Journal of Elasticity

, 83:1 | Cite as

Hierarchy of One-Dimensional Models in Nonlinear Elasticity

Open Access
Article

Abstract

By using formal asymptotic expansions, we build one-dimensional models for slender hyperelastic cylinders submitted to conservative loads. According to the order of magnitude of the applied loads, we obtain a hierarchy of models going from the linear theory of flexible bars to the nonlinear theory of extensible strings.

Key words

elasticity rods strings asymptotic expansions variational methods 

Mathematics Subject Classifications (2000)

74K10 74B05 74G65 74G10 35A15 35C20 

Résumé

On construit, à l'aide de développements asymptotiques formels, des modèles unidimensionnels de cylindres hyperélastiques élancés soumis à des forces conservatives. Suivant l'ordre de grandeur des forces appliquées, on obtient une hiérarchie de modèles allant de la théorie des poutres flexibles jusqu'à la théorie des fils élastiques.

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Laboratoire de Modélisation en Mécanique (UMR 7607)Université Pierre et Marie CurieParis cedex 05France
  2. 2.Laboratoire Jacques-Louis Lions (UMR 7598)Université Pierre et Marie CurieParisFrance

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