Curvature effects on pressure-induced buckling of empty or filled double-walled carbon nanotubes

Abstract

The curvature effects of interlayer van der Waals (vdW) forces on pressure-induced buckling of empty or filled double-walled carbon nanotubes (DWNTs) are studied for various radii, length-to-radius ratios, end conditions and internal-to-external pressure ratios. The analysis is based on a double-elastic shell model and assumes that the interlayer vdW pressure at a point between the inner and outer tubes depends not only on the change of the interlayer spacing, but also on the change of the curvatures of the inner and outer tubes at that point. Here the role of filling substances inside DWNTs is modeled by a uniformly distributed internal pressure. The present work aims to study the curvature effects on critical radial pressure. An explicit formula is obtained for the external buckling pressure of empty or filled DWNTs. The critical value of external pressure is estimated with various internal-to-external pressure ratios. It is shown that the curvature effects play a more significant role in buckling problems under radial pressure for small radii DWNTs than under pure axial stress. Our results show that loading transfer through vdW forces prior to buckling is important for the pressure-induced buckling of DWNTs rather than axially compressed buckling.