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.

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.

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.

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.

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.