Asymptotic Modeling of Nonlinear Bending and Buckling Behavior of Carbon Nanotubes

Abstract

The present work investigates the nonlinear bending and buckling behavior of carbon nanotubes (CNTs) using variational asymptotic method. Considering a CNT as a slender beam structure, an asymptotically-correct nonlinear continuum beam model is presented. Through the resulting nonlinear moment-curvature relationship, the model captures the phenomenon of ovalization of the cross sections and local buckling of the CNT, which arises due to their geometrical nature. Further studies are performed in order to explore the effect of CNT wall thickness on the nonlinear bending behavior of the CNT structure. It is shown that the continuum modeling approach can capture the ovalization and further localization of the CNT deformation under bending. The study aims to provide a reduced-order modeling framework analyzing the inherent nonlinearities associated with the geometrical nature of CNTs.