{"title":"M-integral for finite anti-plane shear of a nonlinear elastic matrix with rigid inclusions","authors":"Victor A. Eremeyev , Konstantin Naumenko","doi":"10.1016/j.ijengsci.2023.104009","DOIUrl":null,"url":null,"abstract":"<div><p>The path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem of rigid inclusions embedded in a Mooney–Rivlin matrix material. With the derived M-integral we compute weighted averages of the shear stress acting on the inclusion surface. Furthermore, we prove that a system of rigid inclusions can be replaced by one effective inclusion.</p></div>","PeriodicalId":14053,"journal":{"name":"International Journal of Engineering Science","volume":"196 ","pages":"Article 104009"},"PeriodicalIF":5.7000,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020722523002008/pdfft?md5=e67d61d8bb70d72a6da796b7b00a6269&pid=1-s2.0-S0020722523002008-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Engineering Science","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0020722523002008","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The path-independent M-integral plays an important role in analysis of solids with inhomogeneities. However, the available applications are almost limited to linear-elastic or physically non-linear power law type materials under the assumption of infinitesimal strains. In this paper we formulate the M-integral for a class of hyperelastic solids undergoing finite anti-plane shear deformation. As an application we consider the problem of rigid inclusions embedded in a Mooney–Rivlin matrix material. With the derived M-integral we compute weighted averages of the shear stress acting on the inclusion surface. Furthermore, we prove that a system of rigid inclusions can be replaced by one effective inclusion.
与路径无关的 M 积分在分析具有不均匀性的固体时发挥着重要作用。然而，现有的应用几乎仅限于线弹性或物理上非线性的幂律型材料，而且是在无穷小应变的假设下。在本文中，我们提出了一类发生有限反平面剪切变形的超弹性固体的 M 积分。作为应用，我们考虑了嵌入穆尼-里夫林矩阵材料中的刚性夹杂物问题。利用推导出的 M 积分，我们计算了作用于夹杂物表面的剪应力的加权平均值。此外，我们还证明了刚性夹杂物系统可以由一个有效夹杂物代替。
期刊介绍：
The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome.
The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process.
Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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