Refining boundary value problems in non-local micropolar mechanics

Abstract

This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous medium. This study revisits the solution for Rayleigh waves obtained within the framework of Eringen’s non-local differential model. It highlights that the equivalence between the non-local differential and integral formulations breaks down for a micropolar half-space and can only be restored under specific additional boundary conditions. For mathematical tractability, equivalence is assumed for a defined subset of stresses. Asymptotic analysis is further employed to capture the effects of the boundary layer within the non-local micropolar half-space. This technique finally derives the refined boundary conditions and as an application to Rayleigh wave propagation problem yields two distinct non-local corrected dispersion relations, with one mode unique to the micropolar characteristics. Phase velocity curves are plotted to describe the dispersion in Rayleigh waves propagating in various modes. Sensitivity analysis reveals the dependence of phase velocity on the non-local and micropolar parameters with Poisson’s ratio, thus providing valuable insights for material design and wave propagation control. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.