Benchmarking data-driven material models on the classic Treloar dataset

2026-08-14

AI Summary

This study addresses the absence of unified benchmarks for data-driven hyperelastic constitutive models by conducting a multidimensional systematic evaluation of six state-of-the-art methods using the Treloar dataset. By establishing an assessment framework that balances accuracy and efficiency, this work comprehensively examines fitting performance, computational cost, and hyperparameter sensitivity, thereby elucidating the trade-off mechanisms between model complexity and predictive accuracy. The research delineates the applicability boundaries and distinct characteristics of each method, offering practical guidelines for model selection. Furthermore, the complete codebase and experimental data are open-sourced to provide standardized practical guidance for method selection in data-driven constitutive modeling, ultimately facilitating more rigorous and reproducible research in this domain.

Abstract

Machine learning is rapidly reshaping constitutive modeling, offers new ways to learn material behavior directly from experimental data, and challenges long-established modeling paradigms. But with a growing number of machine-learning-based approaches available, how do they compare in practice? In this paper, we use the classic experimental data of Treloar to benchmark popular frameworks for hyperelasticity: (Generalized-Invariant) Constitutive Artificial Neural Networks, Physics-Augmented Neural Networks, (Adaptive) Material Fingerprinting, and Efficient Unsupervised Constitutive Law Identification & Discovery. We compare their fitting performance, computational cost, hyperparameter sensitivity, and ease of implementation. Furthermore, we discuss the trade-offs between predictive accuracy and model complexity. The latter is assessed by quantifying both the number of material parameters in the discovered models and the computational time required to evaluate the constitutive model and its derivatives. The results show that all methods can reproduce the benchmark data remarkably well. Rather than identifying a single winner, we highlight the strengths and limitations of each approach and provide practical guidance for their use. The source code for all six methods, including the training and comparison scripts, as well as all results and data used in this study, is publicly available via https://doi.org/10.5281/zenodo.21915635.

Problem

• Constitutive modeling
• Machine learning
• Hyperelasticity
• Benchmarking
• Treloar dataset

Innovation

• Benchmarking
• Hyperelasticity
• Constitutive Modeling
• Machine Learning
• Model Complexity