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Material heterogeneity induced by a surface or interface may be neglected at macroscale since the surface-to-volume ratio is usually small. However, its effect can become significant for structures at nanoscale with a large surface-to-volume ratio. In this paper, we incorporate such surface material heterogeneity into wave propagation analysis of a nanosized transversely isotropic cylinder. This is achieved by using the concept of surface elasticity. Instead of directly using the well-known Gurtin-Murdoch (GM) surface elasticity, we develop here another general framework based on a thin layer model. A novel approach based on state-space formalism is used to derive the approximate governing equations. Three different sources of surface effect can be identified in the first-order surface elasticity, i.e., the elasticity effect, the inertia effect and the thickness effect. It is found that the derived theory becomes identical to the GM surface elasticity if the thickness effect is dropped and when the material is isotropic. The axisymmetric wave propagation in a transversely isotropic cylinder with surface effect is then studied, and an exact solution is presented. Numerical results are finally given to show that the surface effect will play a very pronounced role in wave propagation in cylinders at nanoscale. [ABSTRACT FROM AUTHOR]

Homogenization methods utilizing classical elasticity-based Eshelby tensors cannot capture the particle size effect experimentally observed in particle-matrix composites at the micron and nanometer scales. In this paper, a new homogenization method for predicting effective elastic properties of multiphase composites is developed using Eshelby tensors based on a simplified strain gradient elasticity theory (SSGET), which contains a material length scale parameter and can account for the size effect. Based on the strain energy equivalence, a homogeneous comparison material obeying the SSGET is constructed, and two sets of equations for determining an effective elastic stiffness tensor and an effective material length scale parameter for the composite are derived. By using Eshelby's eigenstrain method and the Mori-Tanaka averaging scheme, the effective stiffness tensor based on the SSGET is analytically obtained, which depends not only on the volume fractions and shapes of the inhomogeneities (i.e., phases other than the matrix) but also on the inhomogeneity sizes, unlike what is predicted by the existing homogenization methods based on classical elasticity. To illustrate the newly developed homogenization method, sample cases are quantitatively studied for a two-phase composite filled with spherical, cylindrical, or ellipsoidal inhomogeneities (particles) using the averaged Eshelby tensors based on the SSGET that were derived earlier by the authors. Numerical results reveal that the particle size has a large influence on the effective Young's moduli when the particles are sufficiently small. In addition, the results show that the composite becomes stiffer when the particles get smaller, thereby capturing the particle size effect. [ABSTRACT FROM AUTHOR]