Universal Response Curves for the Confined Elastica
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 an homogeneous solution to this packing problem, which describes the average behavior of the confined Elastica and allow us to understand, beyond the complex details of the problem, the overall response of the system as the confinement is increased.
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BibTeX
@article{wang2026universal,
title = {{Universal Response Curves for the Confined Elastica}},
author = {Jiayu Wang and Sara Lachat and Anaïs Abramian and Stéphanie Deboeuf and Sébastien Neukirch},
journal = {Journal of the Mechanics and Physics of Solids},
year = {2026},
month = jul,
doi = {10.1016/j.jmps.2026.106778},
url = {https://hal.science/hal-05584154v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Universal Response Curves for the Confined Elastica
AU - Jiayu Wang
AU - Sara Lachat
AU - Anaïs Abramian
AU - Stéphanie Deboeuf
AU - Sébastien Neukirch
PY - 2026
DA - 2026/07/22
JO - Journal of the Mechanics and Physics of Solids
DO - 10.1016/j.jmps.2026.106778
UR - https://hal.science/hal-05584154v2
AB - 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 an homogeneous solution to this packing problem, which describes the average behavior of the confined Elastica and allow us to understand, beyond the complex details of the problem, the overall response of the system as the confinement is increased.
SN - 0022-5096
ER -