A nonlocal continuum mechanics model to estimate the material property of single-walled carbon nanotubes

Abstract

A subject of current technological interest is that of nanotechnology. It would appear that nonlocal continuum mechanics could potentially play a useful role in analysis related to nanotechnology applications. The present work explores this potential in the context of a specific application. The length scales associated with nanotechnology are often sufficiently small to call the applicability of classical continuum models into question. Atomic and molecular models, while certainly conceptually valid for small length scales, are difficult to formulate accurately and are almost always computationally intensive. Nonlocal continuum models represent attempts to extend the continuum approach to smaller length scales while retaining most of its many advantages. Therefore, continuum models need to be extended to consider the scale effect in nanomaterial studies. This can be accomplished through proposing nonlocal continuum mechanics models, where the internal size scale could be simply considered in constitutive equations as a material parameter. Usually, the magnitude of the nonlocal parameter e₀, determines the nonlocal effect in the analysis. The modeling and analyses of nanostructures based on flexural displacement, require an accurate estimate of nonlocal scaling parameter. Such an attempt is made in the present work. From the present analysis, the value of the scale coefficient (e₀a, a is carbon-carbon bond length) is recommended to be about 0.11 nm for the application of the nonlocal theory in the analysis of carbon nanotubes.