Nonlocal continuum models for carbon nanotubes subjected to static loading

Abstract

Static and buckling analyses of carbon nanotubes (CNTs) are carried out with newly developed nonlocal continuum models. Small-scale effects are explicitly derived for bending deformation solutions for CNTs subjected to general flexural loading first. Solutions via nonlocal continuum models are expressed by simple terms related to scale coefficients in addition to remaining terms via local continuum models in which the simplicity of the nonlocal continuum models is clearly observed. Discussions on various derivations of Young's modulus for CNTs from existing experimental work in the literature are provided, revealing the applicability of the nonlocal continuum models. In addition, a simple equation for the buckling load of CNTs with various general boundary conditions subject to axial loading via the nonlocal elastic beam model is explicitly derived for instability analysis. The results of this research provide benchmark solutions for the response of CNTs subject to general static loading, with small-scale effects modeled and revealed. Thus, the work has great potential in studying mechanical properties of CNTs of various sizes.