Efficient multiscale modeling of heterogeneous materials using deep neural networks

authored by: Fadi Aldakheel, Elsayed S. Elsayed, Tarek I. Zohdi, Peter Wriggers
Abstract: Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model.
Organisation(s): Institute of Mechanics and Computational Mechanics
Institute of Continuum Mechanics
External Organisation(s): University of California (UCLA)
Type: Article
Journal: Computational mechanics
Volume: 72
Pages: 155-171
No. of pages: 17
ISSN: 0178-7675
Publication date: 07.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-023-02324-9 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f65b3e695fb8427a819520ab31738b61,
title = "Efficient multiscale modeling of heterogeneous materials using deep neural networks",
abstract = "Material modeling using modern numerical methods accelerates the design process and reduces the costs of developing new products. However, for multiscale modeling of heterogeneous materials, the well-established homogenization techniques remain computationally expensive for high accuracy levels. In this contribution, a machine learning approach, convolutional neural networks (CNNs), is proposed as a computationally efficient solution method that is capable of providing a high level of accuracy. In this work, the data-set used for the training process, as well as the numerical tests, consists of artificial/real microstructural images (“input”). Whereas, the output is the homogenized stress of a given representative volume element RVE . The model performance is demonstrated by means of examples and compared with traditional homogenization methods. As the examples illustrate, high accuracy in predicting the homogenized stresses, along with a significant reduction in the computation time, were achieved using the developed CNN model.",
keywords = "Computational micro-to-macro approach, Convolutional neural networks, Deep learning, Heterogeneous materials",
author = "Fadi Aldakheel and Elsayed, {Elsayed S.} and Zohdi, {Tarek I.} and Peter Wriggers",
note = "Funding Information: Fadi Aldakheel (FA) gratefully acknowledges support for this research by the “German Research Foundation” (DFG) in the Priority Program SPP 2020 within its second funding phase. FA would like to thank N. Noii and A. Khodadadian for the support with mesh generation related to our paper []. ",
year = "2023",
month = jul,
doi = "10.1007/s00466-023-02324-9",
language = "English",
volume = "72",
pages = "155--171",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
number = "1",
}