In-plane nonlinear delocalized vibrations in uniformly stretched single-layer graphene (space group P6mm) are considered with the aid of the group-theoretical methods. These methods were developed by authors earlier in the framework of the theory of the bushes of nonlinear normal modes (NNMs). Each bush represents a set of delocalized NNMs which is conserved in time, and the energy of initial excitation turns out to be trapped in the given bush. The number m of modes entering into the bush defines its dimension. One-dimensional bushes (m=1) represent individual nonlinear normal modes by Rosenberg which describe periodic dynamical regimes, while bushes of higher dimension (m>1) describe quasiperiodic motion with m basis frequencies in the Fourier spectrum. Each bush is characterized by a space group, which is a subgroup of the symmetry group of the system equilibrium state. There exist bushes of NNMs of different physical nature. In this paper, we restrict ourselves to study of vibrational bushes. We have found that only 4 symmetry-determined NNMs (one-dimensional bushes), as well as 14 two-dimensional, 1 three-dimensional and 6 four-dimensional vibrational bushes are possible in the single-layer graphene. These dynamical regimes are exact solutions to the motion equations of this two-dimensional crystal. Prospects of further research are discussed.

Some exact interactions between vibrational modes in systems with discrete symmetry can be described by the theory of the bushes of nonlinear normal modes (NNMs) [G. M. Chechin and V. P. Sakhnenko, Phys. D (Amsterdam, Neth.) 117, 43 (1998)]. Each bush represents a dynamical object conserving the energy of the initial excitation. The existence of bushes of NNMs is ensured by some group-theoretical selection rules. In G. M. Chechin et al. [ Int. J. Nonlinear Mech. 38, 1451 (2003)], existence and stability of the bushes of vibrational modes in the simple octahedral model of mass points interacting via Lennard-Jones potential were investigated. In the present paper, we study these dynamical objects by the density functional theory in the ${\text{SF}}_6$ molecule, which possesses the same symmetry and structure. We have fully confirmed the results previously obtained in the framework of the group-theoretical approach and have found some properties of the bushes of NNMs.

Although carbon materials, particularly graphene and carbon nanotubes, are widely used to reinforce metal matrix composites, understanding the fabrication process and connection between morphology and mechanical properties is still not understood well. This review discusses the relevant literature concerning the simulation of graphene/metal composites and their mechanical properties. This review demonstrates the promising role of simulation of composite fabrication and their properties. Further, results from the revised studies suggest that morphology and fabrication techniques play the most crucial roles in property improvements. The presented results can open up the way for developing new nanocomposites based on the combination of metal and graphene components. It is shown that computer simulation is a possible and practical way to understand the effect of the morphology of graphene reinforcement and strengthening mechanisms.

The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component...