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<p>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 (<i>R</i><sup>2</sup>) = 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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年3月25日

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

摘要

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 (R2) = 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.