Recently, higher-order topological insulators (HOTIs) as a novel frontier of topological phases of matter have been induced in mechanical systems, opening new routes to manipulate the propagation of elastic waves. Here, second-order mechanical topological insulators (SMTIs) implemented by mechanical metamaterials are systematically investigated in the rectangular lattice, the kagome lattice, the square lattice and the hexagonal lattice. The mechanical metamaterials are constructed from the generalized 2D Su–Schrieffer–Heeger (SSH) models. The topological mechanical metamaterials are characterized by the theories of topological indices and Wannier centers. With simulations and experiments, the corner states and edge states are observed in the topological mechanical metamaterials. Interestingly, the numbers of corner, edge and bulk states are respectively equal to the number of sites located at the corners, edges and bulk. This work offers an inspiring and unified model to study the higher-order topology in mechanical systems, and provides a new way for designing functional and integrated topological devices.

最近，在机械系统中引入了高阶拓扑绝缘体（HOTI）作为物质拓扑相的新前沿，开辟了操纵弹性波传播的新途径。在这里，在矩形晶格、kagome 晶格、正方形晶格和六角晶格中系统地研究了由机械超材料实现的二阶机械拓扑绝缘体 (SMTI)。机械超材料由广义二维 Su–Schrieffer–Heeger (SSH) 模型构成。拓扑力学超材料的特征在于拓扑指数和瓦尼尔中心理论。通过模拟和实验，在拓扑机械超材料中观察到了角态和边缘态。有趣的是，角落的数量，边缘和体积状态分别等于位于角、边缘和体积的站点数。这项工作为研究机械系统中的高阶拓扑提供了一个鼓舞人心的统一模型，并为设计功能性和集成拓扑设备提供了一种新方法。