Zigzag Carbon Nanotubes under Simple Torsion – Structural Mechanics Formulation

Najib A. Kasti

doi:10.4028/www.scientific.net/AMR.452-453.1139

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Zigzag Carbon Nanotubes under Simple Torsion – Structural Mechanics Formulation
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Zigzag Carbon Nanotubes under Simple Torsion – Structural Mechanics Formulation

Abstract:

When using structural mechanics to study the deformation of carbon nanotubes (CNTs), one has to pick the structural mechanics properties that are equivalent to the molecular mechanics properties. In a previous publication [1], we have determined the relation between the bending stiffness EI/a used in structural mechanics and the bond bending stiffness C used in molecular mechanics for zigzag carbon nanotubes under simple tension. This paper extends the concept and determines the corresponding relation for simple torsion. We show that the relation obtained is different than that of simple tension; in simple torsion, EI/a is load and chirality dependent. However, for the particular case of a graphene sheet, simple tension and torsion lead to the same value of EI/a, namely C/2. We also include the structural mechanics deformation of the tube that accounts for axial, bending and torsional structural stiffnesses. Unlike simple tension, the deformation in the case of simple torsion has the axial stiffness coupled to the bending and torsional stiffnesses.