{"title":"Eulerian Formulation of the Constitutive Relation for an Electro-Magneto-Elastic Material Class","authors":"Deepak Kumar","doi":"10.1007/s11223-024-00678-w","DOIUrl":null,"url":null,"abstract":"<p>A novel class of electro-magneto-elastic (EME) materials comprises electro-active and magneto-active particles in the polymer matrix that change their elastic behavior with an applied electromagnetic field. The material response for such a material class is usually formulated using Lagrangian strain tensor and Lagrangian electromagnetic field vectors as “push forward” to the current configuration. This article presents a novel formulation of an electro-magnetoelasticity in terms of an Eulerian strain tensor and Eulerian electromagnetic field vectors referring to the current configuration. Such an Eulerian formulation is often favorable from both theoretical and computational standpoints, which avoids the “push forward” operation to get the current configuration. An exercise to deduce the constitutive relation for an EME material class available in the existing literature from the newly proposed relation is also illustrated.</p>","PeriodicalId":22007,"journal":{"name":"Strength of Materials","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Strength of Materials","FirstCategoryId":"88","ListUrlMain":"https://doi.org/10.1007/s11223-024-00678-w","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATERIALS SCIENCE, CHARACTERIZATION & TESTING","Score":null,"Total":0}
引用次数: 0
Abstract
A novel class of electro-magneto-elastic (EME) materials comprises electro-active and magneto-active particles in the polymer matrix that change their elastic behavior with an applied electromagnetic field. The material response for such a material class is usually formulated using Lagrangian strain tensor and Lagrangian electromagnetic field vectors as “push forward” to the current configuration. This article presents a novel formulation of an electro-magnetoelasticity in terms of an Eulerian strain tensor and Eulerian electromagnetic field vectors referring to the current configuration. Such an Eulerian formulation is often favorable from both theoretical and computational standpoints, which avoids the “push forward” operation to get the current configuration. An exercise to deduce the constitutive relation for an EME material class available in the existing literature from the newly proposed relation is also illustrated.
期刊介绍:
Strength of Materials focuses on the strength of materials and structural components subjected to different types of force and thermal loadings, the limiting strength criteria of structures, and the theory of strength of structures. Consideration is given to actual operating conditions, problems of crack resistance and theories of failure, the theory of oscillations of real mechanical systems, and calculations of the stress-strain state of structural components.