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arXiv · 0807.4868

Weakly Nonlinear Theory of Dynamic Fracture

Eran Bouchbinder·Ariel Livne·Jay Fineberg
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Abstract

The common approach to crack dynamics, linear elastic fracture mechanics (LEFM), 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 can not be described in the LEFM framework.

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Eran Bouchbinder, Ariel Livne, Jay Fineberg. 2008-10-07. Weakly Nonlinear Theory of Dynamic Fracture. https://doi.org/10.1103/physrevlett.101.264302

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