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A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams

Lestringant, Claire and Audoly, Basile and Kochmann, Dennis M. (2020) A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams. Computer Methods in Applied Mechanics and Engineering, 361 . Art. No. 112741. ISSN 0045-7825. https://resolver.caltech.edu/CaltechAUTHORS:20191121-100451756

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Abstract

We present an extension of a discrete, geometrically exact beam formulation based on discrete framed curves and discrete parallel transport originally introduced in the computer graphics community. In combination with variational constitutive updates, our numerical scheme decouples the kinematics from the material behavior, and can handle finite rotations as well as a wide class of constitutive laws depending on the stretching, flexural and torsional strain and strain rates. We demonstrate its capabilities through a suite of benchmark problems involving elastic, viscous and visco-elastic beams. The method fits naturally in existing finite element frameworks and is well suited to engineering applications. It can efficiently and accurately simulate the nonlinear deformation of slender beams featuring complex material behavior, such as those found in the topical design of flexible structural metamaterials.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.cma.2019.112741DOIArticle
ORCID:
AuthorORCID
Lestringant, Claire0000-0002-6929-4655
Audoly, Basile0000-0002-0534-1467
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2019 Elsevier B.V. Received 17 June 2019, Revised 30 October 2019, Accepted 6 November 2019, Available online 21 November 2019. D.M.K. gratefully acknowledge the support from the U.S. Office of Naval Research (ONR) through award N00014-16-1-2431. C.L. acknowledges support through an ETH Postdoctoral Fellowship. We thank Manuel Weberndorfer for fruitful discussions on the numerical implementation.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-16-1-2431
ETH ZürichUNSPECIFIED
Subject Keywords:Nonlinear beam theory; Finite element method; Constitutive model; Variational calculus
Record Number:CaltechAUTHORS:20191121-100451756
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191121-100451756
Official Citation:Claire Lestringant, Basile Audoly, Dennis M. Kochmann, A discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beams, Computer Methods in Applied Mechanics and Engineering, Volume 361, 2020, 112741, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2019.112741. (http://www.sciencedirect.com/science/article/pii/S0045782519306310)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99980
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Nov 2019 18:26
Last Modified:28 Jan 2020 18:35

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