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.

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.

Some recent experiments evidenced that the piezoelectric coefficients of such piezoelectric materials as PZT and BiTiO3 have an evident dependence on the grain size. With respect to the success of strain gradient theories in interpreting size effect phenomena of conventional (non-piezoelectric) solids and the dependence of piezoelectricity on rotation of polar clusters, a new piezoelectric theory with rotation gradient effects is formulated in the present paper to elucidate the size effect problems of piezoelectric solids. The constitutive relations of materials with different symmetries are specialized, and their corresponding independent material constants are discussed. For the typical 6 mm class of piezoelectric crystalline materials, a potential function method is presented for solving plane problems. The analytical solution of a thin piezoelectric film bonded on a rigid substrate illustrates the size-dependent prediction of the present theory.

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.

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.