Volume 40 Issue 9
Sep.  2023
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WANG Chen, HE You-quan, SONG Ling-han, FAN Jian-sheng. A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS[J]. Engineering Mechanics, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012
Citation: WANG Chen, HE You-quan, SONG Ling-han, FAN Jian-sheng. A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS[J]. Engineering Mechanics, 2023, 40(9): 29-36. doi: 10.6052/j.issn.1000-4750.2021.12.1012


doi: 10.6052/j.issn.1000-4750.2021.12.1012
  • Received Date: 2021-12-27
  • Accepted Date: 2022-06-24
  • Rev Recd Date: 2022-06-09
  • Available Online: 2022-06-24
  • Publish Date: 2023-09-06
  • Proposed is a theory-aided few-shot learning algorithm applicable to any material elastoplastic relationships utilized in civil engineering. The new algorithm can effectively alleviate the paucity of data in real applications when applying large-scale deep learning models. The framework of the classical elastoplasticity theory is briefly recapped. On this basis, the paper elaborates on how to incorporate the elastoplastic equations into the ordinary deep learning models, wherein the entire processes require neither the concrete form of the underlying models nor its complicated numerical implementation, thus maintaining the simple, direct, and efficient advantages of data-driven techniques. To address the divergence issue caused by the complicated optimization target, a novel training strategy named overfitting-correction method is invented, which is able to stabilize the training and accelerate the convergence. A numerical experiment is performed upon a sophisticated elastoplastic constitutive model of structural steel. The results demonstrate that the theory-aided few-shot learning algorithm succeeds in realizing excellent generalization performance of a large-scale deep learning model on small training datasets. Quantitatively, the new algorithm overwhelms the pure data-driven model by 38.9%. The philosophy of theory-aided driven mode proposed can extend to the structural level in the future, facilitating the introduction of more advanced intelligent technologies into civil engineering.
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  • [1]
    聂建国, 王宇航. ABAQUS中混凝土本构模型用于模拟结构静力行为的比较研究[J]. 工程力学, 2013, 30(4): 59 − 67, 82. doi: 10.6052/j.issn.1000-4750.2011.07.0420

    NIE Jianguo, WANG Yuhang. Comparison study of constitutive model of concrete in ABAQUS for static analysis of structures [J]. Engineering Mechanics, 2013, 30(4): 59 − 67, 82. (in Chinese) doi: 10.6052/j.issn.1000-4750.2011.07.0420
    许立言. 低屈服点钢剪切型阻尼器的力学性能及理论模型研究[D]. 北京: 清华大学, 2017.

    XU Liyan. Research on mechanical behavior and theoretical model of low-yield-point steel shear panel dampers [D]. Beijing: Tsinghua University, 2017. (in Chinese)
    骆晶, 施刚, 毛灵涛, 等. 双相型不锈钢S22053循环本构关系研究[J]. 工程力学, 2021, 38(9): 171 − 181. doi: 10.6052/j.issn.1000-4750.2020.09.0659

    LUO Jing, SHI Gang, MAO Lingtao, et al. Constitutive relation of duplex stainless steel S22053 under cyclic loading [J]. Engineering Mechanics, 2021, 38(9): 171 − 181. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.09.0659
    班慧勇, 梅镱潇, 石永久. 不锈钢复合钢材钢结构研究进展[J]. 工程力学, 2021, 38(6): 1 − 23. doi: 10.6052/j.issn.1000-4750.2020.04.ST01

    BAN Huiyong, MEI Yixiao, SHI Yongjiu. Research advances of stainless-clad bimetallic steel structures [J]. Engineering Mechanics, 2021, 38(6): 1 − 23. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.04.ST01
    刘晓刚, 樊健生, 聂建国, 等. 剪切型消能连梁的塑性强化特性研究[J]. 土木工程学报, 2017, 50(3): 1 − 11. doi: 10.15951/j.tmgcxb.2017.03.001

    LIU Xiaogang, FAN Jiansheng, NIE Jianguo, et al. Research on plastic overstrength of energy-dissipation shear links [J]. China Civil Engineering Journal, 2017, 50(3): 1 − 11. (in Chinese) doi: 10.15951/j.tmgcxb.2017.03.001
    侯帅, 朱有利, 王燕礼, 等. 基于多晶体塑性与唯象学本构模型的纯铝与单晶铝的有限变形分析与对比[J]. 稀有金属材料与工程, 2017, 46(12): 3760 − 3766.

