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首页> 外文期刊>Applied mathematics and computation >Collinear periodic cracks and/or rigid line inclusions of antiplane sliding mode in one-dimensional hexagonal quasicrystal
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Collinear periodic cracks and/or rigid line inclusions of antiplane sliding mode in one-dimensional hexagonal quasicrystal

机译：一维六方准晶体中反平面滑动模式的共线周期性裂纹和/或刚性线夹杂

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摘要

For a one-dimensional (1D) hexagonal quasicrystal (QC), there is the periodic (x(1), x(2))-plane of atomic structures with the quasiperiodic direction x(3)-axis along which there exists a phason displacement. The macroscopically collinear periodic cracks and/or rigid line inclusions are placed on the periodic (x(1), x(2))-plane for finding out the influence of phason displacement on the related physical quantities. These two models are reduced to the Riemann-Hilbert problem of periodic analytic functions to obtain the closed-form solutions for the antiplane sliding mode. It is found that the phonon and phason stress intensity factors of cracks as well as the phonon and phason stress field intensity factors of rigid line inclusions are not related to the coupling of phonon and phason fields. These mean that there is not the influence of phason displacement on both the phonon stress intensity factor (usual stress intensity factor) of cracks and the phonon stress field intensity factor of rigid line inclusions. However, the energy release rates of periodic cracks and/or rigid line inclusions are obtained and affected not only by the periodicity of cracks and/or rigid line inclusions but also by the phason displacement.
机译：对于一维（1D）六方准晶体（QC），存在原子结构的周期（x（1），x（2））平面，其准周期方向x（3）轴沿其存在一个相子移位。宏观上共线的周期性裂纹和/或刚性线夹杂物被放置在周期性（x（1），x（2））平面上，以找出相移对相关物理量的影响。将这两个模型简化为周期解析函数的Riemann-Hilbert问题，以获得反平面滑模的闭合形式解。发现裂纹的声子和声子应力强度因子以及刚性线夹杂物的声子和声子应力场强度因子与声子和声子场的耦合无关。这意味着，声子位移对裂纹的声子应力强度因子（通常的应力强度因子）和刚性线夹杂物的声子应力场强度因子均无影响。然而，获得了周期性裂纹和/或刚性线夹杂物的能量释放率，并且不仅受裂纹和/或刚性线夹杂物的周期性影响，而且受相子位移的影响。

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