Topological mechanical metamaterials: A brief review

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 (omega not equal 0) are related to elastic wave propagation and zero frequency properties (omega = 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.