Xiaoxing Lu

Document Type

Thesis - University Access Only

Award Date

2011

Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering

Abstract

Based on molecular mechanics, a three-dimensional finite element model for armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) has been developed, in which the carbon nanotubes (CNTs), when subjected to load, behave like space-frame structures. The bending stiffness of the graphite layer has been considered. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds: The out-of-plane deformation (inversion) of the bonds was distinguished from the in-plane deformation by considering an elliptical cross-section for the beam elements. The elastic moduli of beam elements are determined by using a linkage between molecular and continuum mechanics. A closed form solution of the sectional properties of the beam element was derived analytically and verified through the analysis of rolling a graphite sheet into a carbon nanotube. This method was validated by its application to a graphene model, and Young's modulus of the model was found, showing agreement with the known values of graphene. Modeling of the elastic deformation of SWCNTs reveals that Young's moduli and the shear modulus of SWCNTs vary with the tube diameter and are affected by their helicity. With increasing tube diameter, Young's moduli of both armchair and zigzag SWCNTs are increasing monotonically and approaching to the Young's modulus of graphite, which are in agreement with the existing theoretical and experimental results. The rolling energy per atom was computed by finite element analysis. By comparing mechanical properties with circular cross section models, it is found that the computational results of the proposed elliptical cross-section model are closer to the results from the atomistic computations. The proposed model is valid for problems where the effect of local bending of the graphite layer in a CNT is significant. This research work shows that the proposed finite element model may provide a valuable tool for studying the mechanical behaviors of CNTs and their integration in nano- composites. Further work should include investigating nonlinear mechanical properties of SWCNTs with large deformation and identifying the response of SWCNTs under experiment condition.

Library of Congress Subject Headings

Nanotubes -- Mechanical properties

Carbon -- Mechanical properties

Finite element method

Format

application/pdf

Number of Pages

86

Publisher

South Dakota State University

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