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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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https://hal.archives-ouvertes.fr/hal-03278697
Contributor : Sébastien Neukirch Connect in order to contact the contributor
Submitted on : Tuesday, October 19, 2021 - 11:28:48 AM
Last modification on : Friday, December 3, 2021 - 11:42:56 AM

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  • HAL Id : hal-03278697, version 2

Citation

Sébastien Neukirch, Basile Audoly. A convenient formulation of Sadowsky model for elastic ribbons. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2021, 477, pp.20210548. ⟨hal-03278697v2⟩

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