A thickness-independent nonlocal shell model for describing the stability behavior of carbon nanotubes under compression

In this article, a nonlocal Flügge shell model incorporating interatomic potentials is developed to study the buckling behavior of an axially loaded single-walled carbon nanotube (SWCNT). The theory incorporates the relations resulting from establishing a linkage between the strain energy induced in the continuum and the potential energy stored in the atomic bonds, using the so-called Cauchy–Born rule, into the constitutive relations of Eringen’s nonlocal elasticity theory. An exact solution is implemented to solve the set of coupled field equations. In comparison to classical models, the present model provides a much better fit to molecular dynamics (MDs) simulations results and proposes the appropriate value of nonlocal parameter for SWCNTs with simply-supported end conditions. Furthermore, the model developed herein is independent of the nanotube wall thickness and Young’s modulus whose values are scattered in the literature.