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.
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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Marigo, JJ., Meunier, N. Hierarchy of One-Dimensional Models in Nonlinear Elasticity. J Elasticity 83, 1–28 (2006). https://doi.org/10.1007/s10659-005-9036-y
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DOI: https://doi.org/10.1007/s10659-005-9036-y