Topological mechanical metamaterials have emerged with the development of topological phases and topological phase transitions in modern condensed matter physics. Their attractive topological properties provide promising applications that are hard to achieve with traditional mechanical metamaterials, such as waveguiding without backscattering loss, vibration isolation, and free motion of structures. In this review, we briefly retrospectively examine the most flourishing works on topological mechanical metamaterials and identify the mechanisms underlying these topological mechanical phases, such as analogs to quantum Hall effects and Weyl semimetals. Topological mechanical phases are classified into two categories of t depending on their behavior when working in different frequency domains, as finite frequency properties (ω ≠ 0) are related to elastic wave propagation and zero frequency properties (ω = 0) are related to quasi-static free motion. We conclude by outlining future challenges and opportunities for the topological mechanism, and the design/fabrication and application of topological mechanical metamaterials.

随着现代凝聚态物理中拓扑相和拓扑相变的发展，出现了拓扑机械超材料。它们引人入胜的拓扑特性提供了有希望的应用程序，而这些应用程序是传统的机械超材料所难以实现的，例如无后向散射损耗的波导，振动隔离和结构的自由运动。在这篇综述中，我们简要地回顾了拓扑机械超材料方面最繁荣的工作，并确定了这些拓扑机械相的基础机制，例如量子霍尔效应和Weyl半金属的类似物。根据拓扑机械相在不同频域中工作时的行为，它们分为t的两类，即有限的频率特性（ω≠0）与弹性波传播有关，零频率特性（ω= 0）与准静态自由运动有关。最后，我们概述了拓扑机制，拓扑机械超材料的设计/制造和应用的未来挑战和机遇。