Stability analysis of carbon nanotubes with continuum mechanics

自20世纪90年代以来，碳纳米管（CNTs）被发现在无数技术创新和应用中具有巨大的潜力，例如极轻且坚固的织物、化学传感器、电子传感器、燃料电池和药物输送。碳纳米管的强度约为钢的100倍，重量仅为钢的1/6。Business Communication Company估计，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受到对其力学行为了解不足的阻碍。在众多挑战中，碳纳米管的稳定性分析，如扭结不稳定性（由于压缩导致曲率突变）和后屈曲（由于压缩导致大变形）需要突破。例如，对碳纳米管扭结不稳定性的不充分了解一直是基于碳纳米管的原子力显微镜（AFM）设计的主要挫折。经典分子动力学只适用于具有少量分子和原子的系统的稳定性分析。

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.