Weakly Nonlinear Theory of Dynamic Fracture

 

Eran Bouchbinder, Ariel Livne, and Jay Fineberg

 

Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel

(Received 30 July 2008; published 30 December 2008)

 

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.