Stability analysis of carbon nanotubes with continuum mechanics

自20世纪90年代以来，碳纳米管(CNT)被发现具有巨大的潜力，可以用于无数的技术创新和应用，如极轻和坚固的织物、化学传感器、电子传感器、燃料电池和药物输送。商业传播公司预计，2006年碳纳米管的全球销售额将达到2.315亿美元。不幸的是，碳纳米管的迅速和广泛应用由于对其力学行为的了解不足而受到阻碍。在众多挑战中，碳纳米管的稳定性分析需要突破，如扭结失稳(压缩引起的曲率突变)和后屈曲(压缩引起的大变形)。例如，对碳纳米管扭结不稳定性的认识不足一直是基于碳纳米管的原子力显微镜(AFM)设计的一个重大挫折。经典分子动力学只适用于含有少量分子和原子的体系的稳定性分析。他说，这项研究旨在通过将碳纳米管的稳定性分析与连续介质力学相结合来解决上述需求，从而使具有大量分子和原子的体系的分析成为可能。为了克服分子动力学的局限性，将线性和非线性弹性梁、壳模型等连续介质模型应用于碳纳米管的扭结失稳和后屈曲分析。此外，这项研究还将弥合宏观结构的连续介质力学原理与具有挑战性的纳米尺度问题之间的差距。研究结果可望为碳纳米管在复合材料等方面的应用提供令人满意的稳定性分析。该计划的长期目标是加强对碳纳米管机械行为的基本了解，从而导致这种材料的革命性开发和应用。预计最终研究成果将体现在波音加拿大有限公司和马尼托巴省综合创新中心等组织的碳纳米管的设计和使用中。

Since 1990s, carbon nanotubes (CNTs), about a hundred times stronger than steel at 1/6th the weight, have been discovered to hold great potential for countless technology innovations and applications, such as extremely lightweight and strong fabrics, chemical sensors, electrical sensors, fuel cells, and drug delivery. Business Communication Company estimates that global sales of CNTs will reach US$231.5 million in 2006. Unfortunately, CNTs' prompt and wide applications are hindered by insufficient understanding of their mechanical behaviour. Among many challenges, CNTs' stability analysis such as kink instability (abrupt changes of curvature due to compression) and post-buckling (large deformation due to compression) calls for a breakthrough. For example, inadequate understanding of CNTs' kink instability has been a major setback to the design of CNT based Atomic Force Microscope (AFM). Classic molecular dynamics is only applicable to stability analysis of systems with a small number of molecules and atoms.      This research aims at addressing the aforementioned needs by advancing CNTs' stability analysis with continuum mechanics to enable the analysis of systems with a large number of molecules and atoms. Continuum models such as linear and nonlinear elastic beam and shell models will be applied to kink instability and post buckling analysis of CNTs so as to circumvent the limitations of molecular dynamics. Besides, this research will bridge the gap between principles in continuum mechanics of macro-structure and challenging nano-scale problems. The research findings are expected to provide satisfactory CNTs' stability analysis for proper design of CNTs' applications such as CNT-reinforced composites. The long-term goal of the program is to enhance fundamental understanding of CNTs' mechanical behaviour leading to revolutionary development and application of the material. It is expected that eventually the research findings will embody into the CNTs' design and usage by organizations like Boeing Canada Ltd and Composite Innovation Centre in Manitoba.