CONSTITUTIVE RELATIONS OF GRANULAR MATERIALS BY INTEGRATING MICROMECHANICAL KNOWLEDGE WITH DEEP LEARNING
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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.Abstract:Constitutive relations of granular materials are of great significance to many fields, such as geotechnical engineering. Different from traditional phenomenological constitutive theory, this study explores a micromechanics-informed data-driven constitutive modelling approach for granular materials via machine learning models. On the basis of Vogit’s homogenization assumption, an analytical small-strain stress-strain relation is established. This relation uniquely determines a group of micromechanical fabric variables associated with the constitutive behavior of granular materials. These recognized variables, together with principal strain and stress sequence pairs reflecting macroscopic properties of granular materials, are obtained via a series of discrete element models of triaxial compression tests. Considering the fact that these microscopic fabric tensors are internal variables, which cannot be directly used as inputs of a material constitutive model, a directed graph is introduced to incorporate microstructural information implicitly in the prediction of stress-strain responses. The gated recurrent unit (GRU) based recurrent neural networks are used as basic deep learning models to describe the mapping relation between nodes in the designed directed graph. In this study, the entire stress-strain prediction model can be assembled with two neural networks that are trained separately, after unfolding the directed graph from the target node to the source node. By testing the trained deep learning model based on brand new datasets, the results demonstrate that the proposed training approach can satisfactorily capture the multi-directional stress-strain responses with reversal loadings, such as conventional triaxial compression with unloading-reloading cycles, true-triaxial compression with constant intermediate principal stress (constant- b), and constant mean effective effective stress (constant- p) conditions with unloading-reloading cycles. The prediction results also show that the trained model possesses satisfactory interpolation and extrapolation capability. Considering the excellent ability of deep learning in terms of capturing the mechanical responses of granular materials and the unique features of open learning when new data is available, integrating a data-driven paradigm with theoretical constitutive models may be one of the important directions for constitutive research of granular materials.
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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
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[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): 789-818doi: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): 429-435doi: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): 207-230doi: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): 105-126doi: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): 161-178doi: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: 216-241doi: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): 467-499doi: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: 113514doi: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): 1315-1335doi: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: 104239doi: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: 103046doi:10.1016/j.ijplas.2021.103046 [19] Hornik K, Stinchcombe M, White H. Multilayer feedforward networks are universal approximators.Neural Networks, 1989, 2(5): 359-366doi: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: 375-392doi: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): 2239-2253doi: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): 1281-1300doi: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: 527-536doi: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: 113454doi: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: 113493doi: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: 104161doi: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: 103154doi: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) -
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