    HOU Shuai, ZHU Youli, WANG Yanli, et al. Analysis and comparison of finite deformation of pure aluminum and single crystal aluminum based on polycrystal plasticity and phenomenological constitutive models [J]. Rare Metal Materials and Engineering, 2017, 46(12): 3760 − 3766. (in Chinese)
    王元清, 关阳, 刘明, 等. 建筑结构钢材及其焊缝循环微观损伤模型的韧性参数校正分析[J]. 工程力学, 2020, 37(增刊): 20 − 31. doi: 10.6052/j.issn.1000-4750.2019.04.S019

    WANG Yuanqing, GUAN Yang, LIU Ming, et al. Correction analysis of toughness parameters of cyclic microscopic damage model for building structural steel and its welds [J]. Engineering Mechanics, 2020, 37(Suppl): 20 − 31. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.04.S019
    WANG C, XU L, FAN J. Cyclic softening behavior of structural steel with strain range dependence [J]. Journal of Constructional Steel Research, 2021, 181: 106658. doi: 10.1016/j.jcsr.2021.106658
    TANG M, LIU Y, DURLOFSKY L J. A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems [J]. Journal of Computational Physics, 2020, 413: 109456. doi: 10.1016/j.jcp.2020.109456
    WANG C, XU L, FAN J. A general deep learning framework for history-dependent response prediction based on UA-Seq2Seq model [J]. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113357. doi: 10.1016/j.cma.2020.113357
    HORNIK K, STINCHCOMBE M, WHITE H. Multilayer feedforward networks are universal approximators [J]. Neural Networks, 1989, 2(5): 359 − 366. doi: 10.1016/0893-6080(89)90020-8
    LEFIK M, SCHREFLER B A. Artificial neural network as an incremental non-linear constitutive model for a finite element code [J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(28/29/30): 3265 − 3283. doi: 10.1016/S0045-7825(03)00350-5
    GHAVAMIAN F, SIMONE A. Accelerating multiscale finite element simulations of history-dependent materials using a recurrent neural network [J]. Computer Methods in Applied Mechanics and Engineering, 2019, 357: 112594. doi: 10.1016/j.cma.2019.112594
    王琛, 樊健生. 具有历史依赖效应的材料及结构响应预测通用深度学习模型MechPerformer[J]. 建筑结构学报, 2022, 43(8): 209 − 219. doi: 10.14006/j.jzjgxb.2021.0115

