Theoretical predictions of size-dependent Young's and shear moduli of single-walled carbon nanotubes

Abstract In this study, based on the Force-Heat Equivalence Energy Density Principle, the energy density stored in Single-walled carbon nanotubes (SWCNTs) with different diameters is assumed as the same when SWCNTs with different diameters undergo the same elastic strain under a uniaxial external tensile loading, which is composed of strain energy density and the equivalent curvature energy density. Then, theoretical models without the thickness of SWCNTs for characterizing size-dependent Young's and shear moduli of SWCNTs are established considering the effect of curvature energy. To verify the proposed models, the Young's and shear modulus of SWCNTs in different diameters are predicted, and good agreement is obtained with the available theoretical and numerical simulation results. Besides, the predictions by our models are normalized by graphene values and found the same trends as other scholars. This work contributes to providing a new method to estimate the size-dependent elastic moduli of SWCNTs.