A multiple-scales approach to crack-front waves

Andrew Norris, I. David Abrahams

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)399-417
Number of pages19
JournalJournal of Engineering Mathematics
Volume59
Issue number4
DOIs
StatePublished - Dec 1 2007

Fingerprint

Multiple Scales
Wave Front
Crack
Cracks
Perturbation
Matched Asymptotic Expansions
Length Scale
Energy Release Rate
Elastodynamics
Energy release rate
Moving Boundary
Wave Speed
Dispersion Relation
Dynamic Equation
Small Parameter
Straight
Boundary value problems
Mechanics
Boundary Value Problem
Radiation

All Science Journal Classification (ASJC) codes

  • Engineering(all)
  • Mathematics(all)

Keywords

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

Cite this

Norris, Andrew ; Abrahams, I. David. / A multiple-scales approach to crack-front waves. In: Journal of Engineering Mathematics. 2007 ; Vol. 59, No. 4. pp. 399-417.
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A multiple-scales approach to crack-front waves. / Norris, Andrew; Abrahams, I. David.

In: Journal of Engineering Mathematics, Vol. 59, No. 4, 01.12.2007, p. 399-417.

Research output: Contribution to journalArticle

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