EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于深度学习和细观力学的颗粒材料本构关系研究

瞿同明 冯云田 王孟琦 赵婷婷 狄少丞

瞿同明, 冯云田, 王孟琦, 赵婷婷, 狄少丞. 基于深度学习和细观力学的颗粒材料本构关系研究. 力学学报, 2021, 53(9): 2404-2415 doi: 10.6052/0459-1879-21-221
引用本文: 瞿同明, 冯云田, 王孟琦, 赵婷婷, 狄少丞. 基于深度学习和细观力学的颗粒材料本构关系研究. 力学学报, 2021, 53(9): 2404-2415 doi: 10.6052/0459-1879-21-221
Qu Tongming, Feng Yuntian, Wang Mengqi, Zhao Tingting, Di Shaocheng. Constitutive relations of granular materials by integrating micromechanical knowledge with deep learning. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2404-2415 doi: 10.6052/0459-1879-21-221
Citation: Qu Tongming, Feng Yuntian, Wang Mengqi, Zhao Tingting, Di Shaocheng. Constitutive relations of granular materials by integrating micromechanical knowledge with deep learning. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2404-2415 doi: 10.6052/0459-1879-21-221

基于深度学习和细观力学的颗粒材料本构关系研究

doi: 10.6052/0459-1879-21-221
基金项目: 国家自然科学基金资助项目(12072217, 41606213, 51639004)
详细信息
    作者简介:

    冯云田, 教授, 主要从事计算力学研究. E-mail: y.feng@swansea.ac.uk

  • 中图分类号: TU4

CONSTITUTIVE RELATIONS OF GRANULAR MATERIALS BY INTEGRATING MICROMECHANICAL KNOWLEDGE WITH DEEP LEARNING

Funds: The project was supported by the National Natural Science Foundation of China (12072217, 41606213, 51639004)
  • 摘要: 颗粒材料的本构关系对岩土工程等众多领域至关重要. 不同于传统的唯象本构理论, 本文基于机器学习模型探索了一种细观力学理论指导下的数据驱动型颗粒材料本构关系预测方法. 根据Vogit均质化假设, 建立了小应变条件下颗粒材料应力−应变解析关系, 此关系唯一地确定了一组与颗粒材料本构行为相关的细观组构变量. 这些变量与反应颗粒材料宏观性质的主应力和主应变信息通过一系列离散元三轴压缩数值试验获得. 考虑到细观组构变量为内变量, 不能直接作为本构模型的输入. 本文基于有向图方法将颗粒材料微观结构信息隐式地包含在应力−应变的预测当中, 并采用门控循环单元(GRU)循环神经网络作为基础深度学习模型描述有向图中结点之间的映射关系. 通过将有向图从目标节点沿源节点展开, 整个应力−应变预测模型可由两个神经网络分别训练并组装而成. 将训练后的深度学习模型在全新的数据集上进行测试, 结果表明该训练策略能有效捕捉到颗粒材料在常规三轴任意加卸载, 等中主应力系数b的真三轴加载, 和等平均有效应力p的真三轴加卸载等复杂多轴加载工况下的应力−应变响应关系, 模型具有良好的内插和外推预测能力. 考虑到深度学习模型捕捉颗粒材料力学响应的能力及其开放式学习的特点, 充分结合数据驱动方法和理论本构模型可能是颗粒材料本构研究的一个重要方向.

     

  • 图  1  基于深度学习的本构模型示意图

    Figure  1.  Diagram of deep learning-based constitutive models

    图  2  人工神经网络的训练过程

    Figure  2.  Basic procedures of training artificial neural networks

    图  3  颗粒接触与接触位移

    Figure  3.  A contact between particles and contact displacements

    图  4  基于有向图包含组构演化的本构训练方式

    Figure  4.  A directed graph-based constitutive training approach incorporating fabric evolution

