AccScience Publishing / MSAM / Volume 5 / Issue 2 / DOI: 10.36922/MSAM025440103
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ORIGINAL RESEARCH ARTICLE

Topology optimization for negative Poisson’s ratio metamaterials with geometric curvature control

Kaixian Liang1 ,  Chengxiang Liu1 ,  Jikai Liu1*
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1 Key Laboratory of High Efficiency and Clean Mechanical Manufacture (Ministry of Education), School of Mechanical Engineering, Shandong University, Jinan, Shandong, China
MSAM 2026, 5(2), 025440103 https://doi.org/10.36922/MSAM025440103
Received: 27 October 2025 | Accepted: 3 December 2025 | Published online: 13 February 2026
© 2026 by the Author(s).. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

Metamaterials with a negative Poisson’s ratio (NPR) exhibit unique auxetic deformation mechanism that enables superior energy absorption and mechanical resilience. Topology optimization (TO) can effectively generate microstructures with NPR characteristics, but conventional optimized designs often suffer from sharp corners and stress concentrations, which compromise durability and limit multicycle energy absorption. To address this issue, we introduced a boundary-fitting derivable geodesics-coupled TO (B-DGTO) framework to construct explicit curvature constraints into the optimization process, ensuring smooth boundaries and more uniform stress distribution with optimal NPR properties. In numerical example and experiment, we provided different types of 2D/3D NPR microstructures under curvature control to demonstrate the versatility of the proposed approach. These results confirm that the curvature constraint significantly improves the stress distribution of NPR microstructures and enhances their robustness and reliability under repeated loading. This study highlights curvature-constrained TO as a general and practical strategy for developing durable NPR metamaterials with superior energy dissipation performance.

Graphical abstract
Keywords
NPR metamaterials
Topology optimization
Curvature constraint
Energy absorption
Funding
The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (grant number 52475290).
Conflict of interest
Jikai Liu serves as the Editorial Board Member of the journal, but did not in any way involve in the editorial and peer-review process conducted for this paper, directly or indirectly. Other authors declare they have no competing interests.
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Materials Science in Additive Manufacturing, Electronic ISSN: 2810-9635 Published by AccScience Publishing
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