Predicting mechanical properties of single-walled carbon nanocones using a higher-order gradient continuum computational framework

The higher-order gradient continuum theory is employed to study the structural parameters and elastic properties of single-walled carbon nanocones (SWCNCs), where the higher-order Cauchy–Born rule is used to link the deformation of the carbon atomic structure to that of the continuum level. Unlike single-walled carbon nanotubes (SWCNTs), mechanical properties of SWCNCs vary along its side edge’s direction, owing to the monotonically increasing radius. In the constitutive model, a representative cell in an initial graphite sheet is selected to study the mechanical property of this domain of SWCNCs. By minimizing the potential energy of the representative cell in the undeformed SWCNC, structural parameters and elastic properties of the domain are obtained. The varying chiralities seem to have a large impact on mechanical properties of SWCNCs. Five kinds of SWCNCs are chosen in our study to test the influence of the apex angle on mechanical properties. The computational results demonstrate that mechanical properties of SWCNCs trend to the constant of graphite sheet when the radius is extremely large but this trend becomes mild as the apex angle increases.