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Published October 18, 2017 | Submitted
Journal Article Open

Nonlinear coherent structures in granular crystals


The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

Additional Information

© 2017 IOP Publishing Ltd. Received 30 March 2016; Accepted 1 June 2017; Published 6 September 2017. This material is based upon work supported by the National Science Foundation via grant number DMS-1615037. PGK gratefully acknowledges the support of the US Air Force Office of Scientific Research via grant number FA9550-12-1-0332 of the ERC under FP7; the Marie Curie Actions, People, International Research Staff Exchange Scheme (IRSES-605096); the ARO via grant number W911NF-15-1-0604; and the Alexander von Humboldt Foundation. CD acknowledges support from the U.S. Air Force Office of Scientific Research via grant number FA9550-12-1-0091.

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August 19, 2023
October 17, 2023