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

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.

Numerical study of contacts between a flat-ended punch and a half-space embedded with inhomogeneities

This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities.Based on the semi-analytical method(SAM)and the equivalent inclusion method,numerical procedures were developed and the effects of inclusion shape and distribution were analyzed.Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress.Interactions of inter-inclusions and inclusion-matrix were taken into account.Numerical results showed the presence of inhomogeneities(i.e.,microstructures in solids)indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions.The effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions.The physical significance of this study is to provide an insight into the relation between the material microstructure and its response to the external load,and the solution approach and procedures may find useful applications,for example,the analysis of fatigue and crack propagation for composite materials,prediction of stress field in solids containing material defects,and study of the mechanism of chemical-mechanical polish(CMP)for inhomogeneous materials,etc.