A quasiconuum method for deformations of carbon nanotubes

Abstract

This research presents an adaptive multiscale simulation of deformations of curved crystalline structures such as CNTs(Carbon NanoTubes), based on quasicontinuum approach, which is a coarse-graining method. For fully non-local quasicontinuum, high-order interpolation functions are adopted for finding deformed positions of atoms on the curved crystal structure. The "cluster" concept, which facilitates accurate energy approximation for crystals, is extended such that the vertices of elements or subdivided regions may be chosen irrespective of the positions of carbon atoms. Defining two remeshing criteria based on the second invariant of the Green strain tensor and its gradient, we implement an automatic adaptive scheme for deformations of curved bodies. Various numerical examples of CNT deformations demonstrate the effectiveness of the present scheme. Furthermore, as we combine the QC algorithm with first principles calculation, the hybrid scheme makes it possible to enlarge the length scale for computational simulation and to predict more accurately the configuration as well as to obtain the electronic structure of the system. Finally, we present the feasibility study, which is intended for exploring the possibility spatial and temporal scales in computational nanomechanics, through the coupling of QC and ADMD methods.