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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MERCI: Mixed Curvature-Based Elements for Computing Equilibria of Thin Elastic Ribbons
Raphaël Charrondière, Sébastien Neukirch, and Florence Bertails-Descoubes
ACM Transactions on Graphics (TOG), 43 issue 5 (2024) art. 160
Abstract : Thin elastic ribbons represent a class of intermediary objects lying in-between thin elastic plates and thin elastic rods. Although the two latter families of thin structures have received much interest from the Computer Graphics community over the last decades, ribbons have seldom been considered and modelled numerically so far, in spite of a growing number of applications in Computer Design. In this paper, starting from the reduced developable ribbon models {sadowsky1929, wunderlich1962} recently popularised in Soft Matter Physics, we propose a both accurate and efficient algorithm for computing the statics of thin elastic ribbons. Inspired by the super-clothoid model for thin elastic rods, our method relies on compact ribbon elements whose normal curvature varies linearly with respect to arc length s, while their geodesic torsion is quadratic in s. In contrast however, for the sake of efficiency, our algorithm avoids building a fully reduced kinematic chain and instead treats each element independently, gluing them only at the final solving stage through well-chosen bilateral constraints.
DOI: 10.1145/3674502
pre-print version and supp. mat.: hal-04601301v2
journal version: PDF