Peridynamics as an analysis tool for wave propagation in graphene nanoribbons

Abstract

The work is devoted to the study on elastic wave propagation in graphene nanoribbons, performed with peridynamics. Graphene nanoribbons have recently gained dramatic increase of interest in the fields of nanoelectronics and nanoelectromechanical systems. They can play a key role as either modern metallic or semiconductor materials, depending on the edge structure, with zigzag or armchair layout, respectively. Moreover, graphene opens new perspectives for the millimeter wave-based measurements systems. The authors present a peridynamic model used as alternative approach to analyze the dynamic behavior of a graphene nanoribbon. The model is considered as a periodic structure, i.e. an assembly of fundamental structural elements, with the first Brillouin zone under study, which undergoes propagation of elastic wave. The commonly applied auxiliary atomistic-continuum model for a C-C bond is used to set equivalent elastic properties, which are applied to find reference dispersion relation via FE model to study the behavior of the peridynamic model. The paper discusses its capability of recovering the physical nature of the reactions at the atomic scale present in a graphene applying dispersion characteristics. The peridynamic model of the graphene nanoribbon results from upscaling process carried out for a small-scale atomic model, making use of reference dispersion curve. The material properties are homogenized over studied domain indirectly by tuning the phase velocity for longitudinal in-plane elastic waves. As shown, nonlocal nature of peridynamics allows to preserve the lengthscale effect, local small-scale inhomogeneity and wave dispersion. Hence, the effect of spatial discretization at nano scale, arising from the distribution of atoms of carbon in the structure of graphene, may be represented with a nonlocal peridynamic model effectively.