Journal ArticleDOI
General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics
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TLDR
In this article, the plane piezoelasticity theory of onedimensional (1D) quasicrystals with all point groups is investigated systematically, including monoclinic, orthorhombic, tetragonal and hexagonal QCs, and closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained.Abstract:
Based on the fundamental equations of piezoelasticity of quasicrystals (QCs), with the symmetry operations of point groups, the plane piezoelasticity theory of onedimensional (1D) QCs with all point groups is investigated systematically. The governing equations of the piezoelasticity problem for 1D QCs including monoclinic QCs, orthorhombic QCs, tetragonal QCs, and hexagonal QCs are deduced rigorously. The general solutions of the piezoelasticity problem for these QCs are derived by the operator method and the complex variable function method. As an application, an antiplane crack problem is further considered by the semi-inverse method, and the closed-form solutions of the phonon, phason, and electric fields near the crack tip are obtained. The path-independent integral derived from the conservation integral equals the energy release rate.read more
Citations
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Journal ArticleDOI
Antiplane analysis for an elliptical inclusion in 1D hexagonal piezoelectric quasicrystal composites
TL;DR: In this paper, an elliptical inclusion embedded in an infinite 1D hexagonal piezoelectric quasicrystal matrix is analyzed in the framework of linear piezoelasticity of quasricrystals.
Journal ArticleDOI
Fundamental solutions and analysis of three-dimensional cracks in one-dimensional hexagonal piezoelectric quasicrystals
TL;DR: In this paper, the authors derived the fundamental solutions for unit point extended displacement discontinuities (including the phonon and phason displacement discontinuity and the electric potential discontinuity) based on the general solutions and Hankel transform.
Journal ArticleDOI
Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: Theoretical solution
TL;DR: In this paper, the extended displacement discontinuity boundary integral equation and boundary element method are extended to analyze a 3D arbitrarily shaped interface crack in a one-dimensional hexagonal, quasicrystal bi-material with both electric and thermal effects under combined phonon-phason-electric-thermal loadings.
Journal ArticleDOI
Green's functions of one-dimensional quasicrystal bi-material with piezoelectric effect
TL;DR: In this paper, the problems of an infinite plane composed of two different quasicrystal half-planes are taken into account, and the solutions of the internal and interfacial Green's functions of quasICrystal bi-material are obtained.
References
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Journal ArticleDOI
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
TL;DR: In this article, a metallic solid with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations, was observed and its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice.
Journal ArticleDOI
Crack Extension Force in a Piezoelectric Material
TL;DR: In this article, a closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium, along with a path-independent integral integral of fracture mechanics.
Journal ArticleDOI
Quasiperiodic GaAs-AlAs Heterostructures
TL;DR: The first realization of a quasiperiodic (incommensurate) superlattice is reported, which consists of alternating layers of GaAs and AlAs to form a Fibonacci sequence in which the ratio of incommensurate periods is equal to the golden mean.
Book ChapterDOI
Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
TL;DR: The icosahedral point group symmetry was shown to be inconsistent with lattice translations in the case of a metallic solid with point group symmetery rn35 (icosahedral) as discussed by the authors.
Journal ArticleDOI
Generalized elasticity theory of quasicrystals.
TL;DR: The classical theory of elasticity describing three- and lower-dimensional systems is generalized to higher-dimensional spaces and the elastic properties of quasicrystals can be derived from this theory, appropriately.
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