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Predicting stress–strain behavior of carbon nanotubes using neural networks

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Abstract

Artificial neural networks are employed to predict stress–strain curves for all single-walled carbon nanotube configurations with diameters up to 4 nm. Three model architectures are investigated for the molecular dynamics-derived dataset: a multilayer perceptron, a one-dimensional convolutional neural network, and a residual neural network. The performance of the three models is compared, and they are found to closely match an atomistic-physics-based paradigm while being orders of magnitude faster. The effect of the dataset size on the prediction quality is analyzed. It is shown that 30% of the entire carbon nanotube configuration dataset is representative of the problem. Remarkably, all models demonstrate high accuracy, capturing even the smallest variations due to thermal fluctuations, and can provide averaged stress–strain curves without thermal fluctuations. Additionally, a sensitivity analysis was performed to investigate how the various input feature combinations affect the quality of elimination or prediction of thermal fluctuations. The results are determined by different combinations of input features, with current diameter in combination with temperature identified as the most important parameters affecting the inclusion or exclusion of thermal fluctuations.

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Acknowledgements

This work has been supported in full by the Croatian Science Foundation under the project IP-2019-04-4703 and partially supported by the University of Rijeka under the project number uniri-tehnic-18-37. These supports are gratefully acknowledged.

Research data

The input dataset file with data about all SWCNT configurations and CNN models are available at Košmerl, Valentina; Štajduhar, Ivan; Čanađija, Marko (2022), SWCNT Dataset and CNN Models, Mendeley Data, V1, doi: 10.17632/t835gsrt66.1.

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Authors and Affiliations

  1. Department of Engineering Mechanics, University of Rijeka, Faculty of Engineering, Vukovarska 58, Rijeka, 51000, Croatia

    Valentina Košmerl & Marko Čanađija

  2. Department of Computer Engineering, University of Rijeka, Faculty of Engineering, Vukovarska 58, Rijeka, 51000, Croatia

    Ivan Štajduhar

Authors
  1. Valentina Košmerl
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  2. Ivan Štajduhar
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  3. Marko Čanađija
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Corresponding author

Correspondence to Marko Čanađija.

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All experiments were carried out on a publicly available data set.

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Appendix: Supplementary figures

Appendix: Supplementary figures

The present study has yielded a variety of results which we hope will be of interest to the reader. For clarity, only the most relevant illustrations are used in the main body of the article; the others are presented in the Appendix. Comments are provided in the main text.

See Figures 11, 12, 13 and 14.

Fig. 11
figure 11

TF-model: stress–strain curves for small diameter CNT (5,2) predicted by: a 2-Dense50, b 1-Conv64-Dense50, c 10-ResNet16 (a color version of this figure can be viewed online)

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Fig. 12
figure 12

TF-model: stress–strain curves for large diameter CNT (26,2) predicted by: a 2-Dense50, b 1-Conv64-Dense50, c 10-ResNet16 (a color version of this figure can be viewed online)

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Fig. 13
figure 13

S-model: stress–strain curves for small diameter CNT (6,3) predicted by: a 2-Dense50, b 1-Conv64-Dense50, c 10-ResNet16 (a color version of this figure can be viewed online)

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Fig. 14
figure 14

S-model: stress–strain curves for large diameter CNT (28,5) predicted by: a 2-Dense50, b 1-Conv64-Dense50, c 10-ResNet16 (a color version of this figure can be viewed online)

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Košmerl, V., Štajduhar, I. & Čanađija, M. Predicting stress–strain behavior of carbon nanotubes using neural networks. Neural Comput & Applic 34, 17821–17836 (2022). https://doi.org/10.1007/s00521-022-07430-y

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