<p>Elastic metamaterials have attracted significant research interest due to their ability to realize unique physical phenomena beyond those found in conventional materials. The exceptional properties of these metamaterials can be leveraged to achieve comprehensive control and manipulation of elastic waves in one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) mechanical structures. These extensive wave control capabilities have a wide range of potential applications, including energy harvesters, waveguides, isolators, filters, sensors, and cloaking devices. To improve the performance and extend the capabilities of elastic wave control, the concepts underpinning topological insulators in condensed matter physics have been extended to elastic metamaterials. Topological metamaterials exhibit localized wave transmission that is robust to disorder and defects. Initial studies into the elastic analogs of topological physics focused on wave control with zero-dimensional (0D) interface states in 1D structures (e.g., rod) and 1D interface (‘edge’) states in 2D structures (e.g., plate). Recently, investigations have shown 2D topological surface states in three-dimensional (3D) structures, which are more difficult to realize than 0D and 1D topological states. This obstacle is due to the inherent difficulties of manufacturing complex 3D mechanical structures and the presence of undesirable wave coupling and mode conversion that are a result of the three distinct mode polarizations contained in elastic systems. The initial studies on topological physics in 3D mechanical structures illustrate some of the many benefits that comprehensive 3D elastic wave control could provide, extending beyond what is achievable in 1D and 2D systems. However, each of the 3D elastic topological metamaterials developed to date are fixed and inflexible after fabrication, limiting their capabilities and potential in applications that require adaptivity to changing operating requirements and external conditions. Therefore, to advance the state of the art, this research proposes a tunable 3D elastic metamaterial that harnesses metastable states to reconfigure the spatial path of a topological 2D surface state. The metastability (<i>metastability</i> indicates the coexistence of multiple internal stable states under a constant global topology) of the metamaterial enables the reconfiguration of localized 2D topological surface states via the switching of bistable internal elements (between two stable states), thus avoiding the need for a continuous control signal. In this paper, a comprehensive numerical analysis is undertaken to develop the tunable 3D elastic metamaterial and obtain adaptive topological wave propagation. The dispersion relation of the metamaterial unit cell is numerically calculated using a finite element solver to identify a two-fold nodal line along the K-H line of high symmetry in reciprocal space. To reduce the symmetries that protect this nodal line and open a topological bandgap, some of the bistable internal elements are ‘switched’ to a new internal state. A switching methodology is developed to obtain topologically distinct lattices containing a band inversion. A supercell containing an interface between topologically distinct lattices is constructed, and calculation of the dispersion relation for the supercell reveals the presence of 2D topological surface states with displacement localized at the interface. Full-scale finite element simulations illustrate topological wave propagation in a 3D structure with a path that is tunable on-demand by switching internal states. The research outcomes presented in this paper could be beneficial to many potential applications requiring programmable and robust energy transport in 3D mechanical structures and serve as an inspiration for further work in adaptive 3D topological metamaterials. &nbsp;</p>

Tunable Topological Wave Control in a Three-Dimensional Metastable Elastic Metamaterial

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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