Scattering of SH-waves by a nano-fiber beneath the interface of two bonded half-spaces within surface/interface elasticity via multipole expansion. (January 2018) - Ghafarollahi, A.; Shodja, H.M.
Abstract: The present work aims to study the anti-plane scattering of SH-waves by an elastic micro-/nano-fiber which is embedded near the interface between exponentially graded and homogeneous half-spaces incorporating interface effects. The fiber is perfectly bonded to the inhomogeneous medium. It is well-known that traditional elasticity theory is incapable of accounting accurately for the nanoscopic-interfaces and, likewise, inappropriate for the prediction of the behavior of nano-sized structures where the surface-to-volume ratio is remarkably large. In the present study, the interface effects are incorporated using the well-known (Gurtin and Murdoch, 1975) surface elasticity theory which permits the use of continuum-based models to examine deformation at the nano-scale. Formulation in the mathematical framework of surface/interface elasticity gives rise to a set of non-classical boundary conditions across the interfaces. The boundary value problem of interest is solved by constructing an appropriate set of multipole functions which satisfy the governing differential equations in each half-space and the boundary conditions along the interface between the two half-spaces. The exact analytical expressions for the amplitude ratios of the reflected and transmitted waves are shown to depend on the elasticity parameters of the interface between the two half-spaces, in addition to the classical parameters of the bulk of these media. In the given numerical examples, the inevitable role of interfaces in the presence of nano-structure is well approved and it is shown that the interface effect is particularly remarkable for short wavelengths which are comparable to the interface characteristic lengths.