A Finite-Deformation Shell Theory for Carbon Nanotubes Based on the Interatomic Potential—Part I: Basic Theory

Abstract

A finite-deformation shell theory for carbon nanotubes (CNTs) is established directly from the interatomic potential for carbon to account for the effect of bending and curvature. Its constitutive relation accounts for the nonlinear multibody atomistic interactions and therefore can model the important effect of CNT chirality and radius. The equilibrium equations and boundary conditions are obtained for the symmetric stresses and bending moments, which are different from many existing shell theories that involve asymmetric stress and bending moments. The theory is used in Part II of this paper to study the instability of carbon nanotubes subjected to different loadings.