{"title":"Necessary conditions for stable equilibrium states of lattice solids based on the Cosserat elasticity theory","authors":"Milad Shirani , Mircea Bîrsan","doi":"10.1016/j.mechmat.2025.105292","DOIUrl":null,"url":null,"abstract":"<div><div>In this work, we derive the necessary conditions for stable equilibrium states for fibrous materials and lattice solids. We use Cosserat elasticity to obtain balance laws and boundary conditions by minimizing the total potential energy. Afterward, we find conditions that have to be satisfied by the solutions of the balance laws and boundary conditions. These conditions are quasi-convexity condition, ordinary convexity condition, and Legendre–Hadamard inequalities. For the surfaces of discontinuity, we derive Maxwell–Eshelby relations.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"204 ","pages":"Article 105292"},"PeriodicalIF":3.4000,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Materials","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167663625000547","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this work, we derive the necessary conditions for stable equilibrium states for fibrous materials and lattice solids. We use Cosserat elasticity to obtain balance laws and boundary conditions by minimizing the total potential energy. Afterward, we find conditions that have to be satisfied by the solutions of the balance laws and boundary conditions. These conditions are quasi-convexity condition, ordinary convexity condition, and Legendre–Hadamard inequalities. For the surfaces of discontinuity, we derive Maxwell–Eshelby relations.
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Mechanics of Materials is a forum for original scientific research on the flow, fracture, and general constitutive behavior of geophysical, geotechnical and technological materials, with balanced coverage of advanced technological and natural materials, with balanced coverage of theoretical, experimental, and field investigations. Of special concern are macroscopic predictions based on microscopic models, identification of microscopic structures from limited overall macroscopic data, experimental and field results that lead to fundamental understanding of the behavior of materials, and coordinated experimental and analytical investigations that culminate in theories with predictive quality.
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