Mechanical Property Prediction and Parameter Design of Auxetic Materials Based on the PSO-LSTM

Hu Yuhan; Han Fang; Yan Zhi

doi:10.21656/1000-0887.460118

Volume 47 Issue 8

Aug. 2026

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Article Navigation > Applied Mathematics and Mechanics > 2026 > 47(8): 990-998

Hu Yuhan, Han Fang, Yan Zhi. Mechanical Property Prediction and Parameter Design of Auxetic Materials Based on the PSO-LSTM[J]. Applied Mathematics and Mechanics, 2026, 47(8): 990-998. doi: 10.21656/1000-0887.460118

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Mechanical Property Prediction and Parameter Design of Auxetic Materials Based on the PSO-LSTM

doi: 10.21656/1000-0887.460118

Hu Yuhan¹,
Han Fang^{2
,
,},
Yan Zhi²

1. School of Mathematics and Systems Science, Wuhan University of Science and Technology, Wuhan 430065, P.R. China;
2. School of Physics and Mechanics, Wuhan University of Science and Technology, Wuhan 430065, P.R. China

Funds:

The National Science Foundation of China(51108358)

Received Date: 2025-06-09
Rev Recd Date: 2025-08-20

Available Online: 2026-07-30

Publish Date: 2026-08-01

Abstract

Abstract

To address the challenges of mechanical property prediction and structural optimization design for auxetic honeycomb materials, a machine learning approach integrating the particle swarm optimization (PSO) and the long short-term memory (LSTM) networks was proposed. A training dataset consisting of 400 groups of geometric parameters (including straight wall lengths, cell heights, wall thicknesses, and cell angles) and their corresponding mechanical properties (including energy absorption, Young’s moduli, and Poisson’s ratios) was constructed through finite element simulation. The PSO algorithm was employed to globally optimize the hyperparameters of the LSTM model, to establish a multi-objective mechanical property prediction model. Furthermore, an inverse design framework based on the PSO-LSTM was developed, enabling the optimization of geometric parameters driven by target mechanical properties. Experimental results show that, the optimized PSO-LSTM model achieves R² values of 0.983 4, 0.974 6, and 0.970 4 for energy absorption, Young’s moduli, and Poisson’s ratios, respectively, with mean squared errors (MSE) below 0.001 2. The relative errors of total energy absorption, Young’s moduli, and Poisson’s ratios for the model obtained through inverse design are 0.432%, 1.05%, and 0.327%, respectively. The proposed method provides theoretical support for the intelligent design and engineering application of auxetic materials.
- particle swarm optimization,
- long short-term memory network,
- auxetic material,
- geometric parameter design

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References(18)

References

[2]Choi J B, Lakes R S. Non-linear properties of metallic cellular materials with a negative Poisson’s ratio[J].Journal of Materials Science,1992,27: 5375-5381.

Gibson L J, Ashby M F, Schajer G S, et al. The mechanics of two-dimensional cellular materials[J].Proceedings of the Royal Society of London A: Mathematical and Physical Sciences,1982,382(1782): 25-42.

[3]Jin X, Wang Z, Ning J, et al. Dynamic response of sandwich structures with graded auxetic honeycomb cores under blast loading[J].Composites Part B:Engineering,2016,106: 206-217.

[4]魏高原. 拉胀材料研究的进展[J]. 材料导报, 2003,17(1): 8-10.(Wei Gaoyuan. Advances in research on auxetic materials[J].Materials Review,2003,17(1): 8-10. (in Chinese))

[5]Lakes R. Deformation mechanisms in negative Poisson’s ratio materials: structural aspects[J].Journal of Materials Science,1991,26: 2287-2292.

[6]Grima J N, Gatt R, Alderson A, et al. On the potential of connected stars as auxetic systems[J].Molecular Simulation,2005,31(13): 925-935.

[7]Grima J N, Evans K E. Auxetic behavior from rotating squares[J].Journal of Materials Science Letters,2000,19: 1563-1565.

[8]姚谦, 杨钊, 王昕, 等. 力学超结构设计方法研究进展[J]. 应用数学和力学, 2024,45(8): 974-1000.(Yao Qian, Yang Zhao, Wang Xin, et al. A review of design methods for mechanical metastructures[J].Applied Mathematics and Mechanics,2024,45(8): 974-1000. (in Chinese))

[9]Zhong S, Zhang K, Wang D, et al. Shedding light on “Black Box” machine learning models for predicting the reactivity of HO radicals toward organic compounds[J].Chemical Engineering Journal,2021,405: 126627.

[10]刘溢凡, 马小敏, 王志勇, 等. 基于ANN的混凝土均匀化方法解析解[J]. 应用数学和力学, 2024,45(5): 554-570. (Liu Yifan, Ma Xiaomin, Wang Zhiyong, et al. Analytical solution of the concrete homogenization method based on the ANN[J].Applied Mathematics and Mechanics,2024,45(5): 554-570. (in Chinese))

[11]何明洋, 傅广, 靳尚坤, 等. 基于机器学习的多孔材料力学性能预测研究进展[J]. 复合材料学报，2025,42(8): 4311-4338.(He Mingyang, Fu Guang, Jin Shangkun, et al. Research progress in prediction of mechanical properties of porous materials based on machine learning[J].Acta Materiae Compositae Sinica,2025,42(8): 4311-4338. (in Chinese))

[12]Tian J, Tang K, Chen X, et al. Machine learning-based prediction and inverse design of 2D metamaterial structures with tunable deformation-dependent Poisson’s ratio[J].Nanoscale,2022,14(35): 12677-12691.

[13]Wang H, Xiao S H, Zhang C. Novel planar auxetic metamaterial perforated with orthogonally aligned oval-shaped holes and machine learning solutions[J].Advanced Engineering Materials,2021,23(7): 2100102.

[14]马佩, 张君华, 权铁汉. 基于机器学习的负泊松比蜂窝的面内力学性能预测[J]. 复合材料学报, 2024,41(7): 3803-3812.(Ma Pei, Zhang Junhua, Quan Tiehan. Prediction of in-plane mechanical properties of auxetic honeycombs based on machine learning[J].Acta Materiae Compositae Sinica,2024,41(7): 3803-3812. (in Chinese))

[15]Chang Y, Wang H, Dong Q. Machine learning-based inverse design of auxetic metamaterial with zero Poisson’s ratio[J].Materials Today Communications,2022,30: 103186.

[16]丁晨, 赵喜东, 亓昌, 等. 弧形双箭头蜂窝动态冲击平台应力神经网络预测方法[J]. 工程力学, 2025,42(7): 265-272.(Ding Chen, Zhao Xidong, Qi Chang, et al. Neural network prediction method for dynamic crushing plateau stress of circular double arrowed honeycomb[J].Engineering Mechanics,2025,42(7): 265-272. (in Chinese))

[17]刘振涛. 机器学习辅助超弹性多孔材料的结构设计[D]. 绵阳: 西南科技大学, 2023.(Liu Zhentao. Structure design of hyperelastic porous materials with machine learning[D]. Mianyang: Southwest University of Science and Technology, 2023. (in Chinese))

[18]周建新, 王鸿滔. 基于相似日理论和改进PSO-LSTM模型的风电短期出力预测[J]. 中国工程机械学报, 2024,22(4): 447-451.(Zhou Jianxin, Wang Hongtao. Short-term wind power prediction based on similar day theory and improved PSO-LSTM model[J].Chinese Journal of Construction Machinery,2024,22(4): 447-451. (in Chinese))

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