Semi-analytical Modeling of the Influence of Macro Bending Effects on Micro Contact-Inhomogeneity Problems

Abstract

This study examines the effects of macroscopic bending and microscopic contact loading in inhomogeneous materials using a semi-analytical model based on Eshelby's equivalent inclusion method. The model accounts for bending effects through the beam theory, with bending stress included in the Eshelby's equivalent inclusion equations. The macroscopic displacement resulting from bending effects is incorporated into the microscopic contact solver, and the final displacement is determined using the conjugate gradient method in an iterative solution. Computational efficiency can be improved by incorporating the discrete convolution and fast Fourier transform. The core scheme is validated using the finite element method, yielding accurate and efficient results for bending-contact problems in inhomogeneous materials. Simulations reveal the interplay between bending, contact loading, and inhomogeneity, as stress around the inhomogeneity alters and the stress concentration area expands under increasing bending moments. Conversely, low-magnitude negative bending moments reduce both contact pressure and stress around the inhomogeneity. The position where inhomogeneities are least affected shifts from the neutral surface depending on the coupling effect. The model provides a valuable bridge for connecting the macroscopic bending effect and microscale contact-inhomogeneity problems by visualizing stress fields and assessing pressure distributions.