Elastic wave scattering by rectangular cracks

Lingwei Guan, Andrew Norris

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Three coupled integral equations are formulated for the direct problem of scattering of obliquely incident longitudinal plane waves from a rectangular crack. Chebyshcv functions are used to expand the unknown crack opening displacements and to convert the integral equations into an infinite linear system of simultaneous equations which are solved by numerical truncation. The static and dynamic stress intensity factors for a square crack under normal incidence show very good agreement with all data reported by other researchers. For a rectangular crack, the ratio between the two local maxima of Mode I stress intensity factors is found to be the square root of the aspect ratio. A Rayleigh wave membrane analogy is used to explain the appearance of peaks in the dynamic responses. All the results for cracks under oblique incidence arc new, as well as the scattered far-fields and their long wavelength or quasi-static limits. The asymptotes of the scattering cross-sections in the high frequency region are found to vary linearly with the cosines of the incident angles, and a corner effect is observed in the scattering patterns for moderately high frequencies.

Original languageEnglish (US)
Pages (from-to)1549-1565
Number of pages17
JournalInternational Journal of Solids and Structures
Issue number12
StatePublished - 1992

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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