一维六方准晶纳米涂层圆柱形夹杂的反平面问题  

Anti-plane Problem of a Nano-coated Inclusion in OneDimensional Hexagonal Quasicrystals

作　　者：赵雪芬[1,2] 卢绍楠 孔德凤 ZHAO Xue-fen;LU Shao-nan;KONG De-feng(Xinhua College,Ningxia University,Yinchuan 750021,China;School of Information Engineering,NingxiaUniversity,Yinchuan 750021,China;School of Mathematical Statistics,Ningxia University,Yinchuan 750021,China)

机构地区：[1]宁夏大学新华学院,银川750021 [2]宁夏大学信息工程学院,银川750021 [3]宁夏大学数学统计学院,银川750021

出　　处：《科学技术与工程》2025年第11期4419-4427,共9页Science Technology and Engineering

基　　金：宁夏大学新华学院院级科学研究基金重点项目(23XHKY01)。

摘　　要：为设计和制备高质量的一维六方准晶纳米复合材料,利用复变函数方法和Gurtin-Murdoch表/界面理论,分别应用界面和界面相模型分别研究了含纳米涂层圆柱形夹杂的一维六方准晶反平面断裂问题。在两种模型下分别获求得基体、涂层和夹杂中声子场和相位子场应力场的级数形式表达式。数值算例分析了界面弹性常数和尺寸效应对夹杂周围应力场的影响。结果表明:界面弹性常数的正负会影响纳米夹杂周围的应力场,随着纳米夹杂尺寸的增大,应力场表现出明显的尺寸依赖性,表面效应对无量纲化声子场和相位子场应力影响有显著差异。可见相关结果对研究准晶纳米夹杂力学行为提供一定的理论参考。To design and prepare high-quality one-dimensional hexagonal quasicrystal nano-composites,the interface and interface phase models were applied to study the infinite one-dimensional hexagonal quasicrystal anti-plane fracture problem with cylindrical inclusions containing nano coatings by using the complex function method and Gurtin-Murdoch's surface/interface elasticity theory.Under two different models,the series form expressions of phonon and phason field stress fields in matrix,coating and inclusion were obtained,respectively.Numerical examples were used to analyze the effects of interface elastic constants and size effects on the stress field around inclusions.The results showed that the positive or negative values of interface elastic constants would affect the stress field around nano-inclusions.As the size of nano-inclusions increased,the stress field exhibited significant size dependence,and surface effects had significant differences in their effects on the stress fields of dimensionless phonon and phason fields.The relevant results provide a certain theoretical reference for studying the mechanical behavior of quasicrystalline nano-inclusions.

关 键 词：一维六方准晶 纳米涂层圆柱形夹杂 尺寸效应 界面模型 界面相模型 

分 类 号：O753.3[理学—晶体学]