Title: Data-driven material constitutive modelling: a framework for method selection and performance evaluation

Authors: Hengli Yu; Yantao Wang; Yingjing Wang; Tong Pang; Tangying Liu

Addresses: School of Electromechanical and Automotive Engineering, Yantai University, Yantai, 264005, China ' School of Electromechanical and Automotive Engineering, Yantai University, Yantai, 264005, China ' School of Information Engineering, Shandong Huayu University of Technology, Dezhou, 253000, China ' College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410082, China ' School of Electromechanical and Automotive Engineering, Yantai University, Yantai, 264005, China

Abstract: Constitutive models are crucial in engineering design and simulations. Traditional models require tedious parameter calibration and have limited generalisation capabilities, while data-driven models offer adaptive learning advantages. However, selecting optimal models remains challenging. This study evaluates eight data-driven methods in material constitutive modelling across sparse and dense parameter spaces. By analysing fitting accuracy, interpolation capability, and extrapolation performance, we found that back-propagation neural networks (BPNNs) provide the most stable generalisation in sparse parameter spaces, while kriging achieves near-perfect performance in dense parameter spaces. Based on these findings, we propose a systematic model selection framework that considers data sampling density and prediction task types, providing a theoretical foundation for model selection across various material constitutive models.

Keywords: constitutive modelling; data-driven methods; DNN; deep neural network; kriging; machine learning; hyperparameter optimisation.

DOI: 10.1504/IJVSMT.2026.153201

International Journal of Vehicle Systems Modelling and Testing, 2026 Vol.20 No.2, pp.133 - 158

Received: 16 May 2025
Accepted: 08 Aug 2025
Published online: 29 Apr 2026 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article