The buckling of single-walled carbon nanotubes upon bending: The higher order gradient continuum and mesh-free method

The bending buckling of single-walled carbon nanotubes (SWCNTs) is studied in the theoretical scheme of the higher order gradient continuum. The deformation of the underlying lattice vectors is approximated with an extended Cauchy–Born rule in which the effect of the second order deformation gradient is considered, and the continuum constitutive responses are determined by minimizing the energy of the representative cell. A mesh-free method is developed to implement the numerical modeling of SWCNTs, and their bending buckling behavior is numerically simulated with the developed method. The results are compared with those obtained with a full atomistic simulation, and it is revealed that the developed mesh-free method can accurately exhibit the bending deformation of SWCNTs. Different types of carbon nanotubes (CNTs) are studied, and the buckling mechanism is investigated.