Analysis of single-walled carbon nanotubes using the moving Kriging interpolation

Abstract

The higher-order Cauchy–Born rule is applied to predict the mechanical response of single-walled carbon nanotubes (SWCNTs). As second-order deformation gradients can describe the bending effect of C–C bond vectors involved in the theoretical scheme of the higher-order gradient continuum, the established constitutive model accords extremely well with physical behavior. From the constitutive relationship constructed, a novel computational method is proposed for numerical simulation of buckling behaviors of SWCNTs. In this study, a new mesh-free method developed from the moving Kriging (MK) interpolation is employed to implement numerical simulation of mechanical properties of SWCNTs under axis-symmetrical loadings. As the mesh-free shape function constructed using the MK interpolation has the delta function property, the shape functions satisfy the essential boundary conditions automatically. Therefore, the essential boundary conditions can be easily implemented. Several numerical examples of buckling behaviors of SWCNTs are presented to test the effectiveness and efficiency of this method. The numerical results are also compared with those obtained from the full atomistic simulation method, and are found to be in agreement. Moreover, this computational method can largely reduce the degrees of freedom of the system, and thus save a large amount of computational resources. As a result, this is a very attractive approach, which has great potential in the engineering field. This mesh-free method is further applied to the study of post-buckling of SWCNTs. The results are compared with those obtained from full atomistic simulation, and demonstrate that this method is truly effective and efficient.