On the determination of the shear modulus of carbon nanotubes

The finite element method was applied to determine the most appropriate method for the determination of the shear modulus of single- and multi-walled carbon nanotubes. The shear modulus can be determined directly from torsion tests or for isotropic materials based on the values of Young's modulus and Poisson's ratio. However, if the material is anisotropic, the shear modulus is an independent material property and cannot be determined based on two other elastic parameters. To clarify the most appropriate approach, the shear modulus of carbon nanotubes was obtained through simulation of two basic tests. First, the modulus was directly calculated from torsion tests. Second, a tensile test was simulated and the corresponding Young's modulus and Poisson's ratio were calculated and the shear modulus of the models was obtained by the relationship based on Young's modulus and Poisson's ratio. The comparison of both methods revealed that carbon nanotubes behave rather as an anisotropic material. The involved error based on the isotropy assumption was quantified for different configurations, number of cell walls and under the influence of imperfections.