Chapter 5 - Mechanics of the High Aspect Ratio Carbon Nanotubes: Beam Models, Nanoscale Buckling, Nanobeams and Phonons

Abstract

This chapter presents the fundamentals of the nanoscale mechanics of nanoscale beams and the high aspect ratio carbon nanotubes, along with the analysis of their unique material properties. The relation between the length scales in the atomic lattice structure of carbon nanotubes and the Cauchy–Born rule is discussed. Kinematic inequalities for the atomic lattices of carbon nanotubes are presented along with the discussion about the nanoscale homogenization correction for the Cauchy–Born approximations. Atomistic analysis methods and molecular dynamics simulations of carbon nanotubes have been discussed. Solution of the thickness paradox for long carbon nanotubes has been presented. Uniqueness of nanoscale beams and carbon nanotubes is reflected in the equivalent-continuum beam models. Ranges of applicability of the continuum beam theories to the mechanics of carbon nanotubes are discussed. The continuum models with the lattice chirality of carbon nanotubes have been presented for the analysis of nanoscale buckling. Nanoscale buckling is examined for the high aspect ratio carbon nanotubes and the carbon nanotube probes for atomic force microscopy. Nanoscale deformation of the zig-zag and the armchair single wall carbon nanotube nanobeams has been discussed, along with the generation of phonons.