Identification of Combined Isotropic–Kinematic Hardening Parameters from Reverse Bending Tests Using Recurrent Neural Networks

Accurate identification of constitutive parameters is essential for reliable finite element simulations of sheet metal forming processes. Conventional inverse identification techniques, such as Finite Element Model Updating (FEMU), generally require iterative optimization procedures involving numerous finite element simulations, resulting in high computational cost. This work proposes a machine learning framework based on a bidirectional Long Short-Term Memory (Bi-LSTM) neural network for the identification of combined isotropic–kinematic hardening parameters from a custom-designed reverse bending test. A synthetic dataset comprising 5000 finite element simulations was generated by systematically varying the parameters of the Swift isotropic hardening law and the Armstrong–Frederick kinematic hardening law using Sobol sampling. The resulting force–displacement histories were used to train the Bi-LSTM network to predict five constitutive parameters (K, σ0, n, C, and γ) directly from force–displacement responses. To improve the physical admissibility of the predictions, a physically constrained loss function was introduced by penalizing negative values of the kinematic hardening parameters during training. The proposed model achieved coefficients of determination, R2 above 0.98 for the isotropic and kinematic hardening parameters while reducing the number of physically inadmissible predictions from approximately 30 to a single case. Experimental validation was performed on DP500 and DP780 advanced high-strength steels, where finite element simulations using the Bi-LSTM predicted parameters reproduced the experimentally measured springback angles with good agreement. The proposed methodology provides near-instantaneous constitutive parameter identification after training, eliminating the need for computationally expensive iterative optimization while maintaining high predictive accuracy and physical consistency.