Cao Ertai, Dong Zhicheng, Jia Ben, Huang Heyuan
School of Aeronautics, Northwestern Polytechnical University, Xi'an, 710072, China.
School of Civil Aviation, Northwestern Polytechnical University, Xi'an, 710072, China.
Mater Horiz. 2025 Jun 30;12(13):4884-4900. doi: 10.1039/d5mh00154d.
Efficiently and precisely designed isotropic auxetic metamaterials present significant challenges due to the inherent uncertainties in their geometric configurations. This study introduces an innovative data-driven structural design strategy that enables accurate prediction of the mechanical properties and inverse design for isotropic auxetic metamaterials. Notably, Kolmogorov-Arnold networks (KANs) are utilized, replacing fixed activation functions with learnable functions, to successfully establish a precise mapping between design parameters and mechanical responses for classical missing rib auxetic metamaterials. The predicted mean square error (MSE) for the stress dataset is as low as 0.81%, only one-fourth of that achieved by multilayer perceptron (MLP) models of equivalent width, while computational efficiency surpasses finite element methods by more than 10 times. Building on this mapping, Model III, optimized using a genetic algorithm, achieves an average MSE of just 0.05%, significantly outperforming the original structure (Model I) and a randomly perturbed structure (Model II) with an average MSE of 2.28% and 1.79%, respectively. Experimental validation and finite element analysis further confirm the accuracy of these results, demonstrating the successful realization of isotropic mechanical response designs. This study presented a data-driven inverse design method as a powerful and efficient tool for the precise design of auxetic metamaterials with isotropic mechanical responses. It holds particular promise for applications in flexible wearable devices and tissue engineering, providing a robust foundation for future innovations in these fields.
由于其几何构型中存在固有的不确定性，高效且精确设计的各向同性负泊松比超材料面临重大挑战。本研究引入了一种创新的数据驱动结构设计策略，能够准确预测各向同性负泊松比超材料的力学性能并进行逆向设计。值得注意的是，利用柯尔莫哥洛夫 - 阿诺德网络（KANs），用可学习函数取代固定激活函数，成功地为经典的缺肋负泊松比超材料在设计参数和力学响应之间建立了精确映射。应力数据集的预测均方误差（MSE）低至0.81%，仅为同等宽度的多层感知器（MLP）模型所达到值的四分之一，而计算效率比有限元方法高出10倍以上。基于此映射，使用遗传算法优化的模型III的平均MSE仅为0.05%，显著优于原始结构（模型I）和随机扰动结构（模型II），其平均MSE分别为2.28%和1.79%。实验验证和有限元分析进一步证实了这些结果的准确性，证明了各向同性力学响应设计的成功实现。本研究提出了一种数据驱动的逆向设计方法，作为精确设计具有各向同性力学响应的负泊松比超材料的强大而高效的工具。它在柔性可穿戴设备和组织工程中的应用具有特别的前景，为这些领域的未来创新提供了坚实的基础。