    WANG Chen, FAN Jiansheng. A general deep learning model MechPerformer for history-dependent response prediction in structural engineering [J]. Journal of Building Structures, 2022, 43(8): 209 − 219. (in Chinese) doi: 10.14006/j.jzjgxb.2021.0115
    MOZAFFAR M, BOSTANABAD R, CHEN W, et al. Deep learning predicts path-dependent plasticity [J]. Proceedings of the National Academy of Sciences, 2019, 116(52): 26414 − 26420. doi: 10.1073/pnas.1911815116
    WANG J J, WANG C, FAN J S, et al. A deep learning framework for constitutive modeling based on temporal convolutional network [J]. Journal of Computational Physics, 2022, 449: 110784. doi: 10.1016/j.jcp.2021.110784
    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]. Journal of Computational physics, 2019, 378: 686 − 707. doi: 10.1016/j.jcp.2018.10.045
    KARNIADAKIS G E, KEVREKIDIS I G, LU L, et al. Physics-informed machine learning [J]. Nature Reviews Physics, 2021, 3(6): 422 − 440. doi: 10.1038/s42254-021-00314-5
    CAI S, MAO Z, WANG Z, et al. Physics-informed neural networks (PINNs) for fluid mechanics: A review [J]. Acta Mechanica Sinica, 2021, 37(12): 1 − 12. doi: 10.48550/arXiv.2105.09506
    HAGHIGHAT E, JUANES R. Sciann: A keras/tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks [J]. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113552. doi: 10.1016/j.cma.2020.113552
    RAISSI M, YAZDANI A, KARNIADAKIS G E. Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations [J]. Science, 2020, 367(6481): 1026 − 1030. doi: 10.1126/science.aaw4741
    SIMO J C, HUGHES T J R. Computational inelasticity [M]. Berlin, Germany: Springer Science & Business Media, 2006.
    WANG C, FAN J, XU L, et al. Cyclic hardening and softening behavior of the low yield point steel: Implementation and validation [J]. Engineering Structures, 2020, 210: 110220. doi: 10.1016/j.engstruct.2020.110220
    BOYD S, BOYD S P, VANDENBERGHE L. Convex optimization [M]. London, UK: Cambridge University Press, 2004.
    WANG Y, YAO Q, KWOK J T, et al. Generalizing from a few examples: A survey on few-shot learning [J]. ACM Computing Surveys (CSUR), 2020, 53(3): 1 − 34.
    CHABOCHE J L. Time-independent constitutive theories for cyclic plasticity [J]. International Journal of Plasticity, 1986, 2(2): 149 − 188. doi: 10.1016/0749-6419(86)90010-0
    CHABOCHE J L. Constitutive equations for cyclic plasticity and cyclic viscoplasticity [J]. International Journal of Plasticity, 1989, 5(3): 247 − 302. doi: 10.1016/0749-6419(89)90015-6
    CHABOCHE J L. On some modifications of kinematic hardening to improve the description of ratchetting effects [J]. International Journal of Plasticity, 1991, 7(7): 661 − 678. doi: 10.1016/0749-6419(91)90050-9
    NAIR V, HINTON G E. Rectified linear units improve restricted Boltzmann machines [C]// The 27th International Conference on Machine Learning (ICML). Haifa Israel, Omnipress, 2010: 807 − 814.
    BOCHKOVSKIY A, WANG C Y, LIAO H Y M. Yolov4: Optimal speed and accuracy of object detection [J]. Computer Vision and Pattern Recognition, 2020, 23: 1 − 17. doi: 10.48550/arXiv.2004.10934
    XU L, NIE X, FAN J, et al. Cyclic hardening and softening behavior of the low yield point steel BLY160: Experimental response and constitutive modeling [J]. International Journal of Plasticity, 2016, 78: 44 − 63. doi: 10.1016/j.ijplas.2015.10.009
    CHO K, VAN MERRIËNBOER B, GULCEHRE C, et al. Learning phrase representations using RNN encoder-decoder for statistical machine translation [C]// Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP). Doha Qatar, Association for Computational Linguistics, 2014: 1724 − 1734.
    SUTSKEVER I, VINYALS O, LE Q V. Sequence to sequence learning with neural networks [C]// Twenty-eighth Conference on Neural Information Processing Systems (NIPS). Montréal Canada, MIT Press, 2014: 3104 − 3112.
    KINGMA D P, BA J. Adam: A method for stochastic optimization [C]// The 3rd International Conference for Learning Representations (ICLR). San Diego US, OpenReview.net, 2015.
    PASZKE A, GROSS S, MASSA F, et al. Pytorch: An imperative style, high-performance deep learning library [C]// Thirty-third Conference on Neural Information Processing Systems (NIPS). Vancouver Canada, MIT Press, 2019: 8026 − 8037.
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