Nanostructure-dependent dispersion of carbon nanostructures: New insights into the modified couple stress theory

This paper presents a size-dependent analysis of carbon nanostructures to put forward some new insights into the conventional modified couple stress theory. In fact, a micro-inertia length scale parameter is added to the equation of motion to compensate the deficiency of the theory in describing the size effect of the longitudinal dispersion. In this study, the longitudinal dispersions of carbon nanotubes, graphene, and graphite layers are investigated to obtain the micro-inertia length scale parameter, and the flexural dispersions of carbon nanotubes and graphene layer are assessed to expose the size dependency of the couple-stress length scale parameter. The results indicate that the micro-inertia length scale parameter can directly be related to the lattice size, while the couple-stress length scale parameter depends on some more factors like geometry, size, and material properties. Finally, some general relations are proposed for the first time to make a connection between these two distinct parameters and other features.