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Stress analysis of a mode‐I crack in a 1D hexagonal quasicrystal based on the non‐local theory
Author(s) -
Liu HaiTao
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900191
Subject(s) - phason , quasicrystal , stress field , singularity , field (mathematics) , mathematics , stress (linguistics) , crack tip opening displacement , fourier transform , mathematical analysis , materials science , geometry , fracture mechanics , stress intensity factor , physics , composite material , pure mathematics , linguistics , philosophy , finite element method , thermodynamics
This paper studies the non‐local theory solution of a Mode‐I crack in a 1D hexagonal quasicrystal (QC) by using the generalized Almansi's theorem and the Schmidt method. Based on the Fourier transform, the boundary value problem is reduced to two pairs of dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. The dual integral equations are derived. Finally, the expression of the phonon stress field and the phason stress field at the crack tip are obtained. Numerical examples are provided to show the effects of the lattice parameter and the crack length on the phonon stress field and the phason stress field near the crack tip. Different from the classical solution, that the present solution exhibits no stress singularity at the crack tips in a 1D hexagonal QC.