The Predicting of the Size Effects in the Buckling of the Carbon Nanotubes

It is well-known that the nanoindentation hardness displays strong indentation size effects. In this paper, the size dependence of the hardness with respect to the depth and the indenter radius for the buckling of multiwalled carbon nanotubes is investigated using the Toupin-Mindlin strain gradient theory. As expected, the indentation hardness is closely related to the depth and the indenter radius. Qualitatively, the responses of the axially compressed multiple walled carbon nanotube agree remarkable well with the experimental observations.