Topological elastic metamaterials for wave manipulation: a comprehensive review

In condensed matter physics, topological elastic metamaterials represent a pioneering field in the exploration of topological phases. Their unique characteristics enable a range of novel applications, including robust waveguiding, energy harvesting, and high-performance vibration control, which surpass the capabilities of conventional elastic materials. This review provides a comprehensive overview of topological elastic metamaterials, which are artificial composite materials designed to manipulate elastic waves through engineered microstructures and topological principles. Starting from the elastic metamaterials, the fundamental aspects of their unique properties, functional design for wave control, and the associated topological concepts and features were retrospectively examined. Subsequently, the topological elastic metama-terials, including their ability to support robust topological phases like the quantum Hall effect, quantum spin Hall effect, quantum valley Hall effect, and Weyl points were discussed. Finally, the latest developments in higher-order topological phases were explored, which offer further degrees of freedom for wave localization and control. Future research directions include the integration of nonlinearity and non-Hermitian effects, advanced intelligent design and fabrication techniques, and the development of multifunctional materials. Overall, topological elastic metamaterials represent a rapidly evolving field with significant potential for practical applications, and this paper provides a comprehensive overview while highlighting key future directions.