Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning

Li Zhou; Mei-Fang Wang; Chao-Kun Huang; Meng Song; Xiu-Juan Wang

doi:10.1007/s10118-026-3606-9

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Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning

RESEARCH ARTICLE | Updated：2026-04-30

- Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning
- Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning
- Chinese Journal of Polymer Science 2026年44卷第5期页码：1562-1573
- Affiliations：
  
  a.State Key Laboratory of Advanced Optical Polymer and Manufacturing Technology/Key Laboratory of Advanced Rubber Material, Ministry of Education, Qingdao University of Science and Technology, Qingdao 266042, China
  b.Shandong Institute of Non-Metallic Materials, Jinan 250031, China
  c.School of Materials Electronics and Energy Storage, Zhongyuan University of Technology, Zhengzhou 450007, China
- Author bio：
  
  chengsimengyin@126.com (M.S.)
  wangxj@qust.edu.cn (X.J.W.)
- Funds：
  
  This work was financially supported by the National Natural Science Foundation of China (Nos. 52173057 and 51703114), Taishan Scholar Talent Program (No. tsqn202408195), and the Foundation of Key Laboratory of Advanced Rubber Material, Ministry of Education (No. XJCL2025012).;The authors declare no interest conflict.Electronic supplementary information (ESI) is available free of charge in the online version of this article at http://doi.org/10.1007/s10118-026-3606-9.The related data (CSTR: https://cstr.cn/31253.11.sciencedb.j00189.00062) for this paper is available in the (Data Repository of China Association for Science and Technology) database (https://www.scidb.cn/c/cjps).
- DOI：10.1007/s10118-026-3606-9
  中图分类号：
- 收稿：2025-12-22，
  
  录用：2026-01-31，
  
  网络首发：2026-03-25，
  
  纸质出版：2026-05-05
- Accepted：
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Zhou, L.; Wang, M. F.; Huang, C. K.; Song, M.; Wang, X. J. Prediction of stress-strain behavior for polyurethane elastomers based on machine learning. Chinese J. Polym. Sci. 2026, 44, 1562–1573

Li Zhou, Mei-Fang Wang, Chao-Kun Huang, et al. Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning[J]. Chinese Journal of Polymer Science, 2026, 44(5): 1562-1573.
Zhou, L.; Wang, M. F.; Huang, C. K.; Song, M.; Wang, X. J. Prediction of stress-strain behavior for polyurethane elastomers based on machine learning. Chinese J. Polym. Sci. 2026, 44, 1562–1573 DOI： 10.1007/s10118-026-3606-9.

Li Zhou, Mei-Fang Wang, Chao-Kun Huang, et al. Prediction of Stress-strain Behavior for Polyurethane Elastomers Based on Machine Learning[J]. Chinese Journal of Polymer Science, 2026, 44(5): 1562-1573. DOI： 10.1007/s10118-026-3606-9.

摘要

The Transformer model predicts polyurethane elastomers (PUE) mechanical properties by analyzing molecular descriptors and hard segment content

guiding the design of high-performance materials.

Abstract

Predicting stress-strain behavior is key to facilitating the design of polymer materials and their products with tailored mechanical responses. However

polyurethane elastomers (PUE) often exhibit highly nonlinear mechanical responses owing to their tunable molecular structure and the complexity of microphase separation for hard segments

which poses challenges for developing models for predicting stress-strain properties. In this study

four machine learning models were constructed to predict the stress-strain curve of PUE

mainly by investigating the

influence of molecular hard segment content and molecular structure characteristics on the mechanical properties of PUE. Based on the Pearson correlation analysis

key variables were screened to effectively capture the evolution law of the mechanical behavior of PUE. The results show that the Transformer model performs the best and can effectively predict the stress-strain behavior of the PUE (coefficient of determination (

) = 0.79

root mean square error (RMSE) = 5.82). Cross-validation was adopted to evaluate the generalization ability of the model. The experimental data further confirmed that this model can effectively fit the stress-strain curve of PUE. The Shapley additive explanation (SHAP) method was adopted to analyze the contribution of key descriptors to the stress response

and the intrinsic correlation between molecular structure characteristics and macroscopic mechanical behavior was revealed. Among them

descriptors such as SlogP_VSA10 were used as structural proxies for soft segments

whereas descriptors such as RingCount quantified the impact of hard segments. In addition

BCUT2D_CHGHI directly affects intermolecular forces (such as hydrogen bonds)

which are crucial for microphase separation and the mechanical properties of elastomers. In conclusion

by using machine-learning algorithms to establish quantitative relationships between these descriptors and mechanical properties

we can adjust the molecular structures related to the descriptors to achieve PUE with customized mechanical responses.

关键词

Keywords

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