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

Qu Tongming; Feng Yuntian; Wang Mengqi; Zhao Tingting; Di Shaocheng

doi:10.6052/0459-1879-21-221

Volume 53 Issue 9

Sep. 2021

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Article Navigation > Chinese Journal of Theoretical and Applied Mechanics > 2021 > 53(9): 2404-2415

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

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

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

doi: 10.6052/0459-1879-21-221

*.
Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea SA1 8EP, UK
†.
College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, China
**.
College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China

Funds: The project was supported by the National Natural Science Foundation of China (12072217, 41606213, 51639004)

Received Date: 2021-05-24
Accepted Date: 2021-06-15

Available Online: 2021-06-16

Publish Date: 2021-09-18

Abstract

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.
- granular materials,
- constitutive relations,
- deep learning,
- micromechanics,
- discrete element models,
- data-driven

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References(32)

References

[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)