In this paper, the conformal mapping from a regular 2n-polygon hole with two collinear asymmetric cracks into a circle is constructed. Based on the Gurtin–Murdoch surface/ interface model and complex potential theory, two collinear asymmetric nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole embedded in an infinite one-dimensional hexagonal piezoelectric quasicrystals with surface effect are investigated. The size-dependent stress intensity factors of phonon field and phason field, electric displacement intensity factor at the nanocrack tip are derived for electrically semi-permeable boundary condition. Numerical examples are illustrated to show that the size of the hole, mechanical load, electric load, cracks relative size change with stress intensity factor of phonon field and electric displacement intensity factor. Also analyzed the change of the electric displacement intensity factor with different electric permeability at the nanocrack tip and the dimensionless intensity factor with n.

中文翻译：

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反平面剪切下一维六方压电准晶体中电半透规则 2n 多边形纳米孔产生的两个纳米裂纹的表面效应

在本文中，来自正则 2 的共形映射n-构造了两个共线不对称裂缝成圆形的多边形孔。基于 Gurtin-Murdoch 表面/界面模型和复势理论，两个共线不对称纳米裂纹源自一个电半透规则 2n研究了嵌入具有表面效应的无限一维六方压电准晶体中的多边形纳米孔。对于电半透边界条件，导出了声子场和相子场的尺寸相关应力强度因子、纳米裂纹尖端的电位移强度因子。举例说明了孔的尺寸、机械载荷、电载荷、裂纹相对尺寸随声子场应力强度因子和电位移强度因子的变化。还分析了纳米裂纹尖端处不同电导率的电位移强度因子和无量纲强度因子随n.