{"title":"A short note on minor and major symmetries in linear elasticity","authors":"Stefan Hartmann, Alexander Düster","doi":"10.1007/s00419-025-02879-4","DOIUrl":null,"url":null,"abstract":"<div><p>Simply applying the directional derivative either twice to the strain-energy density function (hyperelasticity) or once to the stress–strain state (Cauchy elasticity) does not lead to the symmetries of the fourth-order elasticity tensor specified in the literature. Moreover, there are many justifications and arguments for the desired symmetries, which are summarized in this contribution. Thus, a symmetrization operator has to be introduced to guarantee minor symmetry, since the symmetry of the strain tensor is frequently neglected but is needed to obtain results required for particular elasticity relations. A thorough investigation is provided for both Cauchy elasticity and hyperelasticity, and what conclusion can be drawn on by various assumptions.</p></div>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":"95 7","pages":""},"PeriodicalIF":2.5000,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00419-025-02879-4.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00419-025-02879-4","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
Simply applying the directional derivative either twice to the strain-energy density function (hyperelasticity) or once to the stress–strain state (Cauchy elasticity) does not lead to the symmetries of the fourth-order elasticity tensor specified in the literature. Moreover, there are many justifications and arguments for the desired symmetries, which are summarized in this contribution. Thus, a symmetrization operator has to be introduced to guarantee minor symmetry, since the symmetry of the strain tensor is frequently neglected but is needed to obtain results required for particular elasticity relations. A thorough investigation is provided for both Cauchy elasticity and hyperelasticity, and what conclusion can be drawn on by various assumptions.
期刊介绍：
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
