Nonlinear Coherent Structures in Granular Crystals

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