SH波诱发的阵列纳米孔洞周围的弹性波散射和动应力集中

Dynamic stress concentration around nanosized cylindrical holes induced by SH-waves

研究了SH波诱发的阵列纳米孔洞周围的弹性波散射和动应力集中问题。当孔洞的尺寸缩小到纳米尺度时,其比表面积显著增加,表面效应对材料力学特性的影响变得非常重要。基于表面弹性理论和经典弹性理论,采用位移势函数法、波函数展开法、弹性波的多重散射理论,分别求得了无限大空间中一组以正六边形方式排列和一组以正方形方式排列的纳米圆柱孔洞附近由SH波诱发的应力场,分析了表面效应对孔洞周围动应力集中的影响。结果表明纳米圆柱孔洞周围的动应力集中不仅与表面效应有关,而且与孔洞之间的距离有关:表面效应减弱了孔周的动应力集中现象;当孔洞之间的距离增大到一定程度时,孔洞间距对动应力集中的影响可以忽略。这些结果可以作为纳米构件和纳米材料动力学问题研究的基础。

The multiple scattering of SH-waves by a cluster of nanosized cylindrical holes arranged as hexagonal and quadrangular shapes is considered. When the radius of the holes shrinks to nanometers, surface effect plays an important role in their mechanical performance and the surface elasticity theory is adopted to analyze diffraction phenomena. By using the displacement potential method and wave functions expansion method, the multiple scattering fields around the holes are derived. The dynamic stress concentration around the holes is calculated to illustrate the effect of surface effects on the multiple scattering of SH-waves. Results obtained show that the dynamic stress concentration depends not only on the surface effects, but also on the separation between holes. The surface effects decline the dynamic stress concentration almost in all the range and with the increasing of separation between holes, the interaction can be ignored, which can be considered as theoretical foundation to discuss dynamic problem of nano materials and nano components.