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As emerging artificial structures, elastic wave metamaterials can show some unique properties in special frequency regions. In this study, the elastic wave scattering by a pair of parallel semi-infinite cracks in mechanical metamaterials with local resonators is studied. According to the discrete Wiener-Hopf method, the far field displacement solution is obtained. At the same time, the dynamic negative effective mass and band gaps can be observed with local resonators. Our attention is focused on how the internal microstructure affects the crack faces. Numerical results show that because of the stop band, the crack can be prevented from being disturbed by incident waves in specific frequency regions. As a result, the possibility of crack initiation and instability propagation is reduced considerably. This present work is expected to provide a way to improve arrest performance of elastic waves metamaterials.

Previous investigations on wave scattering and crack propagation in the discrete periodic structure are concentrated on the conditional mass–spring model, in which the internal mass is not included. In this work, elastic wave metamaterials with local resonators are studied to show the scattering of elastic waves by a semi-infinite crack and the arrest behaviour. The influences of internal mass–spring structure are analysed and the discrete Wiener–Hopf method is used to obtain the displacement solution. Numerical calculations are performed to show that the dynamic negative effective mass and band gaps can be observed owing to the local resonance of the internal mass. Therefore, the scattering of an elastic wave with a specific frequency by a semi-infinite crack can be avoided by tuning the structural parameters. Moreover, the energy release ratio which characterizes the splitting resistance is presented and the meta-arrest performance is found. It is expected that this study will increase understanding of how to control the scattering characteristics of elastic waves by a semi-infinite crack in locally resonant metamaterials and also help to improve their fracture resistance.

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