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The mechanical behavior and properties of multilayer graphene sheets and nanoribbons have been a subject of intensive research in recent years, due to their potential in electronic, structural and thermal applications. Calculations of effective properties range from molecular dynamic simulations to use of structural mechanical continuum models. Here, structural and elastic parameters are obtained via full atomistic simulations, and a two-dimensional mesoscopic model for a sheet of graphene is developed utilizing coarse-grain bead-spring elements with rotational-spring potentials. The assertion of energy conservation between atomistic and mesoscale models through elastic strain energy is enforced to arrive at model parameters, incorporating normal and shear strains, out-of-plane bending and intramolecular interactions. We then apply our mesoscopic model to investigate the structure and conformational behavior of twisted ultralong multilayer graphene ribbons with lengths of hundreds of nanometers, representing several millions of individual atoms, beyond the accessible regime of full atomistic molecular dynamics. We find a distinct transition from a twisted (saddle-like) configuration to a helical (coil-like) configuration as a function of imposed rotation and number of graphene layers. Further, for single layer graphene ribbons, multiple, stable configurations occur at discrete rotations due to the surface adhesion. The model developed and applied here can be more generally used to investigate properties of other two-dimensional membrane and ribbon-like systems for mesoscale hierarchical material design.
Cranford et al. (Thu,) studied this question.