Parametric Reduced-Order Constitutive Model for High-Strain-Rate and Temperature-Dependent Behavior

We present a multi-parameter reduced-order constitutive model (ROCM) for real-time characterization of metallic material behavior under high-strain-rate loading and elevated temperature. To this end, the proper orthogonal decomposition (POD) technique is utilized to decompose stress–strain responses generated from the Johnson–Cook (J-C) constitutive model and extract their principal components, referred to as POD modes. Multiple neural networks are then trained to learn the nonlinear mapping between the parametric vectors and the corresponding POD projection coefficients, enabling efficient reconstruction of stress–strain curves directly from the input parameters. To enhance the predictive performance of the proposed framework, the loss function is formulated to include the residuals of the reconstructed stress–strain responses and their corresponding energy contributions, in addition to the deviations in the POD projection coefficients. The proposed ROCM framework is encapsulated within a Python-based user interface (UI), enabling intuitive calibration of material parameters against experimental data and real-time prediction of stress–strain curves across various material parameters and loading conditions. The effectiveness of the proposed ROCM is showcased through extensive comparisons with direct numerical simulations and experimental results. Moreover, the ROCM achieves a speedup of approximately five orders of magnitude in the online stage compared to direct numerical analysis, making it highly suitable for large-scale parametric studies.