Session: 01-02-01: Topological Phononics

Paper Number: 165037

Automated Design of Topological Elastic Metamaterials via Band Morphology-Driven Optimization 

Architected materials, including metamaterials, derive their properties from internal geometry rather than chemical composition. Among them, elastic metamaterials enable unprecedented wave control, exhibiting phenomena such as bandgap formation, tunable anisotropy, negative refraction, and superfocusing. Recently, the introduction of topological principles has further expanded this landscape, enabling robust wave phenomena such as polarized elasticity and one-way edge and interface states that are immune against defects and perturbations. These effects arise from k-space topology, where band structure classification reveals topologically nontrivial phonon bands.

One promising approach for discovering mechanical metamaterials with prescribed properties is inverse design via topology optimization (TO), a methodology that strategically allocates material phases within a design domain using mechanics-based algorithms. TO has been applied to phononic structures to optimize wave control capabilities and, more recently, to design topological insulators.

Despite these advances, the systematic design of metamaterials with targeted topological phonon bands remains a challenge due to the complexity of translating topological principles into optimization objectives. Furthermore, theoretical studies have vastly outpaced experimental realizations, with only a relatively small subset being directly confirmed experimentally. This gap highlights the need for an inverse design framework that directly incorporates topological descriptors into the optimization process, enabling the creation of metamaterials with desired topological properties while ensuring structural feasibility for fabrication and testing.

This objective requires distilling topological band requirements into a parsimonious set of simple, mathematically expressible descriptors that can be effectively integrated into optimization algorithms. To address this, we implement the recently developed theory of topological quantum chemistry (TQC) as the foundation of our design strategy. TQC classifies topological bands based on symmetry properties at selected wavevectors, offering an efficient alternative to traditional methods that rely on detailed knowledge of Bloch wave functions across the entire BZ to define topological invariants. The Bilbao Crystallographic Server provides a systematic reference for determining whether a given band structure is topologically trivial or hosts symmetry-protected topological states.

By leveraging TQC, we identify a set of intuitive morphological band descriptors that serve as proxies for topology. These descriptors are incorporated into topology optimization algorithms, enabling the automated design of lattices with prescribed topological properties. This approach streamlines the discovery of new topological metamaterials with targeted band structures while also enabling the creation of a structured database. This database can be designed to pursue secondary objectives, such as tuning bandgap onsets and widths to match specific operational frequency regimes. Ultimately, this work paves the way for the transition from theoretical predictions to experimental realization.

Presenting Author: Pegah Azizi University of Minnesota

Presenting Author Biography: I am currently a PhD candidate at the University of Minnesota, conducting research under the guidance of Professor Gonella. My work revolves around the numerical simulation and experimental exploration, with a specific focus on periodic structures and topological mechanical metamaterials.

Authors:

Pegah Azizi University of Minnesota
Rahul Dev Kundu University of Illinois at Urbana-Champaign
Weichen Li University of Illinois at Urbana-Champaign
Kai Sun University of Michigan
Xiaojia Shelly Zhang University of Illinois at Urbana-Champaign
Stefano Gonella University of Minnesota