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Bochun Liang, Cheng Ji, Xingyi Dai, and Miaoyong Zhu, Mechanism and data dual-driven multimodal deep learning approach for constitutive relationship modeling of bearing steels, Int. J. Miner. Metall. Mater., (2026). https://doi.org/10.1007/s12613-025-3198-3
Bochun Liang, Cheng Ji, Xingyi Dai, and Miaoyong Zhu, Mechanism and data dual-driven multimodal deep learning approach for constitutive relationship modeling of bearing steels, Int. J. Miner. Metall. Mater., (2026). https://doi.org/10.1007/s12613-025-3198-3
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面向轴承钢本构关系建模的机理与数据双驱动多模态深度学习方法

摘要: 在成分波动条件下,材料的本构关系精确建模面临显著挑战。传统机理驱动方法难以有效捕捉材料性能随成分变化的复杂非线性行为。相比而言,深度学习方法具有更好的准确性、鲁棒性和可扩展性。然而,作为一种数据驱动的建模方法,其主要局限是缺乏基于物理冶金机理的严格约束,这可能导致模型预测结果存在较大的偏差。鉴于此,本文提出了一种基于编码器–解码器框架的多模态深度学习模型。将物理冶金理论与深度学习方法相结合,以实现复杂载荷和成分波动条件下材料本构关系的高精度预测。在GCr15轴承钢数据库上评估了各种编码器架构,包括:长短期记忆(LSTM)、门控递归单元(GRU)和时序卷积网络(TCN)。结果表明,基于TCN编码器的模型表现出最优的性能,其平均绝对误差、均方根误差、平均绝对百分比误差和相关系数分别为1.84 MPa、2.75 MPa、4.48%和0.9918。通过与纯数据驱动模型进行对比,证明了物理冶金理论的引入显著提高了模型的准确性和稳定性。此外,本文探索了元素含量对材料力学性能的影响,模型的预测结果与已有的理论知识一致。最后,验证了嵌入多模态深度学习模型的数值模拟框架在域外数据上的准确性。本文提出的方法,为传统的通过热压缩实验获得材料本构曲线提供了一种代替方法,为计算机辅助材料设计和材料加工工艺优化提供了有力的理论支持和应用潜力。

 

Mechanism and data dual-driven multimodal deep learning approach for constitutive relationship modeling of bearing steels

Abstract: Accurate modeling of material constitutive relationships under compositional fluctuations poses significant challenges. Traditional mechanism-driven methods struggle to capture the complex nonlinear behavior of material properties as composition varies, while data-driven deep learning approaches, despite their high accuracy and robustness, lack strict constraints from physical metallurgical mechanisms, often leading to substantial prediction deviations. To address this critical issue, this study proposes a multimodal deep learning model based on an encoder-decoder framework, integrating physical metallurgical theory with machine learning to achieve high-precision prediction of material constitutive relationships under complex loading and compositional fluctuations. Firstly, the performance of three encoder architectures, long short-term memory (LSTM), gated recurrent unit (GRU), and temporal convolutional network (TCN), was systematically compared, with the TCN encoder-based model demonstrating the best performance, achieving mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R) values of 1.84 MPa, 2.75 MPa, 4.48%, and 0.9918, respectively. By comparing with purely data-driven models, the critical guiding role of physical metallurgy in the deep learning process was validated. Furthermore, the accuracy and generalizability of the proposed model in material processing scenarios were verified by embedding it into a numerical simulation framework and applying it to out-of-domain data. Finally, the influence of elemental content on material mechanical properties was analyzed using the developed model. This study provides an efficient and reliable alternative method for obtaining material constitutive relationships, avoiding the high costs associated with traditional experimental approaches, and offering potential for computer-aided material design and process optimization for material processing.

 

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