Sébastien Neukirch
Institut Jean le Rond d'Alembert
Centre National de la Recherche Scientifique
Sorbonne Université, Campus Pierre et Marie Curie
Paris, Francetel: +33 1 44 27 72 61 (secr. 37 90)
e-mail: sebastien.neukirch (-atat-) sorbonne-universite.fr
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Jiayu Wang, Sara Lachat, Anaïs Abramian, Stéphanie Deboeuf, Sébastien Neukirch
Universal Response Curves for the Confined Elastica
Journal of the Mechanics and Physics of Solids, 216 (2026) 106778
Abstract : The confined Elastica is a model problem for several engineering applications such as bore-well drilling or endovascular surgery. As an Elastica is buckled into a rectangular cavity and bends into a series of folds, horizontal and vertical reaction forces work against the corresponding imposed displacements. The number of folds and the reaction forces exhibit complex bifurcations and snapping transitions, and multistability as well as hysteresis occur in this nonlinear problem. We show here that, despite this complexity, there exist universal curves for the reaction forces, the number of folds, and the bending energy of the Elastica. These, analytically derived, curves provide upper and lower bounds for the response of the system to the imposed confinement. Moreover we introduce a homogeneous solution to this packing problem, which describes the average behavior of the confined Elastica and allows us to understand, beyond the complex details of the problem, the overall response of the system as the confinement is increased.
Key words : elastic rods; fibrous packing; contactDOI: 10.1016/j.jmps.2026.106778 (open access)
HAL version: hal-05584154