一维六方准晶中椭圆夹杂与位错的相互作用问题  

Interaction Between Elliptic Inclusion and Dislocation in One-Dimensional Hexagonal Quasicrystals

作　　者：范淑琦 李联和[1,2] FAN Shu-qi;LI Lian-he(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center of Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第2期156-163,170,共9页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11962026);内蒙古自治区自然科学基金资助项目(2020MS01018);内蒙古自治区高等学校科学研究资助项目(NJZY18022,NJZZ21003)。

摘　　要：采用复变函数方法研究无限大一维六方准晶中椭圆夹杂与位错的相互作用问题。利用保角映射和柯西积分理论,获得了势函数之间的复解析关系,给出了界面应力的解析表达式。讨论了位错对声子场与相位子场界面应力的影响,结果表明声子场与相位子场界面应力变化趋势基本一致,界面法向应力在位错作用点附近变化明显,界面切向应力在位错作用点附近的界面上出现了应力集中现象。In the paper,the interaction between elliptic inclusions and dislocations in infinite onedimensional hexagonal quasicrystals is studied by using the complex function method. Based on the conformal mapping and Cauchy integral theory,the analytical relation between complex potential functions is derived,and the analytical expression of interface stress is presented. The analysis on the effect of dislocations on phonon field and phason field interface stress reveals that interface stress of phonon field and phason field show basically similar trend of variation,and the interfacial stress in the normal direction changes more clearly near the dislocation action point and the interfacial stress tangential direction appears phenomena of stress concentration on the interface near the point.

关 键 词：一维六方准晶 椭圆夹杂 位错 界面应力 

分 类 号：O434.1[机械工程—光学工程]