    图  5  离散元三轴试验模型

    Figure  5.  Triaxial compression models via discrete element modelling

    图  6  学习曲线

    Figure  6.  Learning curves

    图  7  两组最佳与最差预测

    Figure  7.  Examples of the two best and worst predictions

    图  8  几组代表性内插预测

    Figure  8.  Some representative interpolation predictions

    图  9  几种代表性外推预测

    Figure  9.  Some representative extrapolation predictions

  • [1] 孙其诚, 辛海丽, 刘建国等. 颗粒体系中的骨架及力链网络. 岩土力学, 2009, 30(S1): 83-87 (Sun Qicheng, Xin Haili, Liu Jianguo, et al. Skeleton and force chain network in static granular material. Rock and Soil Mechanics, 2009, 30(S1): 83-87 (in Chinese)
    [2] 罗汀, 高智伟, 万征等. 土剪胀性的应力路径相关规律及其模拟. 力学学报, 2010, 42(1): 93-101 (Luo Ting, Gao Zhiwei, Wan Zheng, et al. Influence of the stress path on dilatancy of soils and its modeling. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 93-101 (in Chinese)
    [3] 路德春, 姚仰平. 砂土的应力路径本构模型. 力学学报, 2005, 37(4): 451-459 (Lu Dechun, Yao Yangping. Constitutive model of sand considering complex stress paths. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(4): 451-459 (in Chinese) doi: 10.3321/j.issn:0459-1879.2005.04.010
    [4] 刘嘉英, 周伟, 马刚等. 颗粒材料三维应力路径下的接触组构特性. 力学学报, 2019, 51(1): 26-35 (Liu Jiaying, Zhou Wei, Ma Gang, et al. Contact fabric characteristics of granular materials under three dimensional stress paths. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 26-35 (in Chinese)
    [5] 钱劲松, 陈康为, 张磊. 粒料固有各向异性的离散元模拟与细观分析. 力学学报, 2018, 50(5): 1041-1050 (Qian Jinsong, Chen Kangwei, Zhang Lei. Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1041-1050 (in Chinese)
    [6] 万征, 孟达. 复杂加载条件下的砂土本构模型. 力学学报, 2018, 50(4): 929-948 (Wan Zheng, Meng Da. A constitutive model for sand under complex loading conditions. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 929-948 (in Chinese)
    [7] 姚仰平, 张民生, 万征等. 基于临界状态的砂土本构模型研究. 力学学报, 2018, 50(3): 589-598 (Yao Yangping, Zhang Minsheng, Wan Zheng, et al. Constitutive model for sand based on the critical state. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 589-598 (in Chinese)
    [8] Guo N, Zhao J. A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media. International Journal for Numerical Methods in Engineering, 2014, 99(11): 789-818 doi: 10.1002/nme.4702
    [9] Ellis G, Yao C, Zhao R, et al. Stress-strain modeling of sands using artificial neural networks. Journal of Geotechnical Engineering, 1995, 121(5): 429-435 doi: 10.1061/(ASCE)0733-9410(1995)121:5(429)
    [10] Penumadu D, Zhao R. Triaxial compression behavior of sand and gravel using artificial neural networks (ANN). Computers and Geotechnics, 1999, 24(3): 207-230 doi: 10.1016/S0266-352X(99)00002-6
    [11] Ghaboussi J, Pecknold DA, Zhang M, et al. Autoprogressive training of neural network constitutive models. International Journal for Numerical Methods in Engineering, 1998, 42(1): 105-126 doi: 10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V
    [12] Shin H, Pande G. On self-learning finite element codes based on monitored response of structures. Computers and Geotechnics, 2000, 27(3): 161-178 doi: 10.1016/S0266-352X(00)00016-1
    [13] Wang K, Sun W. Meta-modeling game for deriving theory-consistent, microstructure-based traction–separation laws via deep reinforcement learning. Computer Methods in Applied Mechanics and Engineering, 2019, 346: 216-241 doi: 10.1016/j.cma.2018.11.026
    [14] Wang K, Sun W, Du Q. A cooperative game for automated learning of elasto-plasticity knowledge graphs and models with AI-guided experimentation. Computational Mechanics, 2019, 64(2): 467-499 doi: 10.1007/s00466-019-01723-1
    [15] Wang K, Sun W, Du Q. A non-cooperative meta-modeling game for automated third-party calibrating, validating and falsifying constitutive laws with parallelized adversarial attacks. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113514 doi: 10.1016/j.cma.2020.113514
