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

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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.

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