The Variational Approach to Fracture

  • Blaise Bourdin
  • Gilles A. Francfort
  • Jean-Jacques Marigo

Table of contents

  1. Front Matter
    Pages i-x
  2. Pages 1-8
  3. Pages 9-30
  4. Pages 47-69
  5. Pages 70-89
  6. Pages 90-102
  7. Pages 103-106
  8. Pages 107-134
  9. Pages 135-150
  10. Back Matter
    Pages 151-164

About this book

Introduction

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.

Keywords

algorithm brittle fracture crack growth fracture model numerical simulations numerics simulation

Authors and affiliations

  • Blaise Bourdin
    • 1
  • Gilles A. Francfort
    • 2
  • Jean-Jacques Marigo
    • 3
  1. 1.Louisiana State UniversityUSA
  2. 2.Université Paris-NordFrance
  3. 3.Université Pierre et Marie CurieFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4020-6395-4
  • Copyright Information Springer Netherlands 2008
  • Publisher Name Springer, Dordrecht
  • eBook Packages Engineering
  • Print ISBN 978-1-4020-6394-7
  • Online ISBN 978-1-4020-6395-4
  • About this book