×

A deep learning framework for constitutive modeling based on temporal convolutional network. (English) Zbl 07524781

Summary: A novel and efficient deep learning framework adopting the Temporal Convolutional Network (TCN) model is proposed to simulate the ultra-long-history-dependent stress-strain constitutive model. First, the practical requirements for the constitutive models of stress-strain relationship with ultra-long-history-memory are summarized, which is favorable for adopting the TCN model in sequence modeling. The traditional Recurrent Neural Networks (RNNs) for sequence modeling are compared with the TCN model and the advantages of the TCN model for constitutive modeling are illustrated. Subsequently, the architecture of the TCN model for the constitutive modeling of steel and concrete material is illustrated in detail. In the TCN model, multiple dilated convolutional layers achieve long-term history dependence, while the causal convolution guarantees the stress is only updated based on historical strain history instead of the whole loading process. Third, a one-dimensional (1D) concrete stress-strain relationship dataset is established with significant stiffness degradation, strength degradation, and pinching effect. Two 1D reinforced concrete (RC) stress-strain datasets are established with steel content ratios of 1% and 10%. A two-dimensional (2D) low-yield-point steel dataset is also established. Fourth, the performance of the TCN model is evaluated for 1D concrete, steel, and RC datasets and 2D steel dataset. The TCN model achieves higher prediction accuracy and efficiency compared to the traditional RNN model for constitutive modeling. The influence of kernel size, hidden dimension of convolutional filter, and the number of convolutional layers on the test set performance are reported in detail. Finally, three prospective implementations of the proposed TCN model in solid mechanics are proposed, including the physics-informed machine learning, the multi-scale transfer learning framework, and the finite element force method.

MSC:

68Txx Artificial intelligence
74Cxx Plastic materials, materials of stress-rate and internal-variable type
74Axx Generalities, axiomatics, foundations of continuum mechanics of solids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bai, S.; Kolter, J. Z.; Koltun, V., An empirical evaluation of generic convolutional and recurrent networks for sequence modeling (2018)
[2] Belytschko, T.; Liu, W. K.; Moran, B.; Elkhodary, K. I., Nonlinear Finite Elements for Continua and Structures (2014), John Wiley & Sons
[3] Simo, J. C.; Hughes, T. J.R., Computational Inelasticity (1998), Springer: Springer New York · Zbl 0934.74003
[4] Lee, J., Theory and implementation of plastic-damage model for concrete structures under cyclic and dynamic loading (1996), University of California: University of California Berkeley, Doctoral dissertation
[5] Červenka, J.; Papanikolaou, V. K., Three dimensional combined fracture-plastic material model for concrete, Int. J. Plast., 24, 2192-2220 (2008) · Zbl 1419.74046
[6] Červenka, J.; Janda, Z.; Pryl, D., Numerical simulation of prestressed concrete nuclear containments, (Transactions (2011), SMiRT: SMiRT New Delhi, India)
[7] Chaboche, J. L., Constitutive equations for cyclic plasticity and cyclic viscoplasticity, Int. J. Plast., 5, 247-302 (1989) · Zbl 0695.73001
[8] Lee, J.; Fenves, G. L., Plastic-damage model for cyclic loading of concrete structures, J. Eng. Mech., 124, 892-900 (1998)
[9] Moharrami, M.; Koutromanos, I., Triaxial constitutive model for concrete under cyclic loading, J. Struct. Eng., 142 (2016)
[10] Wu, J. Y.; Li, J.; Faria, R., An energy release rate-based plastic-damage model for concrete, Int. J. Solids Struct., 43, 583-612 (2006) · Zbl 1119.74584
