Weakly nonlinear theory of dynamic fracture

Eran Bouchbinder*, Ariel Livne, Jay Fineberg

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


The common approach to crack dynamics, linear elastic fracture mechanics, assumes infinitesimal strains and predicts a r-1/2 strain divergence at a crack tip. We extend this framework by deriving a weakly nonlinear fracture mechanics theory incorporating the leading nonlinear elastic corrections that must occur at high strains. This yields strain contributions "more divergent" than r-1/2 at a finite distance from the tip and logarithmic corrections to the parabolic crack tip opening displacement. In addition, a dynamic length scale, associated with the nonlinear elastic zone, emerges naturally. The theory provides excellent agreement with recent near-tip measurements that cannot be described in the linear elastic fracture mechanics framework.

Original languageAmerican English
Article number264302
JournalPhysical Review Letters
Issue number26
StatePublished - 22 Dec 2008


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