Weakly Nonlinear Theory of Dynamic Fracture
arXiv:0807.4868 · doi:10.1103/PhysRevLett.101.264302
Abstract
The common approach to crack dynamics, linear elastic fracture mechanics (LEFM), assumes infinitesimal strains and predicts a 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 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.
4 pages, 2 figures, second of a two-paper series (theory); no change in content, minor textual revisions