Meshfree Simulation of Compressive Buckling of Single-Walled Carbon Nanotubes Using Higher Order Cauchy-Born Rule

— A meshfree computational scheme is developed to study the compressive deformation of single-walled carbon nanotubes (SWCNTs). The continuum constitutive relationship is based on an extended Cauchy-Born rule, the higher order Cauchy-Born rule, in which the atomic-scale deformed lattice vectors are calculated with both the first and second order deformation gradients. The compression of CNTs is simulated, and the buckling behavior is displayed accurately. A numerical simulation is also carried out with the application of the standard Cauchy-Born rule, and the comparison indicates that consideration of the second-order deformation gradient is necessary for the continuum simulation of CNTs.