Gang-Feng Wang

Effects of surface elasticity and residual surface tension on the natural frequency of microbeams

Surface effects often play a significant role in the physical properties of micro- and nanosized materials and structures. In this letter, the authors presented a theoretical model directed towards investigation of the effects of both surface elasticity and residual surface tension on the natural frequency of microbeams. A thin surface layer was introduced on the upper and lower surfaces to rationalize the near-surface material properties that are different from the bulk material. An explicit solution is derived for the natural frequency of microbeams with surface effects. This study might be helpful for the design of microbeam-based sensors and some related measurement techniques.

SURFACE EFFECTS ON BUCKLING OF NANOWIRES UNDER UNIAXIAL COMPRESSION

Based on the conventional Euler buckling model, uniaxial compression tests have been utilized recently to measure the mechanical properties of nanowires. However, owing to the increasing ratio of surface area to bulk at nanoscale, the influence of surface energy becomes prominent and should be taken into consideration. In this letter, an analytical relation is given for the critical force of axial buckling of a nanowire by accounting for both the effects of surface elasticity and residual surface tension. This study might be helpful to characterize the mechanical properties of nanowires or design nanobeam-based devices in a wide range of applications.

Timoshenko beam model for buckling and vibration of nanowires with surface effects

In this paper, surface effects on the axial buckling and the transverse vibration of nanowires are examined by using the refined Timoshenko beam theory. The critical compression force of axial buckling and the natural frequency of nanowires are obtained analytically, in which the impacts of surface elasticity, residual surface stress, transverse shear deformation and rotary inertia have been included. The buckling and vibration behaviour of a nanowire is demonstrated to be size dependent, especially when its cross-sectional dimension reduces to nanometres. The surface effects with positive elastic constants tend to increase the critical compression force and the natural frequency, especially for slender nanowires, while the shear deformation lowers these values for stubby nanowires. This study may be helpful to accurately measure the mechanical properties of nanowires and to design nanowire-based devices and systems.

Surface effects on the diffraction of plane compressional waves by a nanosized circular hole

In the present letter, the authors consider the diffraction of plane harmonic compressional wave (P wave) by a nanosized circular hole. The surface elasticity theory is employed to incorporate the surface effects. The results show that once the radius of hole reduces to nanometers, surface energy significantly affects the diffraction of elastic waves. For incident waves with different frequencies, the influences of surface elasticity on dynamic stress concentration are discussed in details.

Effect of surface stresses on the vibration and buckling of piezoelectric nanowires

In this letter, we analyze the influence of surface stresses on the vibration and buckling behavior of piezoelectric nanowires by using the Euler-Bernoulli beam model. The effect of surface stresses is considered by applying a curvature-dependent distributed transverse loading along the beam. It is found that the resonant frequency of piezoelectric nanowires can be tuned by adjusting the applied electric potential, and its elastic constant and residual surface stress could be determined experimentally by measuring the critical electric potential at the occurrence of axial buckling. This study is helpful for design of nanowire-based devices and for characterization of the mechanical properties of nanowires.

Deformation around a nanosized elliptical hole with surface effect

In the present letter, the effect of surface energy on the deformation around an elliptical hole is analyzed, and the closed-form solution is obtained by the complex variable formulation. The results show that when the size of the hole reduces to the same order of the ratio of surface energy to applied stress, the contribution from surface becomes important, and the shape of the hole coupled with surface energy has significant effect on the elastic state around the hole.

Interface effects on effective elastic moduli of nanocrystalline materials

Interfaces often play a significant role in many physical properties and phenomena of nanocrystalline materials (NcMs). In the present paper, the interface effects on the effective elastic property of NcMs are investigated. First, an atomic potential method is suggested for estimating the effective elastic modulus of an interface phase. Then, the Mori–Tanaka effective field method is employed to determine the overall effective elastic moduli of a nanocrystalline material, which is regarded as a binary composite consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. Finally, the stiffening effects of strain gradients are examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Our analysis shows two physical mechanisms of interfaces that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the increased atomic spacings in interface regions, and another is the baffling effect due to the existence of boundary layers between the interface phase and the crystalline phase.

Surface Effects on the Near-Tip Stresses for Mode-I and Mode-III Cracks

Based on the surface elasticity theory and using a local asymptotic approach, we analyzed the influences of surface energy on the stress distributions near a blunt crack tip. The dependence relationship of the crack-tip stresses on surface elastic parameters is obtained for both mode-I and mode-III cracks. It is found that when the curvature radius of a crack front decreases to nanometers, surface energy significantly affects the stress intensities near the crack tip. Using a kind of surface elements, we also performed finite element simulations to examine the surface effects on the near-tip stresses. The obtained analytical solution agrees well with the numerical results.

Postbuckling analysis of nanowires with surface effects

Nanowires have many technological applications as manipulators, force sensors and probes in nano-electromechanical systems. With the increasing ratio of surface area to bulk, surface effects play an important role in the mechanical response of nanowires. In this paper, we consider the influence of residual surface stress and surface elasticity on the postbuckling state of nanowires. The geometric nonlinear finite deformation theory is adopted to describe the large deflection and the midplane stretching in postbuckling, and the shooting method is employed to obtain the postbuckling path and the buckled configurations. This study might be helpful to accurately calibrate the nanowire-based force sensors and design nanowire-based devices in a wide range of applications.

The Contact Problem in a Compressible Hyperelastic Material

We consider the contact problem for a particular class of compressible hyperelastic materials of harmonic type undergoing finite plane deformations. Using complex variable techniques, we derive subsidiary results concerning a half-plane problem corresponding to this class of materials. Using these results, we solve the contact problem for a harmonic material in the case of a uniform load acting on a finite area. Finally, we show how we can then deduce the corresponding results for the case of a point load.