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Golden-Ratio–Guided Aperiodic Architected Metamaterials with Simultaneously Enhanced Strength and Toughness

Lookup NU author(s): Dr Xinwei LiORCiD

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This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


Abstract

© 2025 The Author(s). Advanced Functional Materials published by Wiley-VCH GmbH.Architected lattice metamaterials offer tunable, exceptional mechanical performance through precisely engineered microarchitectures, yet an intrinsic trade-off between strength and toughness remains a fundamental design challenge. Here, a class of aperiodic architected metamaterials guided by the golden ratio - a geometric principle emblematic of natural balance and structural harmony—is introduced to overcome this limitation. The concept is validated via additive manufacturing of conventional periodic, hierarchical periodic, and golden-ratio-guided aperiodic lattices, along with their interpenetrating phase composite (IPC) counterparts. The aperiodic architectures exhibit significantly enhanced damage tolerance under monotonic loading, with increases of 84.24% and 42.45% in ultimate load, and 277.43% and 128.13% in initial fracture energy, for the lattice and IPC metamaterials, respectively. Under cyclic loading, only the aperiodic IPC withstands five tensile cycles at 350 N before incurring damage, whereas all other architectures fail during the initial cycle. These improvements stem from the unification of local geometric heterogeneity and global order in the golden-ratio-guided aperiodic architecture, which alleviates stress concentrations and promotes spatial delocalization of damage-tolerence regions. As a result, crack paths become more tortuous and adaptive, enhancing energy dissipation and resistance to fracture. These findings establish golden-ratio-guided aperiodicity as a robust design paradigm for next-generation damage-tolerant metamaterials.


Publication metadata

Author(s): Deng J, Wang X, Zhao R, Li Z, Liu K, Yuan K, An J, Li X, Chua CK, Wang Z

Publication type: Article

Publication status: Published

Journal: Advanced Functional Materials

Year: 2025

Pages: epub ahead of print

Online publication date: 22/11/2025

Acceptance date: 02/04/2018

Date deposited: 08/12/2025

ISSN (print): 1616-301X

ISSN (electronic): 1616-3028

Publisher: John Wiley and Sons Inc

URL: https://doi.org/10.1002/adfm.202516315

DOI: 10.1002/adfm.202516315

Data Access Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request.


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Funding

Funder referenceFunder name
Hunan Provincial Natural Science Foundation of China (2023JJ10074)
Science and Technology Innovation Program of Hunan Province (2023RC1011)

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