Abstract In this study, the dynamic effective mass and effects of local resonators on the crack growth are investigated. Based on Wiener-Hopf method and factorization using Cauchy-type integral, the energy release ratio which denotes crack splitting resistance is derived and the corresponding radiated waves are discussed. The results show that at variance with traditional periodic mass-spring lattice chain, the radiated energy of the present elastic wave metamaterial with local resonators is more sensitive to low crack speeds. The energy barrier before the stable propagates is larger, which means that the ability to resist the crack speed is enhanced. The lower energy release ratio in the subsonic and supersonic regions indicates that the elastic wave metamaterials with local resonators has better crack resistance and shows the meta-arrest property. The present results might have potential application to improve the crack resistance of advanced materials and structures.

中文翻译：

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具有局部谐振器的弹性波超材料中快速传播裂纹的超阻滞

摘要 在这项研究中，研究了局部谐振器的动态有效质量和对裂纹扩展的影响。基于Wiener-Hopf方法和Cauchy型积分分解，推导出代表裂纹分裂阻力的能量释放比，并讨论了相应的辐射波。结果表明，与传统的周期性质量弹簧晶格链不同，具有局部谐振器的本弹性波超材料的辐射能量对低裂纹速度更敏感。稳定传播前的能垒较大，意味着抵抗裂纹速度的能力增强。亚音速和超音速区域较低的能量释放率表明具有局部谐振器的弹性波超材料具有更好的抗裂性并表现出超阻滞特性。目前的结果可能具有提高先进材料和结构的抗裂性的潜在应用。