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Published April 1, 2020 | public
Journal Article

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


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.

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.

Additional details

August 22, 2023
October 18, 2023