Yingyan Zhang

Vibration of nonlocal Timoshenko beams

This paper is concerned with the free vibration problem for micro/nanobeams modelled after Eringens nonlocal elasticity theory and Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using Hamiltons principle. These equations are solved analytically for the vibration frequencies of beams with various end conditions. The vibration solutions obtained provide a better representation of the vibration behaviour of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. The exact vibration solutions should serve as benchmark results for verifying numerically obtained solutions based on other beam models and solution techniques.

Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory

This paper is concerned with the elastic buckling analysis of micro- and nano-rods/tubes based on Eringens nonlocal elasticity theory and the Timoshenko beam theory. In the former theory, the small scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. Explicit expressions for the critical buckling loads are derived for axially loaded rods/tubes with various end conditions. These expressions account for a better representation of the buckling behaviour of micro- and nano-rods/tubes where small scale effect and transverse shear deformation effect are significant. By comparing it with the classical beam theories, the sensitivity of the small scale effect on the buckling loads may be observed.

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

In this paper, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs). The calibration exercise is performed by using vibration frequencies generated from molecular dynamics simulations at room temperature. It was found that the calibrated values of e0 are rather different from published values of e0. Instead of a constant value, the calibrated e0 values vary with respect to length-to-diameter ratios, mode shapes, and boundary conditions of the SWCNTs. In addition, the physical meaning of the scaling parameter is explored. The results show that scaling parameter assists in converting the kinetic energy to the strain energy, thus enabling the kinetic energy to be equal to the strain energy. The calibrated e0 presented herein should be useful for researchers who are using the nonlocal beam theories for analysis of micro and nano beams/rods/tubes.

Mechanical properties of graphynes under tension: A molecular dynamics study

Graphyne is the allotrope of graphene. In this letter, four different graphynes (α, β, γ, and 6,6,12-graphenes) are investigated by molecular dynamics simulations to explore their mechanical properties and failure mechanisms. It is found that the presence of the acetylenic linkages in graphynes leads to a significant reduction in fracture stress and Young’s modulus with the degree of reduction being proportional to the percentage of the linkages. This deterioration in mechanical properties stems from the low atom density in graphynes and weak single bonds in the acetylenic linkages where the facture is initiated.

Bending, Buckling, and Vibration of Micro/Nanobeams by Hybrid Nonlocal Beam Model

The hybrid nonlocal Euler-Bernoulli beam model is applied for the bending, buckling, and vibration analyzes of micro/nanobeams. In the hybrid nonlocal model, the strain energy functional combines the local and nonlocal curvatures so as to ensure the presence of small length-scale parameters in the deflection expressions. Unlike Eringens nonlocal beam model that has only one small length-scale parameter, the hybrid nonlocal model has two independent small length-scale parameters, thereby allowing for a more flexible and accurate modeling of micro/nanobeamlike structures. The equations of motion of the hybrid nonlocal beam and the boundary conditions are derived using the principle of virtual work. These beam equations are solved analytically for the bending, buckling, and vibration responses. It will be shown herein that the hybrid nonlocal beam theory could overcome the paradoxes produced by Eringens nonlocal beam theory such as vanishing of the small length-scale effect in the deflection expression or the surprisingly stiffening effect against deflection for some classes of beam bending problems.

Recent Studies on Buckling of Carbon Nanotubes

This paper reviews recent research studies on the buckling of carbon nanotubes. The structure and properties of carbon nanotubes are introduced to the readers. The various buckling behaviors exhibited by carbon nanotubes are also presented herein. The main factors, such as dimensions, boundary conditions, temperature, strain rate, and chirality, influencing the buckling behaviors are also discussed, as well as a brief introduction of the two most used methods for analyzing carbon nanotubes, i.e., continuum models and atomistic simulations. Summary and recommendations for future research are also given. Finally, a large body of papers is given in the reference section. It is hoped that this paper provides current knowledge on the buckling of carbon nanotubes, reviews the computational methods for determining the buckling loads, and inspires researchers to further investigate the buckling properties of carbon nanotubes for practical applications.

Assessment of continuum mechanics models in predicting buckling strains of single-walled carbon nanotubes

This paper presents an assessment of continuum mechanics (beam and cylindrical shell) models in the prediction of critical buckling strains of axially loaded single-walled carbon nanotubes (SWCNTs). Molecular dynamics (MD) simulation results for SWCNTs with various aspect (length-to-diameter) ratios and diameters will be used as the reference solutions for this assessment exercise. From MD simulations, two distinct buckling modes are observed, i.e. the shell-type buckling mode, when the aspect ratios are small, and the beam-type mode, when the aspect ratios are large. For moderate aspect ratios, the SWCNTs buckle in a mixed beam-shell mode. Therefore one chooses either the beam or the shell model depending on the aspect ratio of the carbon nanotubes (CNTs). It will be shown herein that for SWCNTs with long aspect ratios, the local Euler beam results are comparable to MD simulation results carried out at room temperature. However, when the SWCNTs have moderate aspect ratios, it is necessary to use the more refined nonlocal beam theory or the Timoshenko beam model for a better prediction of the critical strain. For short SWCNTs with large diameters, the nonlocal shell model with the appropriate small length scale parameter can provide critical strains that are in good agreement with MD results. However, for short SWCNTs with small diameters, more work has to be done to refine the nonlocal cylindrical shell model for better prediction of critical strains.

Effect of chirality on buckling behavior of single-walled carbon nanotubes

In this paper, molecular dynamics simulations (MDS) are performed on single-walled carbon nanotubes (SWCNTs) in order to study the effects of chirality on their buckling behavior under axial compression. In the MDS, the Tersoff-Brenner potential is used to describe the interaction of carbon atoms in the SWCNTs. The sensitivity of the buckling strains and buckling modes with respect to the chirality of SWCNT is investigated by modeling SWCNTs with different chiral angles, varying from 0° to 30°, but keeping the length-to-diameter ratio constant. The carbon nanotubes are also analyzed using a continuum cylindrical shell model based on the theory of nonlocal elasticity so as to assess its validity in predicting the buckling strains when compared with the results that are obtained by MDS. The differences between the buckling strains at the continuum scale and that at the nanoscale are also studied. The present analysis and results are helpful in understanding the buckling behaviors of axially compressed carbo...

Effects of temperature and strain rate on the mechanical properties of silicene

Silicene, a graphene-like two-dimensional silicon, has attracted great attention due to its fascinating electronic properties similar to graphene and its compatibility with existing semiconducting technology. So far, the effects of temperature and strain rate on its mechanical properties remain unexplored. We investigate the mechanical properties of silicene under uniaxial tensile deformation by using molecular dynamics simulations. We find that the fracture strength and fracture strain of silicene are much higher than those of bulk silicon, though the Youngs modulus of silicene is lower than that of bulk silicon. An increase in temperature decreases the fracture strength and fracture strain of silicene significantly, while an increase in strain rate enhances them slightly. The fracture process of silicene is also studied and brittle fracture behavior is observed in the simulations.

Buckling of carbon nanotubes at high temperatures

Presented herein is an investigation into the buckling behavior of single-walled carbon nanotubes (SWCNT) subjected to axial compression and torsion at high temperatures. This study is carried out by performing molecular dynamics (MD) simulations at both room temperature and extremely high temperatures. It is observed that the SWCNT becomes more susceptible to buckling in a higher temperature environment, especially when the SWCNT is subject to axial compression. The high thermal energy enhances the vibration of carbon atoms in the SWCNT significantly, which leads to bond breaking and the formation of sp(3) bonds as well as Stone-Wales (SW) defects in the postbuckling stage.