自相似多级纳米蜂窝结构表面效应的有限元模拟

Finite element simulation of surface effects on self-similar hierarchical honeycombs

在传统有限元模型的基础上建立了考虑表面效应的有限元用户子程序,通过数值模拟结果与经典问题理论解的对比验证了本文模型的正确性。在此基础上,建立了自相似多级蜂窝的有限元模型,并以铝蜂窝为例研究了其由于表面效应引起的不同方向弹性模量的尺寸依赖性。研究结果表明:表面效应对自相似多级蜂窝在扶手椅型方向和锯齿型方向的作用效果基本一致;随着蜂窝结构级数的增加,(111)晶面引起的表面效应对结构的增强效果不明显,但(100)晶面表面效应对结构的软化效果显著增强。本文提出的研究方法为纳米多级蜂窝结构力学性能的研究提供了一种新的研究手段。

A user element subroutine is incorporated into the traditional finite element(FE) method for investigating the mechanical behavior of self-similar hierarchical honeycombs(SSHHs), in which the surface elastic effects are considered. The user subroutine is firstly validated by the classical plate-hole model, showing a good agreement with the theoretical results. Then based on the proposed FE SSHH model, the size-dependent mechanical properties of SSHHs along different directions are especially studied. The numerical results indicate that the influences of surface effects are approximately identical along armchair and zigzag directions. With the increase in the order of the SSHHs, the strength enhancing efficiency is not noteworthy due to the(111) surface effect, while the softening effect is significantly growing. The proposed approach provides a new method to study the mechanical properties of hierarchical honeycombs.