准晶材料断裂力学复变函数方法的发展及其应用  

A Brief History of Development and Application of Complex Function Methods in Fracture Mechanics of Quasicrystalline Materials

作　　者：刘昉昉 李联和[1,2] LIU Fang-fang;LI Lian-he(Mathematics Science College,Inner Mongolia Normal University,Hohhot 010022,China;Center of Applied Mathematics,Inner Mongolia Normal University,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]内蒙古师范大学应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2021年第4期336-341,共6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(2020MS01018,2021MS01013);内蒙古自治区高等学校科学研究项目(NJZY18022,NJZZ21003)。

摘　　要：对准晶材料断裂力学复变函数方法的发展进行了简要介绍,并采用复变函数方法研究了含螺型位错的立方准晶压电材料的断裂问题。基于立方准晶压电材料反平面弹性问题的基本方程,获得了控制方程,并给出控制方程一般解的复变函数表示。在此基础上,结合位错边界条件,获得了声子场和相位子场位移与应力的解析表达式,为立方准晶压电材料的应用奠定了理论基础。The development of the complex function method for fracture mechanics of quasicrystalline materials is briefly introduced and the fracture problem of cubic quasicrystalline piezoelectric materials with screw dislocation is studied through the complex function method in the paper.According the basic equation of the antiplane elastic problem of cubic quasicrystal piezoelectric materials,we obtain the governing equation and work out the complex function representation of the general solution of the governing equation.Based on the results,combining with the dislocation boundary conditions,the analytical expressions of the displacements and stresses of phonon field and phase field are obtained,which lay a theoretical foundation for the application of cubic quasicrystal piezoelectric materials.

关 键 词：立方准晶压电 声子场 相位子场 复变函数方法 螺型位错 

分 类 号：O346.1[理学—固体力学]