Last modified: 2015-04-25
Abstract
The work deals with the application of a nonlocal finite difference method to investigate the propagation of elastic waves in a single layer of graphene. During the last decade graphene nanoribbons have gained a significant increase of the researchers’ interest due to their specific properties regarding mechanics as wells as electric and thermal conductivity. Depending on the spatial configuration – including zigzag and armchair layout – related to the edge structure while wrapping a hexagonal sheet of graphene, it may act as either metallic or semiconducting material. This behavior offers attractive perspectives for possible applications of this unique material. Finally, the millimeter wave-based measurements systems can be build based on graphene nanoribbons.
The authors introduce an alternative approach for modeling a graphene nanoribbon undergoing propagation of elastic waves. A nonlocal finite difference discretization scheme is applied to recover physical dispersion of a single-layer graphene structure. It is the well-known fact that periodic structures exhibit physical dispersion manifested with the difference in velocities for waves of various lengths. Therefore, a dispersive medium should be considered in simulations as well. A mechanical assembly of a unit cell defined within the first Brillouin zone is used be the authors to create a reference finite element model to verify the proposed nonlocal finite difference approach. The reference model considers the commonly used auxiliary atomistic-continuum model for a carbon atoms bonds with equivalent mechanical properties. The reference dispersion relations are found, which are then applied to determine the coefficients of the nonlocal finite difference discretization scheme. Finally, the simulations carried out for wave propagations are verified. The capability of recovering the physical dispersion of graphene for the nonlocal finite difference method is discussed.
The carried out analyses are considered as a new tool for homogenization process for graphene. The reference dispersion curves allow to determine the resultant material properties, which are indirectly represented with the coefficients of a finite difference scheme used as an alternative modeling approach. A regular mesh of grids in the final model is applied. The authors take the advantage of nonlocality of the discretization scheme used, which allows to reproduce the given shapes of dispersion relations quite effectively. Hence, recovering of wave properties is possible for in-plane elastic waves in a graphene nanoribbon.
The work was supported by the Foundation for Polish Science (FNP-WELCOME/2010-3/2).