Predicting Stress-strain Behaviors of Additively Manufactured Materials via Loss-based and Activation-based Physics-informed Machine Learning

2026-03-15

AI Summary

This study addresses the limitations of traditional constitutive models, which oversimplify material behavior, and purely data-driven approaches, which often lack physical consistency, in accurately predicting the stress–strain response of additively manufactured materials. To overcome these challenges, the authors propose a segmented physics-informed machine learning (PIML) framework that leverages process parameters to predict yield points and separately models the elastic and plastic deformation stages. The framework innovatively embeds Hooke’s law, the Voce hardening law, and the Hollomon equation into an LSTM architecture through both loss-function constraints and activation functions. Experimental validation on four additively manufactured materials demonstrates that the activation-based PIML model achieves superior performance, with an average mean absolute percentage error (MAPE) of 10.46 ± 0.81% and an R² of 0.82 ± 0.05, significantly outperforming conventional constitutive models and pure data-driven methods.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Humans and AI: Human-in-the-loop Machine Learning
• Planning, Routing, and Scheduling: Planning with Language Models

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Predicting the stress-strain behaviors of additively manufactured materials is crucial for part qualification in additive manufacturing (AM). Conventional physics-based constitutive models often oversimplify material properties, while data-driven machine learning (ML) models often lack physical consistency and interpretability. To address these issues, we propose a physics-informed machine learning (PIML) framework to improve the predictive performance and physical consistency for predicting the stress-strain curves of additively manufactured polymers and metals. A polynomial regression model is used to predict the yield point from AM process parameters, then stress-strain curves are segmented into elastic and plastic regions. Two long short-term memory (LSTM) models are trained to predict two regions separately. For the elastic region, Hooke's law is embedded into the LSTM model for both polymer and metal. For the plastic region, Voce hardening law and Hollomon's law are embedded into the LSTM model for polymer and metal, respectively. The loss-based and activation-based PIML architectures are developed by embedding the physical laws into the loss and activation functions, respectively. The performance of the two PIML architectures are compared with two LSTM-based ML models, three additional ML models, 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 the other models. The segmental predictive model with activation-based PIML architecture achieves the lowest MAPE of 10.46+/-0.81% and the highest R^2 of 0.82+/-0.05 arocss four datasets.

Problem

• stress-strain behavior
• additive manufacturing
• material qualification
• constitutive modeling
• physical consistency

Innovation

• Physics-informed machine learning
• Additive manufacturing
• Stress-strain prediction
• Loss-based PIML
• Activation-based PIML