Mechanical Behaviors of Carbon Nanotubes

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 ...