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Crack solutions and weight functions for plane problems in three-dimensional quasicrystals

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Abstract

The plane problems of an elliptic hole and a crack in three-dimensional quasicrystals subject to far-field loadings are studied. The generalized Stroh formalism is adopted here, and the explicit solutions for the coupled fields are obtained in the closed form. When the elliptic hole reduces to a crack, the analytical expressions for both the entire fields and the asymptotic fields near the crack tip are determined. The crack theory of quasicrystals, including the determination of the field intensity factors, crack opening displacements, crack tip energy release rates and so on, is a prerequisite. Applying Betti’s theorem of reciprocity, the weight functions for a quasicrystal body with a crack are derived. The weight functions provide a means of calculating the intensity factors for the crack when both phonon and phason point forces are imposed at arbitrary locations.

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Authors and Affiliations

  1. College of Science, China Agricultural University, Beijing, 100083, People’s Republic of China

    Yang Gao, Liang-Liang Zhang & Lian-Zhi Yang

  2. Institute of Mechanics, University of Kassel, 34125, Kassel, Germany

    Andreas Ricoeur

  3. College of Engineering, China Agricultural University, Beijing, 100083, People’s Republic of China

    Liang-Liang Zhang & Lian-Zhi Yang

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  1. Yang Gao
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  2. Andreas Ricoeur
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  3. Liang-Liang Zhang
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  4. Lian-Zhi Yang
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Correspondence to Yang Gao.

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Gao, Y., Ricoeur, A., Zhang, LL. et al. Crack solutions and weight functions for plane problems in three-dimensional quasicrystals. Arch Appl Mech 84, 1103–1115 (2014). https://doi.org/10.1007/s00419-014-0868-4

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