    [16] Zhang P, Yin Z, Jin Y, et al. An AI-based model for describing cyclic characteristics of granular materials. International Journal for Numerical and Analytical Methods in Geomechanics, 2020, 44(9): 1315-1335 doi: 10.1002/nag.3063
    [17] Karapiperis K, Stainier L, Ortiz M, et al. Data-Driven multiscale modeling in mechanics. Journal of the Mechanics and Physics of Solids, 2021, 147: 104239 doi: 10.1016/j.jmps.2020.104239
    [18] Qu T, Di S, Feng Y, et al. Towards data-driven constitutive modelling for granular materials via micromechanics-informed deep learning. International Journal of Plasticity, 2021, 144: 103046 doi: 10.1016/j.ijplas.2021.103046
    [19] Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators. Neural Networks, 1989, 2(5): 359-366 doi: 10.1016/0893-6080(89)90020-8
    [20] Qu T, Di S, Feng Y, et al. Deep learning predicts stress-strain relations of granular materials based on triaxial testing data. Computer Modeling in Engineering & Sciences, 2021, 128(1): 129-144
    [21] 陈生水. 土的本构模型研究之浅见——读李广信、杨光华文章有感. 岩土工程学报, 1992, 14(2): 89-92 (Chen Shengshui. On the study of constitutive models of soil—thoughts after reading the paper written by Li Guangxin and Yang Guanghua. Chinese Journal of Geotechnical Engineering, 1992, 14(2): 89-92 (in Chinese) doi: 10.3321/j.issn:1000-4548.1992.02.014
    [22] Kawamoto R, Andò E, Viggiani G, et al. All you need is shape: Predicting shear banding in sand with LS-DEM. Journal of the Mechanics and Physics of Solids, 2018, 111: 375-392 doi: 10.1016/j.jmps.2017.10.003
    [23] Qu T, Feng Y, Wang M. An adaptive granular representative volume element model with an evolutionary periodic boundary for hierarchical multiscale analysis. International Journal for Numerical Methods in Engineering, 2021, 122(9): 2239-2253 doi: 10.1002/nme.6620
    [24] O'Sullivan C. Particulate Discrete Element Modelling: a Geomechanics Perspective. London: CRC Press, 2011.
    [25] Qu T, Feng Y, Zhao T, et al. A hybrid calibration approach to Hertz-type contact parameters for discrete element models. International Journal for Numerical and Analytical Methods in Geomechanics, 2020, 44(9): 1281-1300 doi: 10.1002/nag.3061
    [26] Qu T, Feng Y, Wang M, et al. Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation. Powder Technology, 2020, 366: 527-536 doi: 10.1016/j.powtec.2020.02.077
    [27] Feng Y. An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Basic framework and general contact model. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113454 doi: 10.1016/j.cma.2020.113454
    [28] Feng Y. An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues. Computer Methods in Applied Mechanics and Engineering, 2021, 373: 113493 doi: 10.1016/j.cma.2020.113493
    [29] Sibille L, Benahmed N, Darve F. Constitutive response predictions of both dense and loose soils with a discrete element model. Computers and Geotechnics, 2021, 135: 104161 doi: 10.1016/j.compgeo.2021.104161
    [30] Qu T, Feng Y, Wang Y, et al. Discrete element modelling of flexible membrane boundaries for triaxial tests. Computers and Geotechnics, 2019, 115: 103154 doi: 10.1016/j.compgeo.2019.103154
    [31] 马刚, 刘嘉英, 常晓林等. 堆石体在真三轴应力状态下的非共轴性与剪胀特性. 中南大学学报(自然科学版), 2016, 47(5): 1697-1707 (Ma Gang, Liu Jiaying, Chang Xiaolin, et al. Non-coaxiality and dilatancy of rockfill materials under true triaxial stress condition. Journal of Central South University (Science and Technology), 2016, 47(5): 1697-1707 (in Chinese)
    [32] 杨光华. 土的现代本构理论的发展回顾与展望. 岩土工程学报, 2018, 40(8): 1363-1372 (Yang Guanghua. Review of progress and prospect of modern constitutive theories for soils. Chinese Journal of Geotechnical Engineering, 2018, 40(8): 1363-1372 (in Chinese)
  • 加载中
图(9)
计量
  • 文章访问数:  459
  • HTML全文浏览量:  143
  • PDF下载量:  186
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-05-24
  • 录用日期:  2021-06-15
  • 网络出版日期:  2021-06-16
  • 刊出日期:  2021-09-18

目录

    /

    返回文章
    返回