Asymptotic modelling of a non-local elastic coating on a half-space with a sliding interface

In this paper, an isotropic half-space coated with a thin non-local elastic layer is considered. The interface separating the half-space and layer is assumed to be in sliding contact. An asymptotic method, valid for small layer thickness relative to the wavelength, is employed to derive effective boundary conditions that capture non-local effects through local field quantities. This method reduces the original non-local problem to a classical local elasticity problem with modified surface conditions. The approach is validated through Rayleigh wave analysis, where the resulting dispersion relation shows excellent agreement with full non-local models. The results demonstrate a practical and accurate framework for modelling wave propagation in coated microstructured media.