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Published May 15, 2025 | Published
Journal Article Metadata-only

A multiscale design method using interpretable machine learning for phononic materials with closely interacting scales

Bastawrous, Mary V.1 ORCID icon
Chen, Zhi1 ORCID icon
Ogren, Alexander C.2 ORCID icon
Daraio, Chiara2 ORCID icon
Rudin, Cynthia1 ORCID icon
Brinson, L. Catherine1 ORCID icon
  • 1. ROR icon Duke University
  • 2. ROR icon California Institute of Technology
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Abstract

Manipulating the dispersive characteristics of vibrational waves is beneficial for many applications, e.g., high-precision instruments. architected hierarchical phononic materials have sparked promise tunability of elastodynamic waves and vibrations over multiple frequency ranges. In this article, hierarchical unit-cells are obtained, where features at each length scale result in a band gap within a targeted frequency range. Our novel approach, the "hierarchical unit-cell template method," is an interpretable machine-learning approach that uncovers global unit-cell shape/topology patterns corresponding to predefined band-gap objectives. A scale-separation effect is observed where the coarse-scale band-gap objective is mostly unaffected by the fine-scale features despite the closeness of their length scales, thus enabling an efficient hierarchical algorithm. Moreover, the hierarchical patterns revealed are not predefined or self-similar hierarchies as common in current hierarchical phononic materials. Thus, our approach offers a flexible and efficient method for the exploration of new regions in the hierarchical design space, extracting minimal effective patterns for inverse design in applications targeting multiple frequency ranges.

Copyright and License

© 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Funding

We acknowledge support for this work from the Department of Energy, United States under grant DE-SC0021358, and the National Science Foundation, United States under grants DGE-2022040 and OAC-1835782.

Contributions

Mary V. Bastawrous: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Project administration, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Zhi Chen: Writing – review & editing, Visualization, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Alexander C. Ogren: Validation, Software, Data curation. Chiara Daraio: Funding acquisition. Cynthia Rudin: Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization. L. Catherine Brinson: Writing – review & editing, Supervision, Project administration, Funding acquisition, Conceptualization.

Supplemental Material

Supporting Information is attached, containing more details on the hierarchical unit-cell template method, the solid-mechanics and finite-element formulation, and a few additional results.

  • Supporting Information A. Hierarchical unit-cell template method
  • Supporting Information B. Solid-mechanics model formulation and unit-cell Bloch analysis
  • Supporting Information C. Hierarchical templates optimal set results
  • Supporting Information D. Evolution of scale-transfer precision with band-gap width objective

Additional details

Funding Dates Caltech Custom Metadata
Created:
March 25, 2025
Modified:
March 25, 2025