Nonlinear Coherent Structures in Granular Crystals

TL;DR

This paper reviews recent experimental, computational, and theoretical research on nonlinear coherent structures like solitary waves and breathers in one- and two-dimensional granular crystals, highlighting their dynamics and potential applications.

Contribution

It provides a comprehensive overview of recent advances in understanding nonlinear coherent structures in granular crystals, emphasizing experimental, computational, and theoretical perspectives.

Findings

Identification of traveling solitary waves and dispersive shock waves

Observation of long-lived discrete breathers and their dynamics

Discussion of open problems and engineering applications

Abstract

The study of granular crystals, 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, a type of nonlinear metamaterial, 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 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.