Continuum Mechanics Modeling and Simulation of Carbon Nanotubes |
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Authors: | Marino Arroyo Ted Belytschko |
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Institution: | (1) Departament de Matemàtica Aplicada III, Laboratori de Càlcul Numèric (LaCaN), Universitat Politècnica de Catalunya, E-08034 Barcelona, Spain;(2) Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA |
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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 (CNTs). 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. |
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Keywords: | Continuum mechanics Carbon nanotubes Finite elasticity Atomistic models Nanotube-based devices |
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