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A convenient formulation of Sadowsky model for elastic ribbons

Abstract : Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspectratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviors and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings to the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.
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Contributor : Sébastien Neukirch Connect in order to contact the contributor
Submitted on : Monday, July 5, 2021 - 7:32:21 PM
Last modification on : Monday, October 18, 2021 - 11:51:07 AM
Long-term archiving on: : Wednesday, October 6, 2021 - 9:29:20 PM


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  • HAL Id : hal-03278697, version 1


Sébastien Neukirch, Basile Audoly. A convenient formulation of Sadowsky model for elastic ribbons. 2021. ⟨hal-03278697v1⟩



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