Advertisement

Cracks in Fracture Mechanics : A Time Indexed Family of Energy Minimizers

  • G. A. Francfort
  • J-J. Marigo
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 66)

Abstract

Brittle fracture mechanics is classically thought of as operating under various restrictive premises, two of which seem both drastic and unrealistic: no crack will appear unless a crack is already present; cracks propagate along predefined trajectories. Our main goal is to do away with the above, while departing as little as possible from the sanctity of Griffith’s criterion. In a nutshell, the following will be achieved:
  1. 1.

    crack initiation, and its subsequent evolution till complete failure of the loaded sample,

     
  2. 2.

    complete freedom in the mechanical and geometric characteristics of the sample,

     
  3. 3.

    boundary cracks,

     
  4. 4.

    unilateral contact if needed.

     

Keywords

Displacement Field Unilateral Contact Bulk Energy Actual Crack Boundary Crack 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ambrosio, L. Existence theory for a new class of variational problems. Arch. Rat. Mech. Anal. 111 (1990), 291–322.MathSciNetCrossRefzbMATHGoogle Scholar
  2. De Giorgi, E., Carriero, M., and Leaci, A. Existence theorem for a minimum problem with free discontinuity set. Arch. Rat. Mech. Anal. 108 (1989), 195–218.CrossRefzbMATHGoogle Scholar
  3. Foxseca, I., AND Francfort, G. A. Relaxation in BV versus quasiconvexification in W 1, P; a model for the interaction between fracture and damage. Calculus of Variations 3 (1995), 407–446.Google Scholar
  4. Francfort, G. A., and Marigo, J.-J. Stable damage evolution in a brittle continuous medium. Eur. J. Mech., A/Solids 12, 2 (1993), 149–189.MathSciNetzbMATHGoogle Scholar
  5. Francfort, G. A., and Marigo, J.-J. Griffith’s theory of brittle fracture revisited. In preparation, 1997.Google Scholar
  6. Griffith, A. The phenomena of rupture and flow in solids. Phil Trans. Roy. Soc. London CCXXI-A (1920), 163–198.Google Scholar
  7. Liebowitz, H., Ed. Fracture: An Advanced Treatise, vol. II: Mathematical Fundamentals. Academic Press, New York, London, 1968.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • G. A. Francfort
    • 1
  • J-J. Marigo
    • 1
  1. 1.LPMTM (UP R-CNRS 9001)Institut Galilée, Université Paris-NordVilletaneuseFrance

Personalised recommendations