On the use of continuum mechanics to estimate the properties of nanotubes

In experimental and theoretical investigations of the properties of nanostructures, the equations of continuum beam theory are often used to interpret the mechanical response of nanotubes. In particular, Bernoulli-Euler beam bending theory is being utilized to infer the Young's Modulus. In this work, we examine the validity of such an approach using a simple elastic sheet model and show that at the nanotube scale the assumptions of continuum mechanics must be carefully respected in order to obtain reasonable results. Relations are derived for pure bending of nanotubes that show the explicit dependence of the "material properties" on system size when a continuum cross-section assumption is made. Two alternate approaches are proposed that provide a more reliable scheme for property extraction from experiments. (C) 1999 Elsevier Science Ltd. All rights reserved.