Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Brianna MacNider, Haning Xiu, Caglar Tamur, Kai Qian, Ian Frankel, Maya Brandy, Hyunsun Alicia Kim and Nicholas Boechler ()
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Brianna MacNider: University of California, San Diego
Haning Xiu: University of California, San Diego
Caglar Tamur: University of California, San Diego
Kai Qian: University of California, San Diego
Ian Frankel: University of California, San Diego
Maya Brandy: University of California, San Diego
Hyunsun Alicia Kim: University of California, San Diego
Nicholas Boechler: University of California, San Diego

Nature Communications, 2025, vol. 16, issue 1, 1-14

Abstract: Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Date: 2025
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DOI: 10.1038/s41467-025-58630-8

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