Diffraction and reflection of antiplane shear waves in a cracked couple stress elastic material

Andrea Nobili*, Enrico Radi, Gennady Mishuris

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Proceeding (Non-Journal item)

Abstract

We investigate the effect of a semi-infinite rectilinear crack on diffraction and reflection of antiplane shear waves in an elastic solid with microstructure. Waves are induced by moving shear traction vectors applied at the faces of the crack. The material behavior is described by the indeterminate theory of couple stress elasticity considering micro inertia. This elastic constitutive model accounts for the material microstructure and it is a special case of the micropolar theory; it was developed by Koiter [10] for the quasi-static regime and later extended by Eringen [3] to include dynamic effects. The full-field solution is obtained through integral transforms and the Wiener-Hopf technique [18] and it may be used as a building block to solve general wave propagation problems in a cracked half-space in antiplane deformation. The solution differs significantly from the classical result given in [4] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [17]. A complicated wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves, localized waves irradiating from and body waves scattered by the crack-tip. Wave diffraction and interference brings an important contribution to the stress intensity factors originally presented in [20] in the static framework. Resonance is triggered when the applied loading is fed into the crack-tip at Rayleigh speed and this result is confirmed by the evaluation of the energy release rate.

Original languageEnglish
Title of host publicationProceedings of 24th AIMETA Conference 2019
EditorsAntonio Carcaterra, Giorgio Graziani, Achille Paolone
PublisherSpringer Nature
Pages137-150
Number of pages14
ISBN (Print)9783030410568
DOIs
Publication statusPublished - 31 Mar 2020
Event24th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2019 - Rome, Italy
Duration: 15 Sept 201919 Sept 2019

Publication series

NameLecture Notes in Mechanical Engineering
ISSN (Print)2195-4356
ISSN (Electronic)2195-4364

Conference

Conference24th Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2019
Country/TerritoryItaly
CityRome
Period15 Sept 201919 Sept 2019

Keywords

  • Couple stress
  • Rayleigh waves
  • Wave diffraction

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