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

In experimental and theoretical investigations of the properties of nanostr uctures, 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 mech anics must be carefully respected in order to obtain reasonable results. Re lations are derived for pure bending of nanotubes that show the explicit de pendence of the "material properties" on system size when a continuum cross -section assumption is made. Two alternate approaches are proposed that pro vide a more reliable scheme for property extraction from experiments. (C) 1 999 Elsevier Science Ltd. All rights reserved.