Huygens-Kamerlingh Onnes Laboratory, Universiteit Leiden, P.O. Box 9504, NL-2300 RA Leiden, The Netherlands and AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands.
Phys Rev E. 2019 Aug;100(2-1):021001. doi: 10.1103/PhysRevE.100.021001.
Floppy modes-deformations that cost zero energy-are central to the mechanics of a wide class of systems. For disordered systems, such as random networks and particle packings, it is well-understood how the number of floppy modes is controlled by the topology of the connections. Here we uncover that symmetric geometries, present in, e.g., mechanical metamaterials, can feature an unlimited number of excess floppy modes that are absent in generic geometries, and in addition can support floppy modes that are multibranched. We study the number Δ of excess floppy modes by comparing generic and symmetric geometries with identical topologies, and show that Δ is extensive, peaks at intermediate connection densities, and exhibits mean-field scaling. We then develop an approximate yet accurate cluster counting algorithm that captures these findings. Finally, we leverage our insights to design metamaterials with multiple folding mechanisms.
柔度模式——零能量的变形——是广泛的系统力学的核心。对于无序系统，如随机网络和颗粒堆积，人们已经很好地理解了柔度模式的数量是如何受到连接拓扑结构的控制的。在这里，我们揭示了在例如机械超材料中存在的对称几何形状，可以具有无限数量的额外柔度模式，这些模式在一般几何形状中不存在，并且还可以支持多分支的柔度模式。我们通过比较具有相同拓扑结构的通用和对称几何形状来研究多余柔度模式的数量 Δ，并表明 Δ 是广泛的，在中间连接密度处达到峰值，并表现出平均场标度。然后，我们开发了一种近似但准确的聚类计数算法来捕获这些发现。最后，我们利用我们的见解来设计具有多种折叠机制的超材料。
