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.

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.

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.

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.

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.