Session: 03-05-01: Nanomaterials

Paper Number: 110480

110480 - Continuum Analysis of Geometrically-Nonlinear Behaviour of Carbon Nanotubes Under Combined Bending and Twisting Loads 

Carbon Nanotubes (CNTs), due to their superior mechanical properties and multifunctional capability, have gained significant attention and have numerous potential applications in aerospace structures. However, the geometrical nonlinearity of CNTs, arising from their large radius-to-thickness (R/h) and length-to-radius (L/R) ratios, leads to a unique deformational behaviour
that is yet to be addressed in any continuum modelling approach. This geometric nonlinearity causes incremental ovalisation of the CNT cross section leading to premature failure from buckling under compressive, bending or twisting loads. However, pure loading conditions (of just one of the three aforementioned types) seldom occur in practice. In this study, the mechanical
behaviour of single-walled CNTs subjected to combined bending and twisting loads, accounting for geometrical nonlinearity, is analysed using the variational asymptotic method (VAM) and a nonlinear finite element model.
VAM utilises the inherent small parameters in a problem in an asymptotic manner to derive the governing differential equations and boundary conditions, without invoking any ad hoc assumptions. In the current problem, the small parameters are R/L, h/R and strain ϵ. A 2-D cross-sectional analysis was carried out using this approach, and it was discovered that the stiffness of CNT beams is not constant, as previously assumed in classical continuum approaches like Euler-Bernoulli theory, but instead reduces with the increasing bending curvatures, leading to a nonlinear relationship between the 1-D beam deformation and cross-sectional deformations.
A 1-D nonlinear beam model was developed using the finite element method (FEM) to account for the nonlinear relationship between beam deformation and cross section of CNTs. This study addresses the combined loading case of bending and twisting in CNTs, which has not been fully explored in previous research, particularly through the use of continuum models.
Such loading conditions can be found in aerospace applications, such as sensors and MEMS devices for actuation and switching. The interaction between the bending moment and the twisting moment was effectively analysed, showing that CNTs undergo twist buckling, and the critical buckling torque decreases when the applied bending moment increases, with a higher reduction in the range of 4—5% under higher bending loads (2—3 ∗10⁻⁵ nN/nm). Significant ovalisation of the CNT cross section at buckling onset was observed. Compared to linear analysis, the results indicated that considering the geometrically-nonlinear behaviour of CNTs resulted in a lower critical buckling torque, as the linear analysis assumes circular, planar, and rigid cross sections. The difference between linear and nonlinear results was 4—33%, emphasising the significance of incorporating geometric nonlinearities in the study of CNTs. Using the obtained displacements and rotations from the FE model, the complex 3-D deformed shapes of CNTs were visualised using the open-source software, ParaView. Finally, parametric studies were conducted to investigate the impact of different length-to-radius (L/R) and radius-to-thickness
(R/h) ratios on the buckling loads.
This study provides a valuable alternative to traditional molecular dynamics methods, which are computationally-intensive, time-consuming, and limited to atomistic length scales. The proposed methodology, with the further addition of non-classical elasticity models, could present a computationally-efficient means of modelling CNTs in continuum applications.

Presenting Author: Renuka Sahu Indian Institute of Science IISc

Presenting Author Biography: Renuka Sahu is a PhD candidate in the Department of Aerospace Engineering at the prestigious Indian Institute of Science (IISc) in Bengaluru, India. She holds a bachelor's degree in Mechanical Engineering from the National Institute of Technology (NIT) Raipur, where she was honoured with a silver medal. Renuka's PhD research is focused on the asymptotic modelling of damage in Carbon Nanotube (CNT) and CNT-reinforced composites. She is using the variational asymptotic method and non-local elasticity theories to develop a continuum model of CNTs, which would then be applied to study CNT composites. Her work aims to provide new insights into the mechanical behaviour of CNTs and CNT-reinforced composites, with the goal of enabling the development of continuum-based analysis models for the study of nanocomposites used in aerospace applications. Recently, Renuka received the Indo-German Science & Technology Centre (IGSTC) PhD Industrial Exposure fellowship, which provided her with the opportunity to undertake a research project with Airbus Defence & Space Gmbh in Munich, Germany. During her time at Airbus, she studied the applicability of CNTs for multifunctional aerospace applications and battery systems. Renuka's research interests lie in the fields of nanomaterials, aerospace structures, multifunctional materials, and energy systems. She is a promising young researcher with a passion for advancing our understanding of CNTs and CNT-reinforced composites, and their applications in the aerospace industry.

Authors:

Renuka Sahu Indian Institute of Science IISc
Sathiskumar Anusuya Ponnusami City, University of London
Dineshkumar Harursampath Indian Institute of Science IISc