Characterization method of material constitutive relationship at high strain rates based on GNN/KAN

To accurately characterize the stress-strain constitutive relationship of metal materials under high strain-rate conditions, a novel, high-precision constitutive-relationship-prediction model based on Graph Neural Networks (GNNs) and Kolmogorov-Arnold Networks (KANs) was developed. Traditional Johnson-Cook (JC) models often fail to account for the coupling effects among temperature, strain rate, and strain, all of which are crucial for describing the dynamic behavior of materials under extreme conditions. This limitation was addressed by constructing graph-structured data in the GNN model to capture the nonlinear correlations of multidimensional parameters and by leveraging the Kolmogorov-Arnold theorem in the KAN model to achieve precise mapping of high-dimensional input spaces. The research methodology involved several key steps. Experimental data from ODS copper subjected to high-strain-rate compression were collected using a split Hopkinson pressure bar (SHPB) system and subsequently preprocessed. The dataset included temperature, strain rate, strain, and stress. In the GNN model, when temperature and strain rate were held constant, nodes were connected sequentially based on strain values to form edges. When temperature was held constant, a reasonable threshold was established between nodes with adjacent strain rates, and nodes within this threshold were connected to form edges. The GNN employed a Message Passing Neural Network (MPNN) architecture to learn and predict material properties. Model parameters were optimized using the Adam optimizer, with the Root Mean Squared Error (RMSE) serving as the loss function. The KAN model was constructed based on the Kolmogorov-Arnold representation theorem and consisted of multiple KAN-Linear layers. Each KAN-Linear unit included base weights and spline weights. Base weights handled linear relationships through traditional linear transformations, while spline weights managed nonlinear mappings via B-spline interpolation. Both models were trained on the preprocessed dataset, and their performance was evaluated using metrics such as the Mean Relative Error (MRE), Root Mean Squared Error (RMSE), and the coefficient of determination (R²). The GNN model achieved an average MRE of 9.2% with an R² value exceeding 0.95, while the KAN model recorded an MRE of 9.1% with a similar R² value. Both models significantly outperformed the JC model, which had an MRE of 38% and an R² value of 0.75. Furthermore, the predictive capabilities of the GNN and KAN models were validated through finite element simulations. The simulation results demonstrated that the stress-strain distributions predicted by the GNN and KAN models were more consistent with theoretical expectations compared to those predicted by the JC model, particularly in capturing the material's softening phase. The findings highlight the potential of integrating advanced machine learning techniques, such as GNNs and KANs, into the field of materials science to enhance the accuracy and efficiency of constitutive modeling. These models offer a promising alternative to traditional empirical models and hold significant implications for engineering applications in aerospace, automotive, and other industries where materials are subjected to high strain rates.