Bespoke extensional elasticity through helical lattice systems

Dixon, Maximillian D. X.; O'Donnell, Matthew P.; Pirrera, Alberto; Chenchiah, Isaac V.

Abstract

© 2019 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. Nonlinear structural behaviour offers a richness of response that cannot be replicated within a traditional linear design paradigm. However, designing robust and reliable nonlinearity remains a challenge, in part, due to the difficulty in describing the behaviour of nonlinear systems in an intuitive manner. Here, we present an approach that overcomes this difficulty by constructing an effectively one-dimensional system that can be tuned to produce bespoke nonlinear responses in a systematic and understandable manner. Specifically, given a continuous energy function E and a tolerance ℇ > 0, we construct a system whose energy is approximately E up to an additive constant, with L∞-error no more that ℇ. The system is composed of helical lattices that act as one-dimensional nonlinear springs in parallel. We demonstrate that the energy of the system can approximate any polynomial and, thus, by Weierstrass approximation theorem, any continuous function. We implement an algorithm to tune the geometry, stiffness and pre-strain of each lattice to obtain the desired system behaviour systematically. Examples are provided to show the richness of the design space and highlight how the system can exhibit increasingly complex behaviours including tailored deformation-dependent stiffness, snap-through buckling and multi-stability.

Citation

Dixon, M. D. X., O'Donnell, M. P., Pirrera, A., & Chenchiah, I. V. (2019). Bespoke extensional elasticity through helical lattice systems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475(2232), https://doi.org/10.1098/rspa.2019.0547

• Journal Article Type: Article
• Acceptance Date: Nov 4, 2019
• Online Publication Date: Dec 4, 2019
• Publication Date: Dec 4, 2019
• Deposit Date: May 5, 2020
• Publicly Available Date: May 6, 2020
• Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Electronic ISSN: 1471-2946
• Publisher: Royal Society, The
• Peer Reviewed: Peer Reviewed
• Volume: 475
• Issue: 2232
• DOI: https://doi.org/10.1098/rspa.2019.0547
• Public URL: https://uwe-repository.worktribe.com/output/5914750