Abstract

The understanding of the mechanics of atomistic systems greatly benefits from continuum mechanics. One appealing approach aims at deductively constructing continuum theories starting from models of the interatomic interactions. This viewpoint has become extremely popular with the quasicontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This renders the cornerstone of crystal elasticity, the Cauchy-Born rule, insufficient to describe the effect of curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of carbon nanotubes [1,2,3]. We review recent developments of this theory, which include the study of the convergence characteristics of the proposed continuum models to the parent atomistic models, as well as large scale simulations based on this theory. The latter have unveiled the complex nonlinear elastic response of thick multiwalled carbon nanotubes (MWCNTs), with an anomalous elastic regime following an almost absent harmonic range. We propose a further level of model upscaling, by constructing mesoscopic beam models to describe thick MWCN Ts, which encode the essential complexity arising from the multi-layer structure, the short-range atomistic interactions, and the van der Waals interactions.

[1] Marino Arroyo and Ted Belytschko, “An atomistic-based finite deformation membrane for single layer crystalline films”, Journal of the Mechanics and Physics of Solids 50:1941-1977 (2002).

[2] Marino Arroyo and Ted Belytschko, “Nonlinear mechanical response and rippling of thick multi-walled carbon nanotubes”, Physical Review Letters, 91:215505 (2003)

[3] Marino Arroyo and Ted Belytschko, “Finite element analysis of the nonlinear mechanics of carbon nanotubes”, International Journal for Numerical Methods in Engineering, 59:419-456 (2004).