Study On The Semi-Infinite Defect Problem Of Decagonal Quasicrystals

Quasicrystals as a new solid structure was found in 1984.It is different from crystal also from the non-crystal,and has totally impermissible rotation symmetry of traditional crystal.This break the concepts of condensed matter physics that solid will be divided into crystals and non-crystals.So it has great theoretical significance,and makes significant progress in condensed matter physics in recent years.crystal quasicrystalline materials has high strength,high hardness and the characteristics of light,especially for the working temperature,is a good prospect of new structural materials and functional materials.Since the end of the twentieth century,many studies about the mechanics properties of quasicrystal have been carried.Among them,the theoretical research on elasticity and defects has made great progress.The point group10 mm with ten-fold symmetry which studied in this thesis is one kind of the two-dimensional quasicrystals.Two-dimensional quasicrystal can be understood as a plane symmetric axis of stacking quasi-periodic structure along the cycle,and is three dimensional elasticity.The elasticity of two-dimensional quascrystals can be turned into a superposition of two problems.One is the plane elasticity problem,the other is an anti-plane elasticity problem.In this thesis,extension of classical elastic models to decagonal quasicrystalline composites is to adopt potential function for solving plane defect problems originating from two dimensional quasicrystalline composites.Based on the stress potential function and Fourier transform,this paper makes analytical solutions to the elastic semi-infinite plane problem of quasicrystals with point group 10 mm.With the aid of Fourier transform,the boundary conditions and the stress associated with phonon and phason filed can be redescribed.To clarify effectiveness of the method,we give some examples and the results which can be exactly determined.These results maybe play a positive role in studying the fracture of two-dimensional quasicrystals in the future.