{"title":"连接各向同性超弹性材料的弱非线性弹性理论","authors":"Yangkun Du, Nicholas A Hill, Xiaoyu Luo","doi":"10.1177/10812865241238985","DOIUrl":null,"url":null,"abstract":"Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"131 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials\",\"authors\":\"Yangkun Du, Nicholas A Hill, Xiaoyu Luo\",\"doi\":\"10.1177/10812865241238985\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.\",\"PeriodicalId\":49854,\"journal\":{\"name\":\"Mathematics and Mechanics of Solids\",\"volume\":\"131 1\",\"pages\":\"\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-04-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics and Mechanics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1177/10812865241238985\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATERIALS SCIENCE, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/10812865241238985","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials
Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.
期刊介绍:
Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science.
The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).