Abstract
The main design of this paper is to adopt potential functions for solving plane defect problems originating from two-dimensional decagonal quasicrystals. First, we analyze the strict potential function theory for the plane problems of two-dimensional quasicrystals. To clarify effectiveness of the method, we give some examples and the results which can be precisely determined, including the elasticity and fracture theories of two-dimensional quasicrystals. These results maybe play a positive role in studying the fracture of two-dimensional quasicrystals in the future.
Highlights
A quasicrystal is seen as a new structure and was first observed by Shechtman et al [1] and announced in 1984
The physical basis of the elasticity of quasicrystals is considered to be the phenomenological theory of Landau and Lifshitz on the elementary excitation of condensed matters, in which two types of excitations, phonons and phasons, were considered for quasi-periodicity of materials [2]
The elastic properties of phonons and phasons of quasicrystals immediately led to widespread research, and theoretical and experimental solutions of a variety of defects and new physical thought play pivotal roles in the fracture mechanics of quasicrystalline materials [3,4,5,6,7,8,9,10,11,12,13]
Summary
A quasicrystal is seen as a new structure and was first observed by Shechtman et al [1] and announced in 1984. The elastic properties of phonons and phasons of quasicrystals immediately led to widespread research, and theoretical and experimental solutions of a variety of defects and new physical thought play pivotal roles in the fracture mechanics of quasicrystalline materials [3,4,5,6,7,8,9,10,11,12,13]. In order to use fracture mechanics to solve practical problems, mastering the method of obtaining the solution of various defects in quasicrystalline materials is necessary. In the light of plane static problems of quasicrystals, the method of complex potential may be stringent and effective to obtain the analytic solutions. The method of potential function theory is introduced for studying the plane problem of the quadruple harmonic equation.
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