[11] Caner, F. C.; Bažant, Z. P., Microplane model M7 for plain concrete. I: formulation, J. Eng. Mech., 139, 1714-1723 (2013)
[12] Caner, F. C.; Bažant, Z. P., Microplane model M7 for plain concrete. II: calibration and verification, J. Eng. Mech., 139, 1724-1735 (2013)
[13] Maekawa, K.; Okamura, H.; Pimanmas, A., Non-linear Mechanics of Reinforced Concrete (2003), CRC Press
[14] Liu, C.; Yang, Y.; Wang, J.-J.; Fan, J.-S.; Tao, M.-X.; Mo, Y. L., Biaxial reinforced concrete constitutive models for implicit and explicit solvers with reduced mesh sensitivity, Eng. Struct., 219 (2020)
[15] Wang, J.-J.; Liu, C.; Fan, J.-S.; Hajjar, J. F.; Nie, X., Triaxial concrete constitutive model for simulation of composite plate shear wall-concrete encased: THUC3, J. Struct. Eng., 145 (2019)
[16] Li, V. C., On engineered cementitious composites (ECC), J. Adv. Concr. Technol., 1, 215-230 (2003)
[17] Wang, Y.-H.; Tang, Q.; Nie, X., Comparative investigation on influences of concrete material constitutive models on structural behavior, Constr. Build. Mater., 144, 475-483 (2017)
[18] E, W.; Yu, B., The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems, Commun. Math. Stat., 6, 1-12 (2018) · Zbl 1392.35306
[19] Saha, S.; Gan, Z.; Cheng, L.; Gao, J.; Kafka, O. L.; Xie, X.; Li, H.; Tajdari, M.; Alicia Kim, H.; Liu, W. K., Hierarchical Deep Learning Neural Network (HiDeNN): an artificial intelligence (AI) framework for computational science and engineering, Comput. Methods Appl. Mech. Eng., 373 (2021) · Zbl 1506.68110
[20] Liang, L.; Liu, M.; Martin, C.; Sun, W., A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis, J. R. Soc. Interface, 15 (2018)
[21] Abueidda, D. W.; Koric, S.; Sobh, N. A.; Sehitoglu, H., Deep learning for plasticity and thermo-viscoplasticity, Int. J. Plast., 136, Article 102852 pp. (2021)
[22] Wang, C.; Xu, L.-y.; Fan, J.-s., A general deep learning framework for history-dependent response prediction based on UA-Seq2Seq model, Comput. Methods Appl. Mech. Eng., 372, Article 113357 pp. (2020) · Zbl 1506.74072
[23] Mozaffar, M.; Bostanabad, R.; Chen, W.; Ehmann, K.; Cao, J.; Bessa, M. A., Deep learning predicts path-dependent plasticity, Proc. Natl. Acad. Sci. USA (2019)
[24] LeCun, Y.; Bengio, Y.; Hinton, G., Deep learning, Nature, 521, 436-444 (2015)
[25] Goodfellow, I.; Yoshua, Bengio; Courville, Aaron, Deep Learning (2016), MIT Press: MIT Press MA, USA · Zbl 1373.68009
[26] Sutskever, I.; Vinyals, O.; Le, Q. V., Sequence to sequence learning with neural networks, (Advances in Neural Information Processing Systems 27 (NIPS 2014). Advances in Neural Information Processing Systems 27 (NIPS 2014), Montreal, Canada (2014))
[27] Venugopalan, S.; Rohrbach, M.; Donahue, J.; Mooney, R.; Darrell, T.; Saenko, K., Sequence to sequence-video to text, (2015 IEEE International Conference on Computer Vision (ICCV) (2015), IEEE: IEEE Santiago, Chile)
[28] Ashish Vaswani, N. S.; Parmar, Niki; Uszkoreit, Jakob; Jones, Llion; Gomez, Aidan N.; Kaiser, Łukasz; Polosukhin, Illia, Attention is all you need, (Advances in Neural Information Processing Systems 30 (NIPS 2017). Advances in Neural Information Processing Systems 30 (NIPS 2017), Long Beach, CA (2017))
[29] Parmar, N.; Vaswani, A.; Uszkoreit, J.; Kaiser, L.; Shazeer, N.; Ku, A.; Tran, D., Image transformer, (International Conference on Machine Learning. International Conference on Machine Learning, Stockholm, Sweden (2018)), 4055-4064
[30] Simoyan, K.; Zisserman, A., Very deep convolutional networks for large-scale image recognition, (International Conference on Learning Representations (ICLR 2015). International Conference on Learning Representations (ICLR 2015), San Diego, CA (2015))
[31] Hochreiter, S.; Schmidhuber, J., Long short-term memory, Neural Comput., 9, 1735-1780 (1997)
