Numerical validation of a concurrent atomistic-continuum multiscale method and its application to the buckling analysis of carbon nanotubes

This work applies the framework of a concurrent multiscale approach to the buckling analysis of carbon nanotubes. In particular, the bridging domain method is used to couple a molecular statics model and a continuum mechanics model. The total potential energy of the entire structure is specified by weighted individual energy contributions of overlapping subdomains. In this handshake region, additional kinematics constraints enforce the compatibility between designated atoms and the continuum body. Three different methods are taken into consideration for the kinematics coupling and the corresponding governing equations are presented. The continuum subdomain is handled by means of a finite element approach and the molecular statics is formulated suitable for a common computational implementation. A series of numerical examples investigates the capability of the bridging domain method for its application in the analysis of carbon nanotubes. Initially, the individual approaches for integrating the kinematics constraints into the global equilibrium equations are compared. Then, in the major contribution of the work, the influences of several modelling parameters of the multiscale model on the buckling analysis of a bent single-walled carbon nanotube are numerically studied. In particular, the size of the atomistic section, the extent of the handshake region and the finite element discretisation are varied. Furthermore, the results obtained by the standard and the relaxed variant of the bridging domain method are compared against each other. In addition, the buckling behaviour of a defective carbon nanotube with varying defect locations is presented. The obtained results of the bridging domain multiscale method are persistently validated against full atomistic molecular statics simulations.