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Continuum modeling of nonlinear buckling behavior of CNT using variational asymptotic method and nonlinear FEA

Sahu, R., Harursampath, D. & Ponnusami, S. A. ORCID: 0000-0002-2143-8971 (2023). Continuum modeling of nonlinear buckling behavior of CNT using variational asymptotic method and nonlinear FEA. Mechanics of Advanced Materials and Structures, pp. 1-18. doi: 10.1080/15376494.2023.2211971


Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field.

Publication Type: Article
Additional Information: © 2023 The Author(s). Published with license by Taylor & Francis Group, LLC This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.
Publisher Keywords: CNT, geometric nonlinearity, buckling, combined loading, variational asymptotic method, FEA
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology > Engineering
SWORD Depositor:
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