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Simple deformation measures for Discrete elastic rods and ribbons

Korner, Kevin and Audoly, Basile and Bhattacharya, Kaushik (2021) Simple deformation measures for Discrete elastic rods and ribbons. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210809-205939039

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Abstract

The Discrete elastic rod method (Bergou et al., 2008) is a numerical method for simulating slender elastic bodies. It works by representing the center-line 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, which is equally consistent with the continuous rod model. The first and second gradients of the discrete deformation measures are derived in compact form, making it possible to evaluate the Hessian of the discrete strain energy exactly. A few numerical illustrations are given. The approach is also extended to the simulation of inextensible ribbons described by the Wunderlich model; both the developability constraint and the dependence of the energy of the strain gradients are handled naturally.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2107.04842arXivDiscussion Paper
http://dx.doi.org/10.22002/D1.2024DOISource code
ORCID:
AuthorORCID
Korner, Kevin0000-0002-2967-9657
Audoly, Basile0000-0002-0534-1467
Bhattacharya, Kaushik0000-0003-2908-5469
Additional Information:The source code used for the numerical simulation is available through CaltechDATA at https://data.caltech.edu/records/2024. All three authors conceived of the work and the formulation. KK conducted the theoretical and numerical calculations with advice from BA and KB. KK and BA took the lead in writing the manuscript and all three authors finalized it. The authors declare that there are no competing interests. The work began when BA visited Caltech as a Moore Distinguished Scholar. KK and KB gratefully acknowledge the support of the US Office of Naval Research through Multi-investigator University Research Initiative Grant ONR N00014-18-1-2624.
Funders:
Funding AgencyGrant Number
Gordon and Betty Moore FoundationUNSPECIFIED
Office of Naval Research (ONR)N00014-18-1-2624
DOI:10.22002/D1.2024
Record Number:CaltechAUTHORS:20210809-205939039
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210809-205939039
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110178
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:09 Aug 2021 21:21
Last Modified:16 Nov 2021 19:39

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