{"title":"Semi-analytical Modeling of the Influence of Macro Bending Effects on Micro Contact-Inhomogeneity Problems","authors":"Jinran Li, Linlin Sun, Ning Zhao, Pu Li","doi":"10.1007/s10338-023-00421-z","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":50892,"journal":{"name":"Acta Mechanica Solida Sinica","volume":"36 6","pages":"860 - 874"},"PeriodicalIF":2.0000,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica Solida Sinica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10338-023-00421-z","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics.
The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables