Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals  

作　　者：Dongsheng Yang Guanting Liu 杨东升;刘官厅(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China

出　　处：《Chinese Physics B》2020年第10期328-335,共8页中国物理B（英文版）

基　　金：Project supported by the National Key R&D Program of China (Grant No. 2017YFC1405605);the Innovation Youth Fund of the Ocean Telemetry Technology Innovation Center of the Ministry of Natural Resources, China (Grant No. 21k20190088);the Natural Science Foundation of Inner Mongolia, China (Grant No. 2018MS01005);the Graduate Students' Scientific Research Innovation Program of Inner Mongolia Normal University (Grant No. CXJJS19098).

摘　　要：By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.

关 键 词：one-dimensional quasicrystals PIEZOELECTRICITY surface effect energy release rate 

分 类 号：O346.1[理学—固体力学]