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Published December 2021 | Submitted
Journal Article Open

Simple deformation measures for discrete elastic rods and ribbons


The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph. 27, 63:1–63:12. (doi:10.1145/1360612.1360662)) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Additional Information

© 2021 The Author(s). Published by the Royal Society. Manuscript received 10/07/2021; Manuscript accepted 02/11/2021; Published online 08/12/2021; Published in print 22/12/2021. The work began when B.A. visited Caltech as a Moore Distinguished Scholar. K.K. and K.B. gratefully acknowledge the support of the US Office of Naval Research through Multi-investigator University Research Initiative grant no. ONR N00014-18-1-2624. Data accessibility: The source code used for the numerical simulation is available through CaltechDATA at https://data.caltech.edu/badge/latestdoi/425059053. Authors' contributions: All three authors conceived of the work and the formulation. K.K. conducted the theoretical and numerical calculations with advice from B.A. and K.B. K.K. and B.A. took the lead in writing the manuscript and all three authors finalized it. We declare we have no competing interests.

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August 20, 2023
October 23, 2023