2008/07/31 by Eran Bouchbinder, Ariel Livne, Jay Fineberg · 6 citations
Engineering · Physics and Astronomy · #Numerical methods in engineering #Structural Health Monitoring Techniques #Ultrasonics and Acoustic Wave Propagation #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevlett.101.264302
published as Phys. Rev. Lett. 101, 264302 (2008) · 4 pages, 2 figures, second of a two-paper series (theory); no change in content, minor textual revisions
arxiv created 2008/10/07 · openalex publication_date 2008/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.