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 [3] for the quasi-static regime and later extended by Eringen [1] to include dynamic effects. The full-ﬁeld solution is obtained through integral transforms and the Wiener-Hopf technique [5] and it may be used as a bulding 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 [2] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [4]. 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 [6] 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.

Diffraction and Reflection of Antiplane Shear Waves in a Cracked Couple Stress Elastic Material / Nobili, Andrea; Radi, Enrico; Mishuris, Gennady. - (2020), pp. 137-150. [10.1007/978-3-030-41057-5_11]

### Diffraction and Reflection of Antiplane Shear Waves in a Cracked Couple Stress Elastic Material

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*Nobili, Andrea*^{};Radi, Enrico;Mishuris, Gennady

^{};Radi, Enrico;Mishuris, Gennady

##### 2020

#### 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 [3] for the quasi-static regime and later extended by Eringen [1] to include dynamic effects. The full-ﬁeld solution is obtained through integral transforms and the Wiener-Hopf technique [5] and it may be used as a bulding 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 [2] for isotropic elastic materials. Indeed, unlike classical elasticity, antiplane shear Rayleigh waves are supported in couple stress materials [4]. 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 [6] 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.##### Pubblicazioni consigliate

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