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.

Figure 1

Twisted MWCNTs. (a) Strain energy vs twisting angle log-log plots for various MWCNTs and (b) data collapse upon appropriate rescaling. The power law fits with exponents 2 (blue) and 1.63 (red) are shown for illustration. (c) Rescaled torque vs twisting angle relation highlighting the unified law. (d) 35-walled CNT in torsion, deformed shape (top), Gaussian curvature map (middle; green is zero, red is positive, blue is negative), and energy density map (bottom; red is high, blue is low).

Figure 2

Bent MWCNTs. (a) Strain energy vs curvature log-log plots for various MWCNTs and (b) data collapse upon appropriate rescaling. The power law fits with exponents 2 (blue) and 1.42 (red) are shown for illustration. (c) 40-walled CNT in pure bending, deformed shape (top), Gaussian curvature map (middle), and energy density map (bottom). The color scales coincide with those of Fig. 1.