Controlling and Guiding Stress Waves via Quantum Spin Hall-Based Phononic Topological Insulators
Abstract
Topological insulators (TIs) represent a new state of matter that have attracted significant attention because their properties, such as being a bulk insulator while simultaneously allowing wave propagation along its boundary, emerge from topology, rather than geometry. While offering significant potential in robustly guiding mechanical, electrical, photonic and acoustic wave energy, little is understood about the principles enabling topologically protected and controllable mechanical wave propagation in continuous media. One reason for this is that, despite the significant advances in electrical TIs, particularly in terms of the quantum hall and quantum spin hall-based physics that must be satisfied for the material to be an electrical TI, a similar set of well-defined mathematical conditions that must be satisfied to ensure TI behavior in continuous phononic systems has not emerged. Another important reason is that most of the theoretical and experimental works on phononic TIs have been based on discrete spring-mass, or discrete oscillator representations, rather than in continuous structures. As a result, the fundamental multi- scale understanding needed to translate concepts developed for discrete, electronic TIs to continuous phononic TIs remains lacking. We aim to mimic and adapt the conditions that must be met for discrete electronic quantum spin hall- based TIs, such that we can rationally design continuous phononic TIs to control and guide mechanical stress waves. We aim to develop novel computational topology optimization techniques to pursue some of the fundamental and unresolved questions regarding the mathematical conditions that must be satisfied to enable continuous, phononic TIs. Specifically: (1) Can we mimic spin degeneracy and band inversion in phononic TIs at arbitrary frequencies and for arbitrary mode numbers? (2) Can we generate structure-property relationships for phononic TIs from the optimized structures and unit cells that exhibit topologically non-trivial band structures? (3) Can we tune and maximize the phononic bandgap for stress wave propagation using topology optimization? (4) Can we determine the spatio-temporal forces that should be applied to the phononic TIs to break time-reversal symmetry, and thus enable non- reciprocal stress wave guiding and propagation? If successful, we anticipate several significant benefits and contributions to the ArmyÕs mission. First, we will understand the mechanisms governing topologically protected wave propagation in continuous solids. This understanding will be critical for enabling future developments in force- activated topological materials and structures that can guide and mitigate stress wave propagation to minimize structural damage. In addition, the successful development of a computational design tool for phononic TIs based rigorously on electronic quantum spin hall physics could enable a paradigm shift for ARL engineers in the design and analysis of wave guiding structures. Specifically, enabling realistic simulation-based studies and design of phononic TIs will significantly reduce the design cycle time from concept to application.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1810380
Entities
People
- Harold S. Park
Organizations
- Army Contracting Command
- Boston University
- United States Army