Development of a Mathematical Model to Investigate the Effects of Couple and Surface Stresses in Axisymmetric Surface-Loaded

Abstract

This research presents a mathematical model for analyzing the mechanical behavior of multilayered nanoscale materials under axisymmetric surface loading. The materials are assumed to be homogeneous, isotropic, and exhibit linear elasticity governed by couple stress and surface stress theories. Hankel integral transforms and stiffness matrices are employed to obtain closed-form solutions for stress, displacement, and couple stress, while incorporating surface stress effects at the surface and interfaces.

The findings indicate that increasing the number of material layers enhances the overall stiffness and reduces surface deformation, particularly in systems with on an elastic half-space. The proposed model provides an effective framework for understanding size-dependent mechanical responses, offering valuable insights for the design and optimization of advanced multilayered coatings in micro- and nanoscale applications.