Physics-based neural network as constitutive law for finite element analysis of sintering

In the sintering of advanced ceramics, a digital twin consisted of a finite element model can predict the final shape and microstructure of a sintered ceramic. However, to minimise uncertainties, it is essential to continually update the mechanical properties in the digital twin using data collected from the manufacturing process. One promising approach for achieving this is through artificial neural networks (ANN). This study introduces a machine learning strategy to update the constitutive behaviour of advanced ceramics in finite element analysis of sintering deformation. A major challenge in implementing machine learning in material processing is the huge amount of data required by the training and validation of an ANN, which are often unavailable or incomplete in a real manufacturing process. This study demonstrates that the data requirement can be reduced by employing a two-step training technique. Firstly, the ANN is trained using a nonlinear constitutive law, which describes a general relationship between the strain rates and stresses. Subsequently, the weights and bias of the ANN are transferred for the retraining using limited experimental data for an actual ceramic. It is shown that such approach can successfully capture the nonlinear constitutive behaviour of fine-grained alumina without demanding for large amount of experimental data. A case study is provided, highlighting the feasibility of implementing the ANN in a commercial finite element package, to replace the constitutive law and predict the shrinkage and distortion of a sintering part. In particular, the sintered dumb-bell shape part, simulated using the retrained ANN, showed grain size and relative density that markedly different from those using the nonlinear constitutive law. It is important to note that the proposed methodology is generic and can be used to create ANNs to replace constitutive laws in finite element analysis in digital twins for a wide range of other engineering processes.