Abstract
The thickness of carbon nanotubes is an important issue for the characterization and design of these structures. In this article, thickness free expressions for the shear modulus of single-walled carbon nanotubes have been developed by finite element simulations on the minimum potential energy circle. As a part of this work, some equations have been obtained to define the relation between the thickness and the shear modulus, which are in good agreement with previous studies. Moreover, these expressions are in good agreement with both continuum and quantum mechanics and capable to support “Yakobson's paradox,” that the scattering data for the elastic properties of carbon nanotubes are due to the not-well-defined thickness for these structures. Furthermore, these expressions can provide a tool for the prediction of the shear modulus of single-walled carbon nanotubes in regards to any thickness assumption when the experimental investigations are too difficult to realize.
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