Compressive behavior and buckling response of Carbon Nanotubes Dianyun Zhang * , Aswath Rangarajan † , Anthony M. Waas ‡* College of Engineering, University of Michigan, Ann Arbor, MI-48109, USA Carbon nanotubes (CNTs) are allotropes of Carbon, which are supposed to possess very high strength. There has been relatively less analysis on the buckling response and the compressive behavior of the Carbon Nanotubes. The current study deals with the compressive behavior and buckling response of CNTs, while dealing with it as a spring system as well as by performing lattice calculations using GU LP (General Utility Lattice Program) and Finite Element Analysis (FEA) on the Carbon Nanotube structure, while approximating them to be structures made of beams. The spring model shows responses which are very similar to the buckling response for long nanotubes, as seen in the literature. I. Introduction Carbon Nanotubes (CNTs) are allotropes of Carbon, which are supposed to possess very high strength. The possible applications to which such high strength materials can be used in vary from simple items such as tennis rackets, going right to next generation armors. The stability and buckling of CNTs has been widely discussed, but most of the theories do not conform to the experimental results accurately. There have been a few experimental studies on the axial stability of multi walled CNTs. The work done by Waters et al. on the compression of CNTs having very low aspect ratios shows the CNTs to have an increasing equilibrium load after the initial buckling, which occurs around 2.5 μN . From the work of Akita et al[1], it can be seen that for CNTs having very large aspect ratios, the force displacement curves have a linear slope, and after a decrease in the slope at the buckling load, the linear relationship between the load and displacement is maintained. This behavior of the long CNTs can be com- pared with spring systems which have been designed to have the same force-displacement characteristics. The results also show that carbon nanotube bundles seem to exhibit super elastic behavior, making them suitable candidates for the next generation armors. Hirooka et al[3] have worked on the loading and unloading of CNTs having intermediate aspect ratios (between 40 and 60). These results show that the CNTs come back to their initial states on unloading even after the buckling load has been reached. However, one of the CNTs having a length of 800 mm, shows force-displacement behavior which is similar to the behavior observed by Akita et al[1]. TEM images of buckled configurations of CNTs show ripple like distortions on the CNT . It can also be seen that one side is in tension while the other side is in compression during the buckling of the CNT , and hence, the load bearing capacity of the CNT even upon buckling. Non Local Continuum theories can be used to create a 1D model of the CNT , but that would not capture the exact buckling mechanism of the CNT , since the effects due to the shell type of structure of the nanotube is ignored in this model. * Graduate Student, Department of Aerospace Engineering † Graduate Student, Department of Aerospace Engineering ‡ Professor, Department of Aerospace Engineering and Department of Mechanical Engineering 1 of 12 American Institute of Aeronautics and Astronautics