A membrane–spring model for carbon nanotubes with van der Waals interaction between non-bonded atoms

The membrane?spring model was proposed by the authors to simulate the nonlinear mechanical responses of single-walled carbon nanotubes (CNTs). In order to investigate the complex behavior of multi-walled CNTs or CNT related structures, the van der Waals interaction between the non-bonded atoms should be included. In this paper, the van der Waals interaction is introduced into the membrane?spring model by using the atomic integration method. The nonlinear interaction is calculated at the atomic level, and then mapped to nodes. Consequently, the equations of motion are solved on nodes instead of atoms. The nonlinear deformations of single-?and multi-walled CNTs are investigated by using the proposed model.