A knowledge-distilled artificial neural network constitutive model for finite element simulation of hot-deformed β-C titanium alloy

Accurate, computationally deployable constitutive models are required for reliable finite element (FE) simulations of metallic hot deformation. This study develops a knowledge-distilled artificial neural network (KD-ANN) constitutive model for β-C titanium alloy using 24 flow-stress curves measured at 800-1,050 °C and strain rates of 0.01-10 s-1. An Extra Trees model serves as the teacher, while a compact multilayer perceptron provides a continuous constitutive mapping with explicit derivative evaluation for FE implementation. The student is trained using experimental and teacher supervision, weighted Huber loss, curve-balanced weighting and enhanced weighting in the low-strain region. Following preliminary teacher-algorithm and student-configuration screening, temperature-wise predictive performance is evaluated using curve-grouped leave-one-temperature-out validation. In each fold, all four curves at the target temperature are held out, while the fold-specific KD-ANN and modified Johnson–Cook (J–C) models are fitted using only the retained temperature conditions. Across the six held-out-temperature folds, KD-ANN achieves mean values of the coefficient of determination = 0.984, root mean square error = 11.40 MPa and mean absolute error (MAE) = 9.21 MPa, compared with 0.960, 17.12 and 12.58 MPa, respectively, for the modified J–C model. Sequential ablation and targeted control experiments show that the joint use of experimental stresses and teacher-generated targets produces the largest incremental improvement within the tested training framework. The trained student network is implemented in Abaqus through a VUHARD user subroutine. For the fold in which the lower-boundary temperature of 800 °C is held out from model fitting and validation, the FE load–displacement predictions yield a mean MAE of 0.729 kN, compared with 1.213 kN for the modified J–C model. These results demonstrate improved prediction of complete flow curves at unseen temperatures within the investigated range and support the use of KD-ANN as a constitutive input for hot-compression simulations.