Diffraction of antiplane shear waves and stress concentration in a cracked couple stress elastic material with micro inertia

Andrea Nobili, Enrico Radi, Adam Vellender

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Abstract

We investigate diffraction of reduced traction shear waves applied at the faces of a stationary crack in an elastic solid with microstructure, under antiplane deformation. The material behaviour is described by the indeterminate theory of couple stress elasticity and the crack is rectilinear and semi-infinite. The full-field solution of the crack problem is obtained through integral transforms and the Wiener–Hopf technique. A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack, localized waves irradiating from the crack-tip with, possibly, super-Rayleigh speed and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission. Dynamic stress intensity factors are presented, which generalize to Elastodynamics the corresponding results already obtained in the static framework. The correction brings out the important role of wave diffraction on stress concentration.

Original languageEnglish
Pages (from-to)663-680
Number of pages18
JournalJournal of the Mechanics and Physics of Solids
Volume124
Early online date24 Nov 2018
DOIs
Publication statusPublished - 01 Mar 2019

Keywords

  • couple stress
  • wave diffraction
  • Rayliegh waves
  • dynamic stress intensity factor
  • Wave diffraction
  • Rayleigh waves
  • Dynamic stress intensity factor
  • Couple stress

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