Analytical Solution of the Concrete Homogenization Method Based on the ANN

LIU Yifan; MA Xiaomin; WANG Zhiyong; WANG Zhihua

doi:10.21656/1000-0887.440106

Volume 45 Issue 5

May 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(5): 554-570

LIU Yifan, MA Xiaomin, WANG Zhiyong, WANG Zhihua. Analytical Solution of the Concrete Homogenization Method Based on the ANN[J]. Applied Mathematics and Mechanics, 2024, 45(5): 554-570. doi: 10.21656/1000-0887.440106

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Analytical Solution of the Concrete Homogenization Method Based on the ANN

doi: 10.21656/1000-0887.440106

LIU Yifan^{1, 2
,},
MA Xiaomin^{1, 2},
WANG Zhiyong^{1, 2
,
,},
WANG Zhihua^{1, 2}

1.
Institute of Applied Mechanics, College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R.China
2.
Shanxi Key Laboratory of Material Strength and Structural Impact, Taiyuan 030024, P.R.China

Received Date: 2023-04-13
Rev Recd Date: 2023-12-18
Publish Date: 2024-05-01

Abstract

Abstract

By means of the self-defined artificial neural network (ANN) and its excellent function fitting function, aimed at aggregate-mortar matrix 2-phase concrete, the analytical solutions of the highly nonlinear coupling differential equation of the differential method in the indirect homogenization theory were given, the functional relations between the volume modulus and the shear modulus of concrete and the volume fractions of aggregate were obtained respectively, and the results were compared with those of numerical simulation. The results show that, the method based on the ANN is fast and has higher precision. In addition, the method of deconstructing ANN provides the formula of calculating the elastic modulus of aggregate-mortar matrix-pore 3-phase concrete directly from aggregate volume fractions and initial porosities under constant meso-mechanical parameters. For concrete samples with different aggregate volume fractions and initial porosities, the formula has higher calculation accuracy, and avoids the complex analysis and many assumptions of the traditional homogenization method. The work provides a new idea of homogenization method for composite materials.
- artificial neural network,
- concrete,
- homogenization,
- differential equation,
- elasticity modulus

