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Anti-plane problem of a nano-sharp crack in one-dimensional hexagonal piezoelectric quasicrystals with the electrically semi-permeable condition

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Abstract

Based on the Gurtin–Murdoch surface/interface theory and the complex potential theory, the problem of an electrically semi-permeable nano-sharp crack in one-dimensional (1D) hexagonal piezoelectric quasicrystals is analyzed. By constructing conformal map** of the sharp crack, the analytic solutions of the electroelastic field are determined. Meanwhile, the field intensity factors and the energy release rate (ERR) under the electric boundary conditions of semi-permeable are obtained. Numerical examples are given to analyze the effects of the crack size, dielectric constant, electric loading, and mechanic loadings on the dimensionless field intensity factors and the dimensionless ERR. The results show that the impact of the surface effect becomes weaker along with the growth of the crack length, but increases with the increase in the crack angle. The change of the dielectric coefficient has little influence on the dimensionless stress intensity factors (SIFs), but has a strong influence on the dimensionless electric displacement intensity factor (EDIF). The obtained results are helpful to promote the development of nano-quasicrystal composite mechanics and provide an important theoretical support for the design and application of nano-QC materials.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (12262033, 12062021, 12062022, 12272269 and 11972257), Ningxia Hui Autonomous Region Science and Technology Innovation Leading Talent Training Project (KJT2020001), and the Natural Science Foundation of Ningxia (2022AAC03013; 2022AAC03068).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan, China

    Yuanyuan Ma, Xuefen Zhao & Shenghu Ding

  2. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China

    Yueting Zhou

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  1. Yuanyuan Ma
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Correspondence to Xuefen Zhao or Shenghu Ding.

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Ma, Y., Zhao, X., Zhou, Y. et al. Anti-plane problem of a nano-sharp crack in one-dimensional hexagonal piezoelectric quasicrystals with the electrically semi-permeable condition. Arch Appl Mech 93, 1423–1435 (2023). https://doi.org/10.1007/s00419-022-02336-6

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