Des poutres flexibles aux fils extensibles: une hiérarchie de modèles asymptotiques

We consider slender (homogeneous, Isotropie) elastic cylinders submitted to conservative forces the intensity of which is a parameter. In the framework of the nonlinear three dimensional theory of elastostatics, by using asymptotic expansion methods, we obtain a hierarchy-depending on the order of magnitude of the applied forces-of five asymptotic unidimensional models, starting from the linear theory of flexible beams to the nonlinear theory of extensible strings. © Académie des Sciences/Elsevier, Paris