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

• Proposes a novel multimodal deep learning model integrating physical metallurgical theory with machine learning for high-precision prediction of constitutive relationships under compositional fluctuations. • The TCN encoder-based model achieved superior performance with MAE of 1.84 MPa, RMSE of 2.75 MPa, MAPE of 4.48%, and correlation coefficient of 0.9918. • Comparative analysis validated the critical guiding role of physical metallurgy in deep learning, improving accuracy over purely data-driven models. • Model demonstrated accuracy and generalizability in numerical simulation and out-of-domain data, enabling analysis of elemental effects and offering a cost-effective alternative for material constitutive relationship modeling.