{"title":"具有椭圆形不完全结合夹杂物的稀释固体悬浮液的弹性特性：边界、渐近、近似值","authors":"Martín I. Idiart, Valentin Gallican","doi":"10.1007/s10659-024-10071-y","DOIUrl":null,"url":null,"abstract":"<div><p>The elastic properties of dilute solid suspensions with imperfectly bonded inclusions of ellipsoidal shape are estimated. The imperfect bonding is regarded as a sharp interface across which the displacement jumps in proportion to the surface traction. Elastic compliances of the matrix and inclusion phases can exhibit arbitrary anisotropy while that of the bonding exhibits an anisotropy that depends on the interface normal only. A variational framework is employed to generate pairs of elementary bounds, asymptotically exact results, and approximations for the effective elasticity tensor. Each member of the pair differs in the way the bonding compliance is averaged over the interfacial surface: an ‘arithmetic’ mean in one case and a ‘harmonic’ mean in the other case. The results are used to infer the most convenient approximation for a given range of material parameters.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 3","pages":"701 - 719"},"PeriodicalIF":1.8000,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Elastic Properties of Dilute Solid Suspensions with Imperfectly Bonded Inclusions of Ellipsoidal Shape: Bounds, Asymptotics, Approximations\",\"authors\":\"Martín I. Idiart, Valentin Gallican\",\"doi\":\"10.1007/s10659-024-10071-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The elastic properties of dilute solid suspensions with imperfectly bonded inclusions of ellipsoidal shape are estimated. The imperfect bonding is regarded as a sharp interface across which the displacement jumps in proportion to the surface traction. Elastic compliances of the matrix and inclusion phases can exhibit arbitrary anisotropy while that of the bonding exhibits an anisotropy that depends on the interface normal only. A variational framework is employed to generate pairs of elementary bounds, asymptotically exact results, and approximations for the effective elasticity tensor. Each member of the pair differs in the way the bonding compliance is averaged over the interfacial surface: an ‘arithmetic’ mean in one case and a ‘harmonic’ mean in the other case. The results are used to infer the most convenient approximation for a given range of material parameters.</p></div>\",\"PeriodicalId\":624,\"journal\":{\"name\":\"Journal of Elasticity\",\"volume\":\"156 3\",\"pages\":\"701 - 719\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-05-17\",\"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/s10659-024-10071-y\",\"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/s10659-024-10071-y","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}
The Elastic Properties of Dilute Solid Suspensions with Imperfectly Bonded Inclusions of Ellipsoidal Shape: Bounds, Asymptotics, Approximations
The elastic properties of dilute solid suspensions with imperfectly bonded inclusions of ellipsoidal shape are estimated. The imperfect bonding is regarded as a sharp interface across which the displacement jumps in proportion to the surface traction. Elastic compliances of the matrix and inclusion phases can exhibit arbitrary anisotropy while that of the bonding exhibits an anisotropy that depends on the interface normal only. A variational framework is employed to generate pairs of elementary bounds, asymptotically exact results, and approximations for the effective elasticity tensor. Each member of the pair differs in the way the bonding compliance is averaged over the interfacial surface: an ‘arithmetic’ mean in one case and a ‘harmonic’ mean in the other case. The results are used to infer the most convenient approximation for a given range of material parameters.
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.
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