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References

[1]	杜晨, 彭雄奇. 变厚度连续纤维增强复合材料铺层设计优化方法[J]. 应用数学和力学, 2022, 43(12): 1313-1323. doi: 10.21656/1000-0887.420410 DU Chen, PENG Xiongqi. Lamination design optimization for continuous fiber reinforced composites of variable thicknesses[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1313-1323. (in Chinese) doi: 10.21656/1000-0887.420410
[2]	KUMAR R D, WAGH PH, EMANOIL L. A review on synthetic fibers for polymer matrix composites: performance, failure modes and applications[J]. Materials, 2022, 15(14): 1790.
[3]	张雪琴, 马昆林, 龙广成, 等. 粗骨料形态特征表征参数及其与混凝土性能关系的研究进展[J]. 材料导报, 2023, 38(2): 22060263. https://www.cnki.com.cn/Article/CJFDTOTAL-CLDB202402012.htm ZHANG Xueqin, MA Kunlin, LONG Guangcheng, et al. Research progress in characterization parameters of coarse aggregate morphology and its relationship with concrete properties[J]. Materials Reports, 2023, 38(2): 22060263. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-CLDB202402012.htm
[4]	陈海玉, 徐福卫. 细观等效理论预测再生混凝土宏观力学参数[J]. 应用数学和力学, 2022, 43(7): 772-782. doi: 10.21656/1000-0887.420079 CHEN Haiyu, XU Fuwei. Prediction of the macroscopic mechanics properties of recycled aggregate concrete based on the mesoscopic equivalence theory[J]. Applied Mathematics and Mechanics, 2022, 43(7): 772-782. (in Chinese) doi: 10.21656/1000-0887.420079
[5]	WU L, HUANG D. Peridynamic modeling and simulations on concrete dynamic failure and penetration subjected to impact loadings[J]. Engineering Fracture Mechanics, 2022, 259: 108135. doi: 10.1016/j.engfracmech.2021.108135
[6]	李向南, 左晓宝, 周广盼, 等. 混凝土多尺度应力响应方程及其数值模拟[J]. 力学学报, 2022, 54(11): 3113-3126. doi: 10.6052/0459-1879-22-269 LI Xiangnan, ZUO Xiaobao, ZHOU Guangpan, et al. Equation and numerical simulation on multiscale stress response of concrete[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(11): 3113-3126. (in Chinese) doi: 10.6052/0459-1879-22-269
[7]	孙伟, 包世诚, 张嘎. 基于近场动力学均匀化的混凝土防渗墙等效损伤模型[J]. 同济大学学报(自然科学版), 2022, 50(9): 1240-1250. https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202209004.htm SUN Wei, BAO Shicheng, ZHANG Ga. An equivalent damage model of concrete cut-off wall based on homogenization of peridynamics[J]. Journal of Tongji University(Natural Science), 2022, 50(9): 1240-1250. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TJDZ202209004.htm
[8]	鞠晓喆, 朱加文, 梁利华, 等. 石墨烯纳米复合材料的降阶均匀化方法及其数值实现[J]. 复合材料学报, 2021, 38(12): 4362-4370. https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE202112038.htm JU Xiaozhe, ZHU Jiawen, LIANG Lihua, et al. Reduced order homogenization of graphene nanocomposites and its numerical implementation[J]. Acta Materiae Compositae Sinica, 2021, 38(12): 4362-4370. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE202112038.htm
[9]	SUN Q, ASQARDOUST S, SARMAH A, et al. Elastoplastic analysis of AA7075-O aluminum sheet by hybrid micro-scale representative volume element modeling with really-distributed particles and in-situ SEM experimental testing[J]. Journal of Materials Science & Technology, 2022, 123(28): 201-221.
[10]	邱伊健, 郑萍, 程香平, 等. 随机多尺度短切碳纤维复合结构模型中RVE尺寸效应和方向模量的均一化响应[J]. 兵工学报, 2022, 44(3): 702-717. https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO202303007.htm QIU Yijian, ZHENG Ping, CHENG Xiangping, et al. RVE size effect and homogenization response of directional modulus in stochastic multi-scale chopped carbon fiber composite structure[J]. Acta Armamentarii, 2022, 44(3): 702-717. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-BIGO202303007.htm
[11]	LI R, YANG M, LIANG B. The homogenized transformation method for the calculation of stress intensity factor in cracked FGM structure[J]. International Journal of Computational Methods, 2021, 18(2): 2050014. doi: 10.1142/S0219876220500140
[12]	梁文鹏, 周家作, 陈盼, 等. 基于均匀化理论的含水合物土弹塑性本构模型[J]. 岩土力学, 2021, 42(2): 481-490. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202102020.htm LIANG Wenpeng, ZHOU Jiazuo, CHEN Pan, et al. An elastoplastic constitutive model of gas hydrate bearing sediments based on homogenization theory[J]. Rock and Soil Mechanics, 2021, 42(2): 481-490. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX202102020.htm
[13]	REZAKHANI R, ALNAGGAR M, CUSATIS G. Multiscale homogenization analysis of alkali-silica reaction (ASR) effect in concrete[J]. Engineering, 2019, 5(6): 1139-1154. doi: 10.1016/j.eng.2019.02.007
[14]	CHOU T W. A self-consistent approach to the elastic stiffness of short-fiber composites[J]. Journal of Composite Materials, 1980, 14(3): 178-188. doi: 10.1177/002199838001400301
