Predicting stress–strain behaviors of additively manufactured materials via loss-based and activation-based physics-informed machine learning architectures

Predicting the stress–strain behaviors of additively manufactured materials is crucial for part qualification in additive manufacturing (AM). Conventional physics-based constitutive models of materials have limitations, such as oversimplification of material properties and narrow applicability to limited strain rates, while purely data-driven machine learning (ML) models often lack physical consistency and interpretability. To address these issues, we introduce a physics-informed machine learning (PIML) framework that leverages physical laws in elastic and plastic regions to improve the predictive performance and physical consistency when predicting the stress–strain curves of additively manufactured polymers and metals. A polynomial regression model is first used to predict the yield point based on AM process parameters, and then the stress–strain curves are segmented into elastic and plastic regions using the predicted yield point. Two long short-term memory (LSTM) models are trained to predict the two regions separately. For the elastic region, Hooke’s law is embedded in the LSTM models for both polymers and metals. For the plastic region, Voce hardening law and Hollomon’s law are embedded in the LSTM models for the polymers and metals, respectively. In addition, the PIML framework is implemented by two architectures, including the loss-based and activation-based PIML architectures, where the physical laws are embedded into the loss and activation functions, respectively. The performance of the two PIML architectures is compared with two LSTM-based ML models, three additional ML models, including a ridge polynomial regression model, an artificial neural network, and a transformer, and a physics-based constitutive model. These models are built on experimental data collected from two additively manufactured polymers (i.e., Nylon and carbon fiber-acrylonitrile butadiene styrene) and two additively manufactured metals (i.e., AlSi10Mg and Ti6Al4V). Experimental results demonstrate that two PIML architectures consistently outperform other ML baseline models and the physics-based constitutive model. The segmental predictive model with the activation-based PIML architecture achieves the best overall performance, with the lowest MAPE of 10.46 ± 0.81 %, the lowest MAE of 26.07 ± 2.52 MPa, the lowest RMSE of 29.28 ± 2.83 MPa, and the highest R 2 of 0.82 ± 0.05, indicating superior predictive performance for four different materials.