A multiple-scales approach to crack-front waves

Andrew N. Norris, I. David Abrahams

    Research output: Contribution to journalArticlepeer-review


    Perturbation of a steadily propagating crack with a straight edge is solved using the method of matched asymptotic expansions (MAE). This provides a simplified analysis in which the inner and outer solutions are governed by distinct mechanics. The inner solution contains the explicit perturbation and is governed by a quasi-static equation. The outer solution determines the radiation of energy away from the tip, and requires solving dynamic equations in the unperturbed configuration. The outer and inner expansions are matched via the small parameter ε = L/l defined by the disparate length scales: the crack perturbation length L and the outer length scale l associated with the loading. The method is illustrated for a scalar crack model and then applied to the elastodynamic mode I problem. The crack-front wave-dispersion relation is found by requiring that the energy release rate is unaltered under perturbation and dispersive properties of the crack-front wave speed are described for the first time. The example problems considered demonstrate the potential of MAE for moving-boundary-value problems with multiple scales. © Springer Science+Business Media B.V. 2007.
    Original languageEnglish
    Pages (from-to)399-417
    Number of pages18
    JournalJournal of Engineering Mathematics
    Issue number4
    Publication statusPublished - Dec 2007


    • Crack propagation
    • Crack-front waves
    • Dynamic fracture
    • Matched asymptotic expansions
    • Multiple scales
    • Wiener-Hopf


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