{"title":"A n-layered inclusion-based modeling to estimate permeability of multi-phase porous solids","authors":"V. H. Phan, V. Monchiet","doi":"10.1007/s00707-025-04331-8","DOIUrl":null,"url":null,"abstract":"<div><p>This paper concerns the determination of the permeability of multiporous solids in the framework of homogenization considering the Brinkman equation at the microscopic scale. We provide close form solutions for cylindrical and spherical unit cells constituted of <i>n</i>-layered concentric inclusions. Particular attention is paid to the choice of the conditions at the boundary of the unit cell. Specifically, four kind of boundary conditions are used in the literature and are analyzed here in the light of the Hill–Mandel lemma, leading to a hierarchy of the resulting estimate of the macroscopic permeability. Finally, comparisons for two-phase and three-phase porous solids are proposed and the accuracy of the estimates are compared with numerical solutions.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 6","pages":"3497 - 3513"},"PeriodicalIF":2.9000,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-025-04331-8","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper concerns the determination of the permeability of multiporous solids in the framework of homogenization considering the Brinkman equation at the microscopic scale. We provide close form solutions for cylindrical and spherical unit cells constituted of n-layered concentric inclusions. Particular attention is paid to the choice of the conditions at the boundary of the unit cell. Specifically, four kind of boundary conditions are used in the literature and are analyzed here in the light of the Hill–Mandel lemma, leading to a hierarchy of the resulting estimate of the macroscopic permeability. Finally, comparisons for two-phase and three-phase porous solids are proposed and the accuracy of the estimates are compared with numerical solutions.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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