Chapter 6 - Mechanics of Carbon Nanotubes: Shell Models, Chiral Formulations and Nanoscale Buckling

Abstract

This chapter presents the fundamentals of nanoscale mechanics of atomic lattice shells of carbon nanotubes, along with the analysis of their unique mechanical properties. The Cauchy–Born rule is discussed, as well as the kinematic inequalities for the atomic lattices of thin single wall carbon nanotube (SWCNT) shells and the nanoscale homogenization correction. New lattice-based criteria for the applicability of the thin shell models to different classes of chiral SWCNT lattices are presented without the explicit use of the thickness and the radius. Examples of long SWCNTs with large diameters, the largest thick SWCNT shell, and the largest SWCNT nanobeam are discussed. Equations for molecular dynamics (MD) simulations of carbon nanotubes have been reviewed, along with the expressions for the stresses. A solution of the thickness paradox for carbon nanotube shells has been presented with a review of different estimates for the thickness of SWCNTs. Equivalent-continuum shell models for carbon nanotubes have been reviewed. Ranges of applicability of the continuum shell theories to the mechanics of carbon nanotubes are discussed, along with the assumptions used. A new lattice-sensitive form of a formula for the critical strain of chiral SWCNTs is presented, along with its predictions for nanoscale buckling of SWCNTs for different estimates for their effective thickness. Numerical results compare well with the available data of MD simulations.