evolution in engineering, but only in - cent years has this area been considered seriously by the mathematical science community. In particular, while the age-old Gri?th criterion is inherently energy based, treating fracture strictly from the point of view of variational calculus using ideas of minimization and accounting for the singular nature of the fracture?elds and the various ways that fracture can initiate, is relatively new and fresh. The variational theory of fracture is now in its formative stages of development and is far from complete, but several fundamental and important advances have been made. The energy-based approach described herein establishes a consistent groundwork setting in both theory and computation. While itisphysicallybased, thedevelopmentismathematicalinnatureandit carefully exposes the special considerations that logically arise rega- ing the very de?nition of a crack and the assignment of energy to its existence. The fundamental idea of brittle fracture due to Gri?th plays a major role in this development, as does the additional dissipative feature of cohesiveness at crack surfaces, as introduced by Barenblatt. Thefollowinginvited, expositoryarticlebyB. Bourdin, G. Francfort and J.-J. Marigo represents a masterful and extensive glimpse into the fundamentalvariationalstructureoffracture."@en

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  • "Electronic books"@en
  • "Electronic books"
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  • "The Variational Approach to Fracture"
  • "The variational approach to fracture"@en
  • "The variational approach to fracture"

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