三维二十面体准晶圆弧形界面刚性线的平面弹性问题  

The plane elasticity problem of circular arc interface rigid lines in three-dimensional icosahedral quasicrystals

作　　者：翟婷 马园园 赵雪芬[2] ZHAI Ting;MA Yuanyuan;ZHAO Xuefen(School of Mathematical Statistics,Ningxia University,750021 Yinchuan,China;Xinhua College,Ningxia University,750021 Yinchuan,China)

机构地区：[1]宁夏大学数学统计学院,银川750021 [2]宁夏大学新华学院,银川750021

出　　处：《应用力学学报》2025年第1期81-90,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.12062021);宁夏高等学校科学研究资助项目(No.NGY2020101);宁夏大学新华学院科学研究资助项目(No.20XHKY03)。

摘　　要：作为颗粒材料去强化基体材料是准晶的重要应用之一,因此研究基体和夹杂(微小颗粒材料可看成是夹杂)界面刚性线问题具有重要的理论和现实意义。基于复变函数方法,研究了平面集中力和无限远处均匀拉伸应力作用下,含界面刚性线的圆形准晶夹杂的三维二十面体准晶平面弹性问题,得到应力分量和位移分量的封闭解,给出了刚性线夹杂尖端奇异应力场的解析表达式。数值计算讨论了耦合系数、夹杂半径和相位子场弹性常数对应力奇异因子的影响。结果表明:在平面载荷作用下,圆弧形刚性线尖端的应力场具有奇异性;夹杂半径对应力奇异因子的影响大于耦合系数以及相位子场参数对应力奇异因子的影响。It is one of the important applications of quasicrystals to strengthen matrix materials as granular materials.Therefore,it is of great theoretical and practical significance to study the interface rigid line between matrix and inclusions(micro granular materials can be regarded as inclusions).Based on the method of complex function,the plane elasticity problem of three-dimensional icosahedral quasicrystals with circular rigid line inclusions under the action of plane concentrated force and infinite uniform tensile stress is studied.The closed solutions of stress and displacement components in several typical cases are obtained,and the analytical expressions of singular stress field at the tip of rigid line inclusion are given.The effects of the radius of inclusion and coupling coefficient on the stress singularity factor are discussed numerically.The results show that the stress field at the tip of the circular rigid line inclusion has singularity under the plane load,and the influence of the radius of the inclusion on the stress singularity factor is greater than that of the coupling coefficient and phase field elastic constant.

关 键 词：准晶 圆形夹杂 刚性线 复变函数方法 应力奇异因子 

分 类 号：O753.3[理学—晶体学]