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Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

Tongming Qu1, Shaocheng Di2, Y. T. Feng1,3,*, Min Wang4, Tingting Zhao3, Mengqi Wang1
1 Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, Wales, SA1 8EP, UK
2 College of Shipbuilding Engineering, Harbin Engineering University, Harbin, 150001, China
3 Institute of Applied Mechanics and Biomedical Engineering, Taiyuan University of Technology, Taiyuan, 030024, China
4 Fluid Dynamics and Solid Mechanics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
* Corresponding Author: Y. T. Feng. Email:
(This article belongs to this Special Issue: Computational Mechanics of Granular Materials and its Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 128(1), 129-144.

Received 13 February 2021; Accepted 08 April 2021; Issue published 28 June 2021


This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed.


Deep learning; granular materials; constitutive modelling; discrete element modelling; coordinate transformation; LSTM; GRU

Cite This Article

Qu, T., Di, S., Feng, Y. T., Wang, M., Zhao, T. et al. (2021). Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data. CMES-Computer Modeling in Engineering & Sciences, 128(1), 129–144.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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