The variational approach to fracture

Blaise Bourdin (1) , Gilles A. Francfort (2) , Jean-Jacques Marigo (3)

1 Department of Mathematics
2 LPMTM - Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux
3 DALEMBERT - Institut Jean Le Rond d'Alembert

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.

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

Blaise Bourdin, Gilles A. Francfort, Jean-Jacques Marigo. The variational approach to fracture. Journal of Elasticity, 2008, 91 (1-3), pp.5-148. ⟨10.1007/s10659-007-9107-3⟩. ⟨hal-00551079⟩