A new formula for elastic bending modulus of monolayer graphene is derived analytically from an empirical potential for solid-state carbon-carbon bonds. Two physical origins are identified for the non-vanishing bending modulus of the atomically thin graphene sheet, one due to the bond angle effect and the other resulting from the bond order term associated with dihedral angles. The analytical prediction compares closely with ab initio energy calculations. Pure bending of graphene monolayers are simulated by a molecular mechanics approach, showing slight nonlinearity and anisotropy in the tangent bending modulus as the bending curvature increases. An intrinsic coupling between bending and in-plane strain is noted for graphene monolayers rolled into carbon nanotubes.

The unique lattice structure and properties of graphene has drawn tremendous interests recently.By combining continuum and atomistic approaches, this paper investigates the mechanical properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear continuum mechanics is developed for graphene under both in-plane and bending deformation.Atomistic simulations are carried out to deduce the effective mechanical properties. It is found that graphene becomes highly nonlinear and anisotropic under finite-strain uniaxial stretch, and coupling between stretch and shear occurs except for stretching in the zigzag and armchair directions. The theoretical strength (fracture strain and fracture stress) of perfect graphene lattice also varies with the chiral direction of uniaxial stretch. By rolling graphene sheets into cylindrical tubes of various radii, the bending modulus of graphene is obtained. Buckling of graphene ribbons under uniaxial compression is simulated and the critical strain for the onset of buckling is compared to a linear buckling analysis.

Atomistic simulations are performed to study the nonlinear mechanical behavior of graphene nanoribbons under quasistatic uniaxial tension, emphasizing the effects of edge structures (armchair and zigzag, without and with hydrogen passivation) on elastic modulus and fracture strength. The numerical results are analyzed within a theoretical model of thermodynamics, which enables determination of the bulk strain energy density, the edge energy density and the hydrogen adsorption energy density as nonlinear functions of the applied strain based on static molecular mechanics simulations. These functions can be used to describe mechanical behavior of graphene nanoribbons from the initial linear elasticity to fracture. It is found that the initial Young's modulus of a graphene nanoribbon depends on the ribbon width and the edge chirality. Furthermore, it is found that the nominal strain to fracture is considerably lower for graphene nanoribbons with armchair edges than for ribbons with zigzag edges. Molecular dynamics simulations reveal two distinct fracture nucleation mechanisms: homogeneous nucleation for the zigzag-edged graphene nanoribbons and edgecontrolled heterogeneous nucleation for the armchair-edged ribbons. The modeling and simulations in this study highlight the atomistic mechanisms for the nonlinear mechanical behavior of graphene nanoribbons with the edge effects, which is potentially important for developing integrated graphene-based devices.

Change of the bonding environment at the free edges of graphene monolayer leads to excess edge energy and edge force, depending on the edge morphology (zigzag or armchair). By using a reactive empirical bond-order potential and atomistic simulations, we show that the excess edge energy in free-standing graphene nanoribbons can be partially relaxed by both in-plane and out-of-plane deformation. The excess edge energy and edge force are calculated for graphene nanoribbons with parallel zigzag or armchair edges. Depending on the longitudinal constraint, the compressive edge force leads to either in-plane elongation of the ribbon or out-of-plane buckling deformation. In the former case, the longitudinal strain is inversely proportional to the ribbon width. In the latter case, energy minimization predicts an intrinsic wavelength for edge buckling to be 6.2 nm along the zigzag edge and 8.0 nm along the armchair edge. For graphene nanoribbons of width less than the intrinsic wavelength, interaction between the two free edges becomes significant, leading to anti-phase correlation of the buckling waves.Comment: 8 pages, 10 figures, and 1 tabl

The remarkable mechanical properties of carbon nanotubes (CNTs) have generated a lot of interest in recent years. While CNTs are found to have ultra-high stiffness and strength, an enormous scatter is also observed in available laboratory results. This randomness is partly due to the presence of nanoscale defects, heterogeneities etc., and this paper studies the effects of randomly distributed Stone-Wales (SW or 5-7-7-5) defects on the mechanical properties of single-walled nanotubes (SWNTs) using the technique of atomistic simulation (AS). A Matern hard-core random field applied on a finite cylindrical surface is used to describe the spatial distribution of the Stone-Wales defects. We simulate a set of displacement controlled tensile loading up to fracture of SWNTs with (6,6) armchair and (10, 0) zigzag configurations and aspect ratio around 6. A modified Morse potential is adopted to model the interatomic forces. We found that fracture invariably initiates from a defect if one is present; for a defect-free tube the crack initiates at quite random locations. The force-displacement curve typically behaves almost linearly up to about half way, although there is no obvious yield point. Three mechanical properties -stiffness, ultimate strength and ultimate strain  are calculated from the simulated force and displacement time histories. The randomness in mechanical behavior resulting only from initial velocity distribution was found to be insignificant at room temperature. The mean values of stiffness, ultimate strength and ultimate strain of the tube decrease as the average number of defects increases although the coefficients of variation do not show such monotonic trend. The introduction of an additional defect has the most pronounced effect on the randomness in mechanical properties when the tube is originally defect free. We also found that, for a given mean number of defects in the tube, the zigzag configuration has less strength and less ultimate strain on the average, but more uncertainty in its stiffness and ultimate strain, compared with the armchair tube.

SUMMARYWe present a multiscale method that couples atomistic models with continuum mechanics. The method is based on an overlapping domain-decomposition scheme. Constraints are imposed by a Lagrange multiplier method to enforce displacement compatibility in the overlapping subdomain in which atomistic and continuum representations overlap. An efficient version of the method is developed for cases where the continuum can be modelled as a linear elastic material. An iterative scheme is utilized to optimize the coupled configuration. Conditions for the regularity of the constrained matrices are determined. A method for computing strain in atomistic models and handshake domains is formulated based on a moving least-square approximation which includes both extensional and angle-bending terms. It is shown that this method exactly computes the linear strain field. Applications to the fracture of defected single-layer atomic sheets and nanotubes are given.

Monitoring the spatio-temporal characteristics of microcirculation is crucial for studying the functional activities of biotissue and the mechanism of disease. However, conventional methods used to measure blood flow suffer from limited spatial resolution or the injection of exogenous substances or the need of scanning to obtain the dynamic of regional blood flow. Laser speckle imaging (LSI) technique makes up these disadvantages by obtaining the regional blood flow distribution with high spatio-temporal resolution without the need to scan. In this paper, LSI was introduced to investigate the dynamic responses of the rat mesenteric microcirculation to an incremental dose of phentolamine. The results showed that when the dose of phentolamine was less than 4 microg ml(-1), local application of phentolamine on the mesentery would increase the blood perfusion as the concentration increased. When the dose increased further, the improvement decreased. At a dose of 200 microg ml(-1), a microcirculation impediment was caused. At the same time, different responses between veinules and arterioles were manifested. These suggested that LSI is promising to be a useful contribution to drug development and testing.

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