Session: 13-15-02: Mechanics of Soft Materials II

Paper Number: 172655

Eliminating Case-by-Case Modeling: A General Physics-Informed Framework for Thermoset Shape Memory Polymers 

Amorphous shape memory polymers (SMPs) have drawn significant interest for applications in soft robotics, biomedical devices, and deployable structures due to their programmable shape transformation in response to external thermal stimuli. Despite their promise, modeling the thermomechanical behavior of SMPs remains a formidable challenge.  First, many existing models are highly material-specific, making them unsuitable for generalization across different SMP systems. Second, particularly for polymers with multiple phases, these models often require a large number of fitting parameters—typically ranging from 15 to 40—which complicates calibration. Third, the calculation of current stress or strain typically requires tracking the entire loading history, leading to high computational cost and inefficiency.

To address these limitations, we propose a Physics-Informed Artificial Neural Network (PIANN) framework that integrates data-driven learning with mechanistic understanding to model the constitutive behavior of thermoset SMPs. In this study, the model inputs were carefully selected based on physical principles, and a detailed mathematical framework was developed to support the architecture and demonstrate its feasibility. Unlike conventional black-box neural networks, PIANN embeds a storage-strain based constitutive model directly into its structure, enabling it to account for thermal transitions without requiring explicit history tracking. This physics-guided design enhances extrapolation capability, reduces overfitting, and significantly improves generalizability across different types of polymers.

The PIANN model is developed and validated using five temperature–stress datasets and four temperature–strain datasets, comprising both experimental data from four representative thermoset SMPs—polyurethane, epoxy, polyester, and poly(ethylene terephthalate)-glycol (PETG)—and simulation results from a widely accepted theoretical model. All experimental data were obtained from recognized sources, with temperature ranges spanning 250–400 K. Despite training on only a small subset of the data, the model exhibits strong generalization and robust predictive accuracy under unseen conditions. Remarkably, PIANN achieves excellent predictions of key shape memory behaviors using as few as two temperature–stress curves for training.

The framework reliably captures four hallmark behaviors of SMPs:

Stress evolution during hot programming, where the polymer is deformed at elevated temperatures and cooled under constraint.

Stress recovery following cold programming, where stress is recovered upon reheating after deformation below transition temperature.

Stress recovery following hot programming, capturing recovery behavior when the programming and activation temperatures are both above the transition range.

Free strain recovery during the heating branch, where the shape recovery occurs without external load.

Another particularly compelling outcome of this work is that PIANN predicts recovery strain in the heating branch without using any heating data during training, underscoring its capacity to learn the underlying thermomechanical response from limited input.

This model marks a significant departure from traditional modeling approaches that require data across all previous time history and extensive parameter calibration. By eliminating the need for stepwise integration of history-dependent terms, the proposed model not only simplifies simulation workflows but also dramatically improves computational speed and stability.

Comparison with experimental data reveals excellent agreement in both programming and recovery branches across a broad range of conditions, suggesting that PIANN is capable of generalizing to new materials with minimal retraining. Meanwhile, the comparison also suggests that the PIANN has similar or even better performance than some recognized constitutive models. Furthermore, the proposed approach opens opportunities for modeling highly complex SMP behaviors using a simple and accessible framework, making it suitable for practical engineering applications without requiring extensive customization or computational resources.

In summary, this study introduces a robust, generalizable, and physically grounded framework for modeling amorphous thermoset SMPs. By integrating machine learning with domain knowledge, PIANN bridges the gap between empirical fitting and fundamental understanding, providing a scalable solution for smart polymer modeling. This work lays the foundation for next-generation design and simulation tools that can accelerate the discovery and deployment of multifunctional polymer systems in engineering practice.

 

Presenting Author: CHENG YAN Southern University and A&M College

Presenting Author Biography: Dr. Cheng Yan is an Assistant Professor in the Department of Mechanical Engineering at Southern University and A&M College. His research lies at the convergence of machine learning, solid mechanics, and advanced polymer design, with a particular focus on shape memory polymers, vitrimers, and multifunctional smart materials. Dr. Yan currently leads several federally funded research projects, securing over $7.5 million in total funding from agencies such as the NSF and NASA. He has authored approximately 30 peer-reviewed journal articles, including several highlighted on journal covers for their innovative contributions. His recent efforts emphasize the development of physics-informed neural networks for constitutive modeling, as well as machine learning-assisted design of adaptive and multifunctional polymer systems.

Authors:

CHENG YAN Southern University and A&M College