Surface/interface effects on the effective propagation constants of coherent waves in composites with random parallel nanofibers

Abstract

The effective propagation constants of elastic waves in an inhomogeneous medium with randomly distributed parallel cylindrical nanofibers are studied. First, the surface energy theory proposed by Huang and Wang (Handbook of Micromechanics and Nanomechanics, 2013) is used to derive the nontraditional boundary conditions on the surfaces of the nanoholes and the interfaces between the nanofibers and the host. Then, the scattering matrix of individual scatterer (cylindrical hole or nanofiber) is derived from the nontraditional boundary condition. The total wave field is obtained by considering the multiple scattering processes among the dispersive scatterers. The configuration average of the total wave field results in the coherent waves or the averaged waves. By using the corrected Linton-Martin formula, the effective propagation constants (effective speed and effective attenuation) of the coherent waves are estimated. The in-plane waves (P and SV waves) and the anti-plane waves (SH wave) are considered, respectively, and the numerical results are shown graphically. Apart from the effects of surface elasticity, the effects of inertia of surface/interface and the effects of residual surface tension (which are often ignored in the previous literature) are also considered. Moreover, the influences of the nonsymmetric parts of in-plane surface stress and the out-of-plane parts of the surface stress are both discussed first based on the numerical examples. These investigations show the underestimation and overestimation of effective propagation constants caused by various simplifications.