Hybrid constitutive law with machine learning for sintering of advanced ceramics

Predictive simulation of sintering-induced distortion remains challenging for ceramic components subjected to gravity and mechanical constraint. Classical constitutive sintering laws reproduce free densification reliably but lack the flexibility required to accurately capture stress-driven deformation within finite-element (FE) frameworks when calibrated solely from dilatometer data. This study presents a hybrid machine-learning-assisted constitutive framework for modelling constrained sintering of an industrial ceramic material. Dilatometer densification data and a gravity-loaded beam-bending experiments were obtained for the same material system, enabling simultaneous evaluation of volumetric sintering kinetics and part-level deformation. Two independently calibrated parameter sets of an Olevsky-type constitutive law reproduce densification behaviour but underpredict gravity-driven curvature (A) when applied within FE simulations, highlighting an inherent trade-off between densification fitting and deformation prediction. To overcome this limitation, the analytical volumetric strain-rate term is replaced by an artificial neural network trained directly on experimental densification data, while analytical formulations for mean and deviatoric stress response are retained. This hybrid framework decouples densification kinetics from shear-dominated deformation, enabling modulation of the effective viscous stiffness governing beam bending without compromising physical interpretability or numerical robustness. The results establish a simple, computationally efficient, and physically interpretable pathway toward predictive modelling of constrained sintering, providing a scalable foundation for industrial process optimisation and future digital-twin development.