Chapter 7 - Nonlocal Elasticity Theories

Abstract

Despite the efficiency of classical continuum models with relatively simple formulae in carbon nanotube (CNT) mechanical analysis, their applicability to the identification of the small-scale effect on the mechanical behavior of CNTs is questionable. This limited applicability of the classical or local continuum models at small length scales is partly due to the fact that classical modeling does not admit intrinsic size dependence in the elastic solutions of inclusions and inhomogeneities. The nonlocal elasticity theory assumes that the stress state at a given reference point is a function of the strain field at every point in the body. Therefore, the scale effect can be considered in constitutive equations simply as a material parameter. This chapter aims to investigate the applicability of nonlocal beam, nonlocal rod models, and nonlocal shell models for free transverse, longitudinal, and torsional vibrations and waves in single-walled and double-walled CNTs through verifications from molecular dynamics (MD) simulations. Beam models and MD simulations are employed to study the transverse vibration of single-walled CNTs (SWCNTs). The nonlocal rod model is used to predict the MD results for longitudinal and torsional vibrations of SWCNTs. The nonlocal shell model is applied to study transverse and torsional wave in single-walled and double-walled CNTs.