A review on the application of nonlocal elastic models in modeling of carbon nanotubes and graphenes

This paper reviews recent research studies on the application of the nonlocal continuum theory in modeling of carbon nanotubes and graphene sheets. A variety of nonlocal continuum models in modeling of the two materials under static and dynamic loadings are introduced and reviewed. The superiority of nonlocal continuum models to their local counterparts, the necessity of the calibration of the small-scale parameter, and the applicability of nonlocal continuum models are discussed. A brief introduction of the nonlocal beam, plate, and shell models is particularly presented. Summary and recommendations for future research are also provided. This paper is intended to provide an introduction of the development of the nonlocal continuum theory in modeling the two nano-materials, review the different nonlocal continuum models, and inspire further applications of the nonlocal continuum theory to nano-material modeling.