十次对称二维准晶含Ⅱ型Griffith裂纹的动力学问题  

Dynamic Problems in a Decagonal Quasicrystal with a Mode Ⅱ Griffith Crack

作　　者：周建敏 李联和[1] 王桂霞[1] ZHOU Jian-min;LI Lian-he;WANG Gui-xia(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022)

机构地区：[1]内蒙古师范大学数学科学学院,呼和浩特010022

出　　处：《工程数学学报》2021年第1期136-150,共15页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11962026);国家重点研究发展计划(2017YFC1405600);内蒙古自治区自然科学基金(2019LH01001).

摘　　要：基于波动―电报方程组的初边值问题,用有限差分方法研究了含Ⅱ型Griffith裂纹的点群10mm十次对称二维准晶的动力学问题.首先分析了载荷的加载时间、加载位置以及试样尺寸对裂纹尖端处动态应力强度因子的影响;其次分析了声子―相位子场耦合弹性常数、摩擦系数和有效质量密度对相位子场的位移分量的影响,从而得到相位子场波传播的变化特性.结果表明,不同相关参数对应曲线的变化特性与实际物理意义相符,且相位子场中存在着波动,但主要是扩散.Based on the initial boundary value problem of wave-telegraph equations, dynamic problems of the decagonal symmetric two-dimensional quasicrystal material of point group 10 mm with a mode Ⅱ Griffith crack are investigated by using the finite difference method. First, the effects of the loading time, loading location, and specimen size on the crack-tip dynamic stress intensity factor are discussed. Second, the effects of the phonon-phason coupling elastic constant, friction coefficient, and effective mass density on the displacement component of the phason field are discussed,and thus for the movement characteristic of the propagation of the phason wave.The results show that the variation characteristics of the curves corresponding to different related parameters are consistent with the actual physical characteristics.At the same time, while there is a fluctuation characteristic in the phason field, the diffusion characteristic still plays a dominating role.

关 键 词：点群10mm十次准晶 有限差分法 Ⅱ型Griffith裂纹 应力强度因子 位移分量 

分 类 号：O346.1[理学—固体力学] O343[理学—力学]