De Domenico, D. and Askes, H. orcid.org/0000-0002-4900-1376 (2018) Stress gradient, strain gradient and inertia gradient beam theories for the simulation of flexural wave dispersion in carbon nanotubes. Composites Part B: Engineering, 153. pp. 285-294. ISSN 1359-8368
Abstract
Flexural wave propagation in carbon nanotubes (CNTs) can be described through higher-order elasticity theories so as to capture the dispersive behavior induced by the inherent nanoscale heterogeneity. Motivated by experimental dispersion characteristics of metal nano-structured crystals, a new three-length-scale gradient formulation has been recently developed by the authors. In addition to the Laplacian of the strain, this model incorporates two higher-order inertia gradients for an improved dispersion behavior. A discrete medium with lumped masses at multiple scales of observation and combination of lumped mass and distributed mass at the macro-scale is introduced here to provide a micro-mechanical background to the proposed three-length-scale gradient model. The next aim of this paper is to assess the ability of this model to simulate flexural wave dispersion occurring in CNTs. We employ gradient-enriched Euler-Bernoulli and Timoshenko beam theories incorporating either stress gradients, or a combination of both strain gradients and inertia gradients – the latter leading to novel gradient-enriched beam theories. It is demonstrated that the proposed three-length-scale gradient elasticity formulation is able to capture the wave dispersion characteristics of armchair single-walled (5,5) and (10,10) CNTs arising from Molecular Dynamics simulations with high accuracy for a wide range of wave numbers. Advantages over alternative formulations of higher-order beam theories with stress gradients or combined strain-inertia gradient enrichments are discussed for comparative purposes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 Elsevier. This is an author produced version of a paper subsequently published in Composites Part B: Engineering. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Carbon nanotubes; Wave dispersion; Nonlocal elasticity; Gradient elasticity; Internal length scale; Euler-Bernoulli beam; Timoshenko beam; Stress gradient; Strain gradient; Inertia gradient |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 Sep 2018 14:34 |
Last Modified: | 23 Aug 2019 00:42 |
Published Version: | https://doi.org/10.1016/j.compositesb.2018.08.083 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.compositesb.2018.08.083 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135180 |
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