Buckling of single-walled carbon nanotubes using two criteria

We use molecular mechanics simulations with the MM3 potential to study instabilities in clampedclamped single-walled carbon nanotubes (SWCNTs) deformed in torsion and axial compression. The following are the two criteria employed to find the critical buckling strain: (i) a sudden drop in the potential energy and (ii) an eigenvalue of the mass weighted Hessian of the deformed configuration becoming zero. The instability under axial compression is investigated for zigzag and armchair SWCNTs, and that under torsional deformations is also studied for chiral tubes. In general, values of critical strains from the 2nd criterion are found to be substantially less than those from the 1st criterion. For chiral SWCNTs, the critical strains from the 2nd criterion and the potential energies at the onset of instability markedly depend upon the twisting direction. Values of buckling strains predicted from the column and the shell buckling theories are found to agree well with those obtained using the 2nd criterion. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4954686]