一维正方准晶中裂纹和刚性线夹杂的封闭形式解（英文）  

Closed-Form Solutions to the Crack and/or Rigid Line Inclusion in 1D Orthorhombic Quasicrystals

作　　者：汪文帅 袁宏婷 WANG Wenshuai;YUAN Hongting(School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学数学统计学院

出　　处：《应用数学》2019年第3期715-728,共14页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11561055);the Scientific Research Foundation of the Higher Education Institutions of Ningxia(NGY2017056);the Natural Science Foundation of Ningxia(2018AAC03057)

摘　　要：通过引入广义复变函数方法,研究含裂纹和刚性体夹杂物的反平面模型的一维正方准晶问题.对于一维正方准晶,考虑周期平面为(x1;x2),含有宏观裂纹或刚性线夹杂,具有准周期x3方向的原子结构存在相位位移,本文重点研究相位位移对相关物理量的影响.利用广义复变函数方法,将这两个模型简化为Riemann-Hilbert问题,得到反平面的声子场与相位场的封闭解.同时求得声子场和相位场的应力强度因子的显式解,这在断裂力学和工程领域具有广泛的应用价值.结果表明,反平面情形下,含裂纹和刚性体夹杂物的声子和相位的应力强度因子,与声子场和相位场的耦合无关.The problem of the one-dimensional(1D) orthorhombic quasicrystals with a crack and/or rigid line inclusion of antiplane mode is investigated through introducing the generalized complex variable method. For 1D orthorhombic quasicrystals, considering of the periodic (x 1, x 2)-plane of atomic structures with the quasiperiodic direction x 3-axis along which there exists a phason displacement, and the macroscopical crack and/or rigid line inclusion, which is placed on the periodic (x 1, x 2)-plane, we focus on finding out the influence of phason displacement on the related physical quantities. By the generalized complex variable method, these two models are reduced to the Riemann–Hilbert problems, and the closed-form solutions of the phonon and phason fields for antiplane mode are obtained. The explicit solutions of stress intensity factors for phonon field and phason field are obtained respectively, which are very useful in the fields of fracture mechanics and engineering. The results show that the phonon and phason stress intensity factors of crack as well as the factors of rigid line inclusion are not related to the coupling of phonon and phason fields. These imply that, for antiplane mode, there is no influence of phason displacement on both the phonon stress intensity factor (usual stress intensity factor) of crack and the phonon stress field intensity factor of rigid line inclusion. The obtained analytical solutions will provide necessary reference for material design and numerical solutions.

关 键 词：正方准晶 裂纹 刚性线夹杂 广义复变函数方法 应力强度因子 

分 类 号：O346.1[理学—固体力学]