{"title":"小体积分数极硬各向异性纤维增强各向异性弹性材料的均匀化。非局部效应。弯曲的影响。扭转效应","authors":"Michel Bellieud","doi":"10.1007/s10659-023-09986-9","DOIUrl":null,"url":null,"abstract":"<div><p>We study the homogenization of a linear elastic solid reinforced by a small volume fraction of very stiff fibers. The effective material is characterized by the emergence of concentrations of strain energies around and within the fibers. The former is expressed in terms of the discrepancy appearing between the averaged effective displacements in the fibers and in the matrix, by means of a tensor-valued capacity of the cross-sections of the fibers. The latter corresponds to a combination of stretching, bending and torsional energies, where the torsional contribution is specific to anisotropic constitutive components.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Homogenization of an Anisotropic Elastic Material Reinforced by a Small Volume Fraction of Very Stiff Anisotropic Fibers. Non Local Effects. Bending Effects. Torsional Effects\",\"authors\":\"Michel Bellieud\",\"doi\":\"10.1007/s10659-023-09986-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the homogenization of a linear elastic solid reinforced by a small volume fraction of very stiff fibers. The effective material is characterized by the emergence of concentrations of strain energies around and within the fibers. The former is expressed in terms of the discrepancy appearing between the averaged effective displacements in the fibers and in the matrix, by means of a tensor-valued capacity of the cross-sections of the fibers. The latter corresponds to a combination of stretching, bending and torsional energies, where the torsional contribution is specific to anisotropic constitutive components.</p></div>\",\"PeriodicalId\":624,\"journal\":{\"name\":\"Journal of Elasticity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Elasticity\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10659-023-09986-9\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-023-09986-9","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Homogenization of an Anisotropic Elastic Material Reinforced by a Small Volume Fraction of Very Stiff Anisotropic Fibers. Non Local Effects. Bending Effects. Torsional Effects
We study the homogenization of a linear elastic solid reinforced by a small volume fraction of very stiff fibers. The effective material is characterized by the emergence of concentrations of strain energies around and within the fibers. The former is expressed in terms of the discrepancy appearing between the averaged effective displacements in the fibers and in the matrix, by means of a tensor-valued capacity of the cross-sections of the fibers. The latter corresponds to a combination of stretching, bending and torsional energies, where the torsional contribution is specific to anisotropic constitutive components.
期刊介绍:
The Journal of Elasticity was founded in 1971 by Marvin Stippes (1922-1979), with its main purpose being to report original and significant discoveries in elasticity. The Journal has broadened in scope over the years to include original contributions in the physical and mathematical science of solids. The areas of rational mechanics, mechanics of materials, including theories of soft materials, biomechanics, and engineering sciences that contribute to fundamental advancements in understanding and predicting the complex behavior of solids are particularly welcomed. The role of elasticity in all such behavior is well recognized and reporting significant discoveries in elasticity remains important to the Journal, as is its relation to thermal and mass transport, electromagnetism, and chemical reactions. Fundamental research that applies the concepts of physics and elements of applied mathematical science is of particular interest. Original research contributions will appear as either full research papers or research notes. Well-documented historical essays and reviews also are welcomed. Materials that will prove effective in teaching will appear as classroom notes. Computational and/or experimental investigations that emphasize relationships to the modeling of the novel physical behavior of solids at all scales are of interest. Guidance principles for content are to be found in the current interests of the Editorial Board.