Mechanical response of the carbon nanotube bundle to uniaxial and biaxial lateral compression followed by unloading is modeled under plane strain conditions. The chain model with a reduced number of degrees of freedom is employed with high efficiency. During loading, two critical values of strain are detected. Firstly, period doubling is observed as a result of the second order phase transition, and at higher compressive strain, the first order phase transition takes place when carbon nanotubes start to collapse. The loading-unloading stress-strain curves exhibit a hysteresis loop and, upon unloading, the structure returns to its initial form with no residual strain. This behavior of the nanotube bundle can be employed for the design of an elastic damper.

Structure evolution and mechanical response of the carbon nanotube (CNT) bundle under lateral biaxial compression is investigated in plane strain conditions using the chain model. In this model, tensile and bending rigidity of CTN walls, and the van der Waals interactions between them are taken into account. Initially the bundle in cross section is a triangular lattice of circular zigzag CNTs. Under increasing strain control compression, several structure transformations are observed. Firstly, the second-order phase transition leads to the crystalline structure with doubled translational cell. Then the first-order phase transition takes place with the appearance of collapsed CNTs. Further compression results in increase of the fraction of collapsed CNTs at nearly constant compressive stress and eventually all CNTs collapse. It is found that the potential energy of the CNT bundle during deformation changes mainly due to bending of CNT walls, while the contribution from the walls tension-compression and from the van der Waals energies is considerably smaller.

Close packed carbon nanotube bundles are materials with highly deformable elements, for which unusual deformation mechanisms are expected. Structural evolution of the zigzag carbon nanotube bundle subjected to biaxial lateral compression with the subsequent shear straining is studied under plane strain conditions using the chain model with a reduced number of degrees of freedom. Biaxial compression results in bending of carbon nanotubes walls and formation of the characteristic pattern, when nanotube cross-sections are inclined in the opposite directions alternatively in the parallel close-packed rows. Subsequent shearing up to a certain shear strain leads to an appearance of shear bands and vortex-like displacements. Stress components and potential energy as the functions of shear strain for different values of the biaxial volumetric strain are analyzed in detail. A new mechanism of carbon nanotube bundle shear deformation through cooperative, vortex-like displacements of nanotube cross sections is reported.

Crystal lattices support delocalized nonlinear vibrational modes (DNVMs), which are determined solely by the lattice point symmetry, and are exact solutions of the equations of atomic motion for any interatomic potential. DNVMs are interesting for a number of reasons. In particular, DNVM instability can result in the formation of localized vibrational modes concentrating a significant part of the lattice energy. In some cases, localized vibrational modes can be obtained by imposing localizing functions upon DNVM. In this regard, stability of DNVMs is an important issue. In this paper, molecular dynamics is employed to address stability of all four delocalized modes in a graphene lattice in the presence of small perturbations both in the plane and normal to the plane of the lattice. When DNVM amplitude is above the stability threshold, atom trajectories deviate from the mode pattern exponentially in time. Critical exponents are calculated for the in-and out-of-plane displacements. Stability threshold amplitudes are established. Interestingly, in three of the studied DNVMs the in-plane displacements diverge faster, but in one of them the instability develops through the out-of-plane displacements. This result can be explained by the difference in atomic vibration patterns of DNVMs. Reported results refine our understanding of the nonlinear dynamics of graphene lattice and can be useful in the design of electro-mechanical resonators and sensors.

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