Deviations from continuum mechanics are always expected in nanoscale structures. We investigate the validity of the plate idealization of ultrathin graphene by gaining insight into the response of chemical bonds to bending deformations. In the monolayer, a bond orbital model reveals the breakdown of the plate phenomenology. In the multilayer, objective molecular dynamics simulations identify the validity margin and the role of discreteness in the plate idealization. Our result has implications for a broad class of phenomena where the monolayer easily curves, and for the design of mass and force detection devices.

We investigate helical single-walled nanotubes of BN and ZnO described with density functional based tight-binding models. The employed objective molecular dynamics computational framework accounts for the helical instead of the translational symmetry and allows for simulating chiral nanotubes as the result of the nanomechanical process of a nearly-axial glide 2 . At large diameters, by comparing the microscopic strain stored in the tube wall with the continuum predictions, we observe the invalidity of the continuum shell idealization of the one-athom thick layer. At small diameters, by comparing the computed Eshelby twist executed by the one-atom thick layers with the one predicted by pure rolling of the mono-layer, we find that a large catalog of nanotubes store intrinsic twists. This unusual intrinsic twist effect is shown to be dependent on chirality and diameter, as part of the general trend to depart from the standard rolled-up construction. While changes in the electronic structures and Young's modulus are dominated by curvature, the shear elastic constants vary both with curvature and chirality.

Twisted zinc oxide nanowires and nanotubes were recently synthesized by screw-dislocation growth. We show theoretically that once their diameter increases above a critical size of the order of a few atomic spacings, the existence of these structures can be rationalized in terms of the energetics of surfaces and veritable Eshelby's twist linear elasticity mechanics supplemented by a nonlinear core term. For Burgers vector larger than the minimum allowed one, a twisted nanotube with well-defined thickness, rather than a nanowire, is the most stable nanostructure. Results are assistive for designing ultrathin nanostructures made out of nonlayered materials.

Edge-stress-induced spontaneous twisting of graphene nanoribbons Ramasubramaniam, A.; Koskinen, Pekka; Kit, Oleg; Shenoy, V.B. We present a continuum model for spontaneous twisting of graphene nanoribbons driven by compressive edge stresses. Based on a geometrically nonlinear theory of plates, we identify scaling laws for the dependence of twist angles on ribbon width. Strikingly, we find the existence of a critical width below which a ribbon will not undergo spontaneous twisting, preferring an in-plane stretching mode instead. The model predictions are shown to be in excellent qualitative and quantitative agreement with density-functional tight-binding simulations. More generally, our model provides a unifying picture of twisting in graphene nanoribbons with different edge orientations and chemical functionalizations that have been reported recently in the literature. V C 2012 American Institute of Physics. [http://dx.

We propose distinct element method modeling of carbon nanotube systems. The atomic-level description of an individual nanotube is coarse-grained into a chain of spherical elements that interact by parallel bonds located at their contacts. The spherical elements can lump multiple translational unit cells of the carbon nanotube and have both translational and rotational degrees of freedom. The discrete long ranged interaction between nanotubes is included in a van der Waals contact of nonmechanical nature that acts simultaneously with the parallel bonds. The created mesoscopic model is put into service by simulating a realistic carbon nanotube ring. The ring morphology arises from the energy balance stored in both parallel and van der Waals bonds.