{"title":"Data-Based Approach to Hyperelastic Membranes","authors":"Claudia Grabs, Werner Wirges","doi":"10.1007/s10659-025-10155-3","DOIUrl":null,"url":null,"abstract":"<div><p>We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying three-dimensional formulation. To assess the predictive capabilities of membrane theory, we compare numerical solutions to experimental data from axisymmetric deformations of a silicone rubber film. Five hyperelastic models—Neo-Hookean, Mooney-Rivlin, Gent, Yeoh, and Ogden—are evaluated by fitting their material parameters to our experimental data using TensorFlow. Our results provide a systematic comparison of these models based on their accuracy in capturing observed deformations, establishing a framework for integrating theory, experiment, and data-based parameter identification.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-025-10155-3","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 study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying three-dimensional formulation. To assess the predictive capabilities of membrane theory, we compare numerical solutions to experimental data from axisymmetric deformations of a silicone rubber film. Five hyperelastic models—Neo-Hookean, Mooney-Rivlin, Gent, Yeoh, and Ogden—are evaluated by fitting their material parameters to our experimental data using TensorFlow. Our results provide a systematic comparison of these models based on their accuracy in capturing observed deformations, establishing a framework for integrating theory, experiment, and data-based parameter identification.
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.
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