G. F. Wang

Effects of surface stresses on contact problems at nanoscale

Based on the surface elasticity theory, we examined the effects of surface stresses on nanosized contact problems. The Fourier integral transform method is adopted to derive the general solution for the contact problem under pressure. As two examples, the deformations induced, respectively, by a uniform distributed pressure and a concentrated force are analyzed in detail. The results indicate some interesting characteristics in contact mechanics, which are distinctly different from those in classical elasticity theory. Both the contact normal stress and the deformation gradient on the deformed surface vary smoothly across the loading boundary as a result of surface stress. In addition, the indent depth and the maximum normal contact stress depend strongly on the surface stress for nanoindentation.

Interface effects on the diffraction of plane compressional waves by a nanosized spherical inclusion

Effects of surfaces/interfaces become prominent in micro- and nanosized materials and devices. In the present paper, the diffraction of plane harmonic compressional waves (P wave) by a spherical nanoinclusion is studied theoretically using the surface/interface elasticity theory. The results demonstrated that when the inclusion size shrinks to nanometers, surface/interface elasticity plays a significant role in the diffraction of elastic waves. For incident waves of different frequencies, the interface effects on the dynamic stress concentration around the spherical inclusion are examined in detail.

SURFACE BUCKLING OF A BENDING MICROBEAM DUE TO SURFACE ELASTICITY

In the present letter, we studied the surface buckling of a bending beam using the surface elasticity theory, and the corresponding buckling wave number was obtained analytically. It is found that surfaces with positive surface elastic modulus may buckle under compression, while surfaces with negative surface elastic modulus are possible to wrinkle irrespective of the sign of surface strain. By this method, various surface buckling phenomena happened in thin films or carbon nanotubes can be elucidated.

Multiple diffraction of plane compressional waves by two circular cylindrical holes with surface effects

In the present paper, the multiple diffraction of plane harmonic compressional waves (P-wave) by two nanosized circular cylindrical holes embedded in an elastic solid is investigated. The surface elasticity theory is adopted to account for the effect of surface energy at nanoscales. It is found that when the radii of holes reduce to nanometers, surface energy significantly affects the diffraction of elastic waves. The dynamic stresses around the holes under incident waves of different frequencies are examined to display the influence of surface energy and the interaction between holes in the multiple scattering phenomena.

Diffraction of shear waves by a nanosized spherical cavity

Surface effects become important in the mechanical performances of nanostructured devices and materials, owing to the increasing ratio of surface to bulk volume. In the present paper, the diffraction of shear waves (S-wave) by a nanosized spherical cavity is studied theoretically based on the surface elasticity theory. It is found that when the cavity size reduces to nanometers, surface effects play a significant role in the diffraction of elastic waves. As an example, the surface effects on the dynamic stress concentration around the spherical cavity are discussed in detail.

Beam characteristics of short-pulse radiation with electromagnetic missile effect

Beam characteristics such as beamwidth and beam intensity of short-pulse radiation with electromagnetic missile effect, not restricted to the electromagnetic missile, are generally range dependent in pulse propagation. An effective measure to study such beam characteristics is to investigate the local drop rate of the energy pattern in the beam profile and the local decay rate of energy in the pulse beam. It is shown that both the energy decay rate and the energy drop rate are definitely determined by the time–space source parameters so that the beam characteristics can be readily evaluated and properly controlled. Moreover, the underlying relation between the slow decay rate and the energy drop rate are constructed, which shows perfect harmony in achieving slower-energy decay and higher-energy concentration in the beam.

A remark on fast decay effect in the electromagnetic missile theory

The fast decay effect of energy in electromagnetic (EM) radiation as deduced from the EM missile theory is demonstrated to be unrealistic. The inferences drawn from the EM missile results involving such a fast decay effect must be modified by taking into account the contribution from the band-limited spectrum, which will yield reasonable results.

Influence of surface tension on fractal contact model

Almost all solid surfaces have roughness on different length scales, from macro, micro to nano. In the conventional fractal contact model, the macroscopic Hertzian contact theory is employed to predict the contact load-area relation for all sizes of contact spots. However, when the contact radius of an asperity shrinks to nanometers, surface tension may greatly alter the contact behavior. In the present paper, we address surface effects on the contact between a rigid sphere and an elastic half space, and we demonstrate that the contact load-area relation is size-dependent, especially for nanosized asperities. Then, the refined contact relation is incorporated into the Majumdar-Bhushan fractal contact model. It is found that the presence of surface tension requires higher load than the conventional fractal contact model to generate the same real contact area.

Influence of surface energy on the elastic compression of nanosphere

The influence of surface energy on the elastic compression of nanosphere is addressed through the principle of minimum potential energy. By using the displacement potential approach, the elastic field of nanosphere under diametrical compression is derived analytically. Firstly, surface energy induces a uniform pre-existing hydrostatic compression in the entire nanosphere. More importantly, when the ratio of surface energy density to the radius of sphere is comparable with the elastic modulus, the response of nanosphere to external loading will be evidently distinct from the classical prediction. When the compressive load-depth curve is used to calculate the elastic modulus of nanosphere, the presence of surface energy predicts the size dependence of elastic modulus, which enhances significantly as the radius of sphere decreases below 100 nm. This study provides an efficient tool to analyze the elastic deformation of nanoparticles and measure their elastic properties.