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

Chaorui Duan, Dazhong Wu|arXiv (Cornell University)|Mar 15, 2026

Machine Learning in Materials Science0 citations

TL;DR

A physics-informed ML framework (loss-based and activation-based) predicts AM material stress-strain curves by segmenting elastic/plastic regions and embedding Hooke's law, Voce/Hollomon hardening, and yield-point prediction; activation-based PIML achieves best accuracy.

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.

Motivation & Objective

• Motivate accurate prediction of stress-strain behavior for AM polymers and metals beyond traditional constitutive models.
• Develop a PIML framework that preserves physical consistency and interpretability in predictions.
• Segment stress-strain curves into elastic and plastic regions and embed relevant physical laws into ML models.

Proposed method

• Predict yield point from AM process parameters using a polynomial regression model.
• Segment stress-strain curves into elastic and plastic regions.
• Train two LSTM models to predict elastic and plastic regions separately.
• Embed Hooke's law into the elastic-region LSTM for both polymer and metal.
• Embed Voce hardening (polymer) and Hollomon's law (metal) into the plastic-region LSTM.
• Develop loss-based and activation-based PIML architectures by embedding physical laws into the loss and activation functions, respectively.

Experimental results

Research questions

• RQ1 Can physics-informed ML improve predictive accuracy and physical consistency for AM stress-strain curves compared to conventional ML models and physics-based constitutive models?
• RQ2 How do loss-based and activation-based PIML architectures compare in predicting elastic and plastic regions of AM materials?
• RQ3 What are the gains in accuracy (MAPE, R^2) when using activation-based PIML across different AM materials (polymers and metals)?

Key findings

• Two PIML architectures consistently outperform other models across four AM datasets.
• Activation-based, segmental PIML achieves the lowest MAPE of 10.46%±0.81 and highest R^2 of 0.82±0.05.
• Elastic-region predictions incorporate Hooke's law within the LSTM; plastic-region predictions use Voce hardening for polymer and Hollomon's law for metal.
• Datasets include Nylon and carbon fiber-ABS (polymers) and AlSi10Mg and Ti6Al4V (metals).