纳米阵列结构失稳机理的研究

Nano-forest are the fundamental building blocks of nano devices and widely used as laser technique and data storage in nano-electromechanical system (NEMS). Nano-forest are composed of nano-beams in a certain way. For manufacture and using of nano-forest, the analysis of instability mechanism is an important part. For typical nano- forest in nano-electro-mechanical systems, there are only dozens of nanometers in thickness and the initial separation of the beams in the forest. When the initial separation decreases to sub-micrometers, the intermolecular effects such as Casimir force and van der Waals force play a dominate role in the instability mechanism of nano- forest. The van der Waals force is known to be dominant when the initial separation is less than 20 nm, while the Casimir force is known to be more profound when the initial separation is more than 20 nm. And due to the inherently large surface area to volume ratio, surface effects are expected to contribute significantly to the mechanical response of nano-beams, which are the main components of the nano-forest. Both the surface effects and intermolecular forces play an important role in the mechanical performance of nano-forest. In this project, theoretical analysis, finite element analysis and molecular simulation are performed to investigate the instability and vibration of nano-forest with both surface effects and intermolecular forces. Based on the surface elasticity, we analyze elastic response of nano-forest under loading. It is expected to found the dependence of the deformation as well as the vibration frequency, amplitude on the nano-forest extrinsic geometry, boundary conditions and loading mode. These works are helpful to measure and evaluate the mechanical properties of nano-forest and importance to manufacture and using of reliable and durable nano-forest.

纳米梁阵列由纳米梁按一定方式排列与组装构成，它是下一代纳米结构器件设计的材料基础，在亚微米器件中有着潜在的应用前景。无论对于它的制造还是使用，稳定性都是一个重要环节。然而，其失稳机制尚未明确，振动响应方面的研究有待进一步深入。纳米阵列内部的纳米梁尺度达到纳米级，呈现出极大的表面积，形成表面效应。同时，伴随结构内部单根纳米梁之间距离减小，仅为几十纳米。分子间作用力凸显，与表面效应一起成为影响纳米阵列力学行为的重要影响因素。本项目拟采用理论分析、有限元与分子模拟相结合的方法研究纳米阵列的静态与动态失稳机制，计及表面效应与分子间作用力，建立纳米阵列弹性变形及振动频率、振幅等与结构尺寸、边界条件和外加载荷的定量关系，探明结构的静态与动态失稳机制。本项目的开展将能用于纳米阵列的力学性能测试和评估，对纳米阵列的设计和使用提供理论安全数据和指导。

纳米阵列由纳米梁按一定方式排列与组装构成，它是下一代纳米结构器件设计的材料基础。在传感器、储存器、驱动器等器件中常常少不了纳米阵列的存在。无论对于它的制造还是使用，其力学行为分析都是一个重要环节。然而，其失稳机制尚未明确，有待进一步深入。纳米阵列内部的纳米梁尺寸达到纳米级，呈现出极大的表面积，形成表面效应。同时，伴随结构内部单根纳米梁之间距离减小，仅为几十纳米。分子间作用力凸显，与表面效应一起成为影响纳米阵列力学行为的重要影响因素。. 本项目通过表面应力模型与等效刚度引入表面效应，研究了包含表面效应及Casimir力的纳米阵列弯曲行为和纳米阵列的稳定性。基于Euler-Bernoulli梁模型，运用最小势能原理推导了控制纳米阵列弯曲变形的一组基本方程并进行数值求解，结果表明仅表面效应和Casimir力不会使纳米阵列相互粘附。主要计算分析了纳米梁根数N=7，N=20和N=50的纳米阵列。可以看出与阵列始末两端的纳米梁变形相比，纳米阵列中间部分纳米梁的变形可忽略不计。因此，对于包含纳米梁的纳米阵列，仅需要关注阵列始末两端的纳米梁变形即可。本项目还分析了表面效应对纳米压痕力学行为的影响。具体讨论了一个大尺寸的球形压头压入分布均匀的纳米阵列中的压痕实验。在整个压痕实验中，纳米阵列经历了复杂的变形过程，包括压痕初期的轴向压缩变形、屈曲变形及超过屈曲变形后的过屈曲变形。具体分析了由一端简支一端固支的纳米梁组成的纳米阵列与一端自由一端固支的纳米阵列。分析结果表明，由于纳米阵列材料固有的大比表面积，使得表面效应的作用在纳米阵列的压痕实验中有着显著的表现，与忽略表面效应的经典理论计算结果相比，表面效应使得一端简支一端固支的纳米阵列变形更小，更加坚硬。而对于一端自由一端固支的纳米阵列，表面效应使得其变形更大，阵列刚度减小，变得更软。这部分研究结论对纳米压痕实验的设计和结果的校正有重要的指导意义。