Application of the higher-order Cauchy-Born rule in mesh-free continuum and multiscale simulation of carbon nanotubes

This paper investigates the application of a recently proposed higher-order Cauchy-Born in the continuum simulation and multiscale analysis of carbon nanotubes (CNTs). A mesh-free computational framework is developed to implement the numerical computation of the hyper-elastic constitutive model that is derived from the higher-order Cauchy-Born rule. The numerical computation reveals that the buckling pattern of a single-walled carbon nanotube (SWCNT) can he accurately displayed by taking into consideration the second-order deformation gradient, and fewer mesh-free nodes can provide a good simulation of homogeneous deformation. The bridging domain method is employed to couple the developed mesh-free method and the atomistic simulation. The coupling method is used to simulate the bending buckling of an SWCNT and the tensile failure of an SWCNT with a single-atom vacancy defect, and good computational results are obtained. Copyright (C) 2008 John Wiley & Sons, Ltd.