[32] Cho, K.; Merrienboer, B.v.; Gulcehre, C.; Bahdanau, D.; Bougares, F.; Schwenk, H.; Bengio, Y., Learning phrase representations using RNN encoder-decoder for statistical machine translation, (Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP) (2014), Association for Computational Linguistics: Association for Computational Linguistics Doha, Qatar), 1724-1734
[33] Aäron van den Oord, S. D.; Zen, Heiga; Simonyan, Karen; Vinyals, Oriol; Graves, Alex; Kalchbrenner, Nal; Senior, Andrew; Kavukcuoglu, Koray, Wavenet a generative model for raw audio, (9th ISCA Speech Synthesis Workshop. 9th ISCA Speech Synthesis Workshop, Sunnyvale, US (2016))
[34] Kalchbrenner, N.; Espeholt, L.; Simonyan, K.; Oord, A.v.d.; Graves, A.; Kavukcuoglu, K., Neural machine translation in linear time (2016)
[35] Prabhavalkar, R.; Rao, K.; Sainath, T. N.; Li, B.; Johnson, L.; Jaitly, N., A comparison of sequence-to-sequence models for speech recognition, (Interspeech 2017 (2017)), 939-943
[36] Gehring, J.; Auli, M.; Grangier, D.; Yarats, D.; Dauphin, Y. N., Convolutional sequence to sequence learning, (Proceedings of the 34th International Conference on Machine Learning (2017)), 1243-1252
[37] Long, J.; Shelhamer, E.; Darrell, T., Fully convolutional networks for semantic segmentation, (Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (2015)), 3431-3440
[38] Yu, F.; Koltun, V., Multi-scale context aggregation by dilated convolutions, (4th International Conference on Learning Representations, ICLR 2016. 4th International Conference on Learning Representations, ICLR 2016, San Juan, Puerto Rico (2016))
[39] He, K.; Zhang, X.; Ren, S.; Sun, J., Deep residual learning for image recognition, (Conference on Computer Vision and Pattern Recogonition (CVPR 2016). Conference on Computer Vision and Pattern Recogonition (CVPR 2016), Las Vegas, NV (2015)), 770-778
[40] Nair, V.; Hinton, G. E., Rectified linear units improve restricted Boltzmann machines, (Proceedings of the 27th International Conference on Machine Learning (ICML). Proceedings of the 27th International Conference on Machine Learning (ICML), Haifa, Israel (2010))
[41] Xu, L.; Nie, X.; Fan, J.; Tao, M.; Ding, R., Cyclic hardening and softening behavior of the low yield point steel BLY160: experimental response and constitutive modeling, Int. J. Plast., 78, 44-63 (2016)
[42] Kingma, D. P.; Ba, J. L., Adam: a method for stochastic optimization, (3rd International Conference on Learning Representations, ICLR 2015. 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA (2015))
[43] Srivastava, N.; Hinton, G.; Krizhevsky, A.; Sutskever, I.; Salakhutdinov, R., Dropout: a simple way to prevent neural networks from overfitting, J. Mach. Learn. Res., 15, 1929-1958 (2014) · Zbl 1318.68153
[44] Razvan, P.; Mikolov, T.; Bengio, Y., Understanding the exploding gradient problem (2012)
[45] Lim, B.; Arik, S. O.; Loeff, N.; Pfister, T., Temporal fusion transformers for interpretable multi-horizon time series forecasting, Int. J. Forecast., 37, 1748-1764 (2021)
[46] Raissi, M.; Perdikaris, P.; Karniadakis, G. E., Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., 378, 686-707 (2019) · Zbl 1415.68175
[47] Haghighat, E.; Raissi, M.; Moure, A.; Gomez, H.; Juanes, R., A deep learning framework for solution and discovery in solid mechanics (2021), Preprint
[48] Zhang, L.; Cheng, L.; Li, H. Y.; Gao, J. Y.; Yu, C.; Domel, R.; Yang, Y.; Tang, S. Q.; Liu, W. K., Hierarchical deep-learning neural networks: finite elements and beyond, Comput. Mech., 67, 207-230 (2021) · Zbl 07360501
[49] Zhu, M.; McKenna, F.; OpenSeesPy, M. H. Scott, Python library for the OpenSees finite element framework, SoftwareX, 7, 6-11 (2018)
[50] Masters, D.; Luschi, C., Revisiting small batch training for deep neural networks (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.