{"title":"A Direct Approach to the Polar Representation of Plane Tensors","authors":"Marco Picchi Scardaoni","doi":"10.1007/s10659-024-10085-6","DOIUrl":null,"url":null,"abstract":"<div><p>We show we can derive the so called polar representation of 2D symmetric second and fourth order real tensors essentially just relying on the spectral theorem for unitary tensors in the complex field. The use of a coordinate-free approach allows us to clearly and methodically detect rotation-invariant quantities and to readily (and directly) deduce the representation theorems.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 4-5","pages":"1065 - 1084"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-024-10085-6.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-024-10085-6","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}
引用次数: 0
Abstract
We show we can derive the so called polar representation of 2D symmetric second and fourth order real tensors essentially just relying on the spectral theorem for unitary tensors in the complex field. The use of a coordinate-free approach allows us to clearly and methodically detect rotation-invariant quantities and to readily (and directly) deduce the representation theorems.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
