Size-Dependent Nonlinear Elastic Scaling of Multiwalled Carbon Nanotubes

We characterize through large-scale simulations the nonlinear elastic response of multiwalled carbon nanotubes (MWCNTs) in torsion and bending. We identify a unified law consisting of two distinct power law regimes in the energy-deformation relation. This law encapsulates the complex mechanics of rippling and is described in terms of elastic constants, a critical length scale, and an anharmonic energy-deformation exponent. The mechanical response of MWCNTs is found to be strongly size dependent, in that the critical strain beyond which they behave nonlinearly scales as the inverse of their diameter. These predictions are consistent with available experimental observations.