{"title":"Some Remarks on the Principal Stretch Versus Invariant Formulation for Constitutive Modeling of Incompressible Isotropic Hyperelastic Materials","authors":"C. O. Horgan, J. G. Murphy","doi":"10.1007/s10659-025-10142-8","DOIUrl":null,"url":null,"abstract":"<div><p>It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10142-8.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Elasticity","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10659-025-10142-8","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
It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.
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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