Accurate modeling of buckling of single- and double-walled carbon nanotubes based on shell theories.

The accuracy of widely employed classical shell-theory-based formulae to calculate the buckling strain of single- and double-walled carbon nanotubes is assessed here. It is noted that some simplifications have been made in deriving these widely employed formulae. As a result critical buckling strains calculated from these formulae are independent of aspect ratio (length/diameter). However, molecular dynamics simulation results in the literature show an aspect ratio dependence of buckling strain. Therefore, analytical expressions are derived in this paper to calculate buckling strains of single- and double-walled carbon nanotubes based on classical shell theory without simplifications. Applicability of these expressions is further verified through molecular dynamics simulations based on the COMPASS force field. In addition, improvement in results achieved through a refinement of classical shell theory is assessed by calculating buckling strains based on first-order shell theory. Results show that simplified formulae introduce a significant error at higher aspect ratios and smaller diameters. The formulae derived here show reasonable agreement with the molecular dynamics results at all aspect ratios and diameters. First-order shell theory is found to produce a slight improvement in results for CNTs with smaller diameters and lower aspect ratios.