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Extraction of hyper-elastic material parameters using BLSTM neural network from instrumented indentation

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Abstract

Instrumented indentation is a versatile method of extracting hyper-elastic material parameters, particularly useful for applications where stress-strain data are difficult to be in-situ measured. Because the analytical force-displacement relation is still unavailable for the indentation of hyper-elastic materials, identifying hyper-elastic parameters often requires an iterative optimization strategy that fits finite element simulations with experimental data. However, the optimization strategy is burdened by heavy computation and its prediction accuracy is greatly influenced by the choice of optimization algorithm. To address these challenges in this study, a bidirectional long short-term memory (BLSTM) neural network is presented that directly predicts hyper-elastic material parameters from indentation load-displacement data, focusing on Mooney-Rivlin hyper-elasticity as an example. To improve the predication accuracy, the condition numbers for the inverse identification of the hyper-elastic parameters are investigated. And, a normalization procedure is proposed to treat the input data, which can guarantee the BLSTM network is well-conditioned. During evaluation, the trained BLSTM network significantly outperforms the iterative optimization strategy using a genetic algorithm. Furthermore, the effect of the normalization procedure is demonstrated.

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Acknowledgments

This work was supported by Natural Science Foundation of Nan**g University of Posts and Telecommunications (NY 222145) and Postgraduate Research and Practice Innovation Program of Jiangsu Province (KYCX21_0755).

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Authors and Affiliations

  1. College of Automation & College of Artificial Intelligence, Nan**g University of Posts and Telecommunications, Nan**g, 210023, China

    **g ** Shen & Jia Ming Zhou

  2. Shanghai Academy of Spaceflight Technology, Shanghai, 201109, China

    Shan Lu & Yue Yang Hou

  3. College of Electronic and Optical Engineering & College of Microelectronics, Nan**g University of Posts and Telecommunications, Nan**g, 210023, China

    Rong Qing Xu

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  1. **g ** Shen
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  3. Shan Lu
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Correspondence to **g ** Shen.

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**g ** Shen is an Associate Professor of the College of Automation & College of AI, Nan**g University of Posts and Telecommunications, China. He got his Ph.D. in Mechanical Engineering from Nan**g University of Astronautics and Aeronautics. His research interests include solid mechanics, contact mechanics and robotics.

Jia Ming Zhou is a postgraduate of the College of Automation & College of Artificial Intelligence, Nan**g University of Posts and Telecommunications, China. His research interests include solid mechanics, material parameter identification and artificial intelligence.

Shan Lu is a Professor of Shanghai Institute of Aerospace Control Technology, China. He got his Ph.D. in Mechanical Engineering from Beihang University. His research interests include robotics, control theory and signal processing.

Yue Yang Hou is a Senior Engineer of Shanghai Institute of Aerospace Control Technology, China. He got his Ph.D. in Mechanical Engineering from HIT University. His research interests include robotics, mechanism and tactile sensing.

Rong Qing Xu is a professor of the College of Electronic and Optical Engineering & College of Flexible ElectronicsI, Nan**g University of Posts and Telecommunications, China. He got his Ph.D. in Measurement Engineering from Nan**g University of Science and Technology. His research interests include tactile sensing, optics and robotics.

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Shen, J.J., Zhou, J.M., Lu, S. et al. Extraction of hyper-elastic material parameters using BLSTM neural network from instrumented indentation. J Mech Sci Technol 37, 6589–6599 (2023). https://doi.org/10.1007/s12206-023-1130-1

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  • DOI: https://doi.org/10.1007/s12206-023-1130-1

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