Curvature effects on buckling of double-walled carbon nanotubes under combined axial compression and lateral pressure

Based on a curvature model for van der Waals (vdW) pressure between the interlayer of a double-walled carbon nanotube (DWNT), explicit expressions are derived for the critical buckling load of a DWNT which is modeled as a double-elastic shell under combined axial compression and lateral pressure. The critical load is calculated for various radii, length-to-radius ratios and load combinations. New results show that the curvature effects play a significant role in buckling problems for DWNTs of small radii. Neglecting the curvature effect usually leads to an under-estimate of the critical load for DWNTs when lateral pressure dominates. In addition, unlike Wang et al (2003b Int. J. Solids Struct. 40 3893) and Qian et al (2005 Int. J. Solids Struct. 42 5426), the buckling mode corresponding to the minimum axial buckling strain is unique, even when the lateral pressure is very small. For the DWNTs under combined axial compression and lateral pressure, the critical axial strain is reduced due to the external pressure.