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Two non‐elliptical decagonal quasicrystalline inclusions with internal uniform hydrostatic phonon stresses
Author(s) -
Wang Xu,
Schiavone Peter
Publication year - 2018
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.201800106
Subject(s) - phason , quasicrystal , phonon , hydrostatic equilibrium , matrix (chemical analysis) , condensed matter physics , internal stress , stress field , stress (linguistics) , hydrostatic stress , materials science , field (mathematics) , geometry , mechanics , physics , composite material , mathematics , quantum mechanics , thermodynamics , finite element method , linguistics , philosophy , pure mathematics
We use complex variable techniques to prove that the phonon stresses inside two non‐elliptical decagonal quasicrystalline inclusions can be uniform and hydrostatic provided four specific conditions are met. The first condition is a restriction on the phonon elastic constants of the two inclusions, whilst the remaining three conditions can be considered as constraints on the remote phonon and phason stresses for given material and geometric parameters. Once these conditions are satisfied, the hoop phonon stress in the matrix is found to be uniformly distributed along the two inclusion‐matrix interfaces. Moreover, the two inclusions are found to satisfy the harmonic field condition.