Mesh-free simulation of single-walled carbon nanotubes using higher order Cauchy–Born rule

A mesh-free computational framework is developed to study the deformation behavior of single-walled carbon nanotubes (SWCNTs) by considering the effect of the second-order deformation gradient. The analysis is based on a hyper-elastic constitutive model derived from 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. Within the theoretical scheme of the higher order Cauchy–Born rule, the structural properties of SWCNTs and the constitutive response of the system are determined by minimizing the energy of the representative cell. The compression and torsion tests of SWCNTs are numerically simulated with the developed method. The numerical computations reveal that a less amount of mesh-free nodes can provide a good simulation for the homogeneous deformation stage, and the buckling pattern can be truly displayed with the application of the increasing amount of nodes.