Effect of Adhesion on a Beam with Surface Effects Interacting with an Elastic Foundation

Abstract

This study investigates the contact behavior of a long beam interacting with an elastic foundation under the influence of surface effects and adhesion forces. Using the Bernoulli-Euler beam theory and energy-based analysis, the research examines how surface residual stress and adhesion energy affect the beam's deformation and contact interaction. The analysis involves deriving governing equations for the beam's deflection in contact and separation regions, while the equilibrium configuration is determined by minimizing the total potential energy. This energy includes elastic strain, interface effects, and external work, enabling the determination of the beam's separation length and deformation profile. The results indicate that surface residual stress significantly reduces the sensitivity of the separation length to lifting forces due to increased stiffness at the contact interface. Conversely, when adhesion forces dominate, the separation length becomes more responsive to lifting forces. These contrasting effects underscore the interplay between surface stress and adhesion in determining the mechanical response of the beam. The findings contribute to a deeper understanding of microscale contact mechanics and provide essential insights for the design and optimization of MEMS and NEMS devices, where surface and adhesive forces critically influence performance.