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

Scattering of waves impinging along a rectilinear semi-illimitate crack is investigated in an elastic solid with microstructure under antiplane deformation. The material behavior is described by the indeterminate theory of couple stress elasticity. The propagation of Rayleigh waves is investigated first for, in contrast to classical elasticity, it may occur also in the absence of rotatory inertia. The full-field solution is obtained through the Wiener-Hopf technique and integral transform inversion. This solution provides dynamic stress intensity factors which appear as generalization of the corresponding results obtained in statics. Resonance, wave transmission and energy release rate are also discussed. Finally, it is shown that the maximum stress criterion can be hardly generalized in a time-harmonic framework.