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
e-mail: sebastien.neukirch (-atat-) upmc.fr
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A convenient formulation of sadowsky’s model for elastic ribbons
Sébastien Neukirch, Basile Audoly
Proc. R. Soc. A, 477 (2021) 20210548
Abstract : Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect-ratios 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 Moebius 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.
Key words : boundary value problems; elastic plates; twisted rods
HAL version: hal-03278697
journal version: PDF
supplementary material: 10.6084/m9.figshare.c.5705318
1st sent July 5th, 2021
Reviews received Oct. 14th, 2021
Accepted Oct. 20th, 2021
Reviewer 1
This paper addresses a very important theoretical problem which has a wide range of applications. It definitely deserves publication.Reviewer 2