[15]	田十方, 李彪. 梯度优化物理信息神经网络(GOPINNs): 求解复杂非线性问题的深度学习方法[J/OL]. 物理学报[2023-04-13]. https://kns.cnki.net/kcms/detail//11.1958.O4.20230201.2155.004.html. TIAN Shifang, LI Biao. Gradient-optimized physical information neural networks (GOPINNs): deep learning methods for solving complex nonlinear problems[J/OL]. Acta Physica Sinica[2023-04-13]. https://kns.cnki.net/kcms/detail//11.1958.O4.20230201.2155.004.html. (in Chinese)
[16]	SHANG M, LI H, AHMAD A, et al. Predicting the mechanical properties of RCA-based concrete using supervised machine learning algorithms[J]. Materials, 2022, 15(2): 647. doi: 10.3390/ma15020647
[17]	HAN T, SIDDIQUE A, KHAYAT K, et al. An ensemble machine learning approach for prediction and optimization of modulus of elasticity of recycled aggregate concrete[J]. Construction and Building Materials, 2020, 244: 118271. doi: 10.1016/j.conbuildmat.2020.118271
[18]	LI X, LIU Z, CUI S, et al. Predicting the effective mechanical property of heterogeneous materials by image based modeling and deep learning[J]. Computer Methods in Applied Mechanics and Engineering, 2019, 347: 735-753. doi: 10.1016/j.cma.2019.01.005
[19]	查文舒, 李道伦, 沈陆航, 等. 基于神经网络的偏微分方程求解方法研究综述[J]. 力学学报, 2022, 54(3): 543-556. https://cdmd.cnki.com.cn/Article/CDMD-10358-1023101497.htm ZHA Wenshu, LI Daolun, SHEN Luhang, et al. Review of neural network-based methods for solving partial differential equations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 543-556. (in Chinese) https://cdmd.cnki.com.cn/Article/CDMD-10358-1023101497.htm
[20]	闫海, 邓忠民. 基于深度学习的短纤维增强聚氨酯复合材料性能预测[J]. 复合材料学报, 2019, 36(6): 1413-1420. https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE201906007.htm YAN Hai, DENG Zhongmin. Prediction of properties of short fiber reinforced urethane polymer composites based on deep learning[J]. Acta Materiae Compositae Sinica, 2019, 36(6): 1413-1420. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-FUHE201906007.htm
[21]	KANI J, ELSHEIKH A. Reduced-order modeling of subsurface multi-phase flow models using deep residual recurrent neural networks[J]. Transport in Porous Media, 2019, 126(3): 713-741. doi: 10.1007/s11242-018-1170-7
[22]	YANG H, GUO X, TANG S, et al. Derivation of heterogeneous material laws via data-driven principal component expansions[J]. Computational Mechanics, 2019, 64: 365-379. doi: 10.1007/s00466-019-01728-w
[23]	ZHANG J, CHEN W S, HAO H, et al. Performance of concrete targets mixed with coarse aggregates against rigid projectile impact[J]. International Journal of Impact Engineering, 2020, 141: 103565. doi: 10.1016/j.ijimpeng.2020.103565
[24]	NORRIS A N. A differential scheme for the effective moduli of composites[J]. Mechanics of Materials, 1985, 4(1): 1-16. doi: 10.1016/0167-6636(85)90002-X
[25]	WANG H L, LI Q B. Prediction of elastic modulus and Poisson's ratio for unsaturated concrete[J]. International Journal of Solids and Structures, 2007, 44(5): 1370-1379. doi: 10.1016/j.ijsolstr.2006.06.028
[26]	ZHANG J, WANG Z Y, YANG H W, et al. 3D meso-scale modeling of reinforcement concrete with high volume fraction of randomly distributed aggregates[J]. Construction and Building Materials, 2018, 164: 350-361. doi: 10.1016/j.conbuildmat.2017.12.229
[27]	周杰, 赵婷婷, 陈青青, 等. 基于GoogLeNet的混凝土细观模型应力-应变曲线预测[J]. 应用数学和力学, 2022, 43(3): 290-299. doi: 10.21656/1000-0887.420136 ZHOU Jie, ZHAO Tingting, CHEN Qingqing, et al. Prediction of concrete meso-model stress-strain curves based on GoogLeNet[J]. Applied Mathematics and Mechanics, 2022, 43(3): 290-299. (in Chinese) doi: 10.21656/1000-0887.420136
[28]	LI B B, JIANG J F, XIONG H B, et al. Improved concrete plastic-damage model for FRP-confined concrete based on true tri-axial experiment[J]. Composite Structures, 2021, 269: 114051. doi: 10.1016/j.compstruct.2021.114051
[29]	CHEN P, LIU J X, CUI S M, et al. Mesoscale analysis of concrete under axial compression[J]. Construction and Building Materials, 2022, 337: 127580. doi: 10.1016/j.conbuildmat.2022.127580
[30]	苏捷. 混凝土受压与受拉性能的尺寸效应研究[D]. 长沙: 湖南大学, 2012. SU Jie. The research on the size effect of concrete behavior in compression and tension[D]. Changsha: Hunan University, 2012. (in Chinese)
[31]	秦庆华, 杨庆生. 非均匀材料多场耦合行为的宏细观理论[M]. 北京: 高等教育出版社, 2006: 17-19. QIN Qinghua, YANG Qingsheng. Macro-Micro-Theory on Multi-Field Coupling Behavior of Heterogeneous Materials[M]. Beijing: Higher Education Press, 2006: 17-19. (in Chinese)
[32]	毛晓敏, 张慧华, 纪晓磊, 等. 基于XFEM和GA-BP神经网络的裂纹智能识别研究[J]. 应用数学和力学, 2022, 43(11): 1268-1280. doi: 10.21656/1000-0887.420250 MAO Xiaomin, ZHANG Huihua, JI Xiaolei, et al. Intelligent crack recognition based on XFEM and GA-BP neural networks[J]. Applied Mathematics and Mechanics, 2022, 43(11): 1268-1280. (in Chinese) doi: 10.21656/1000-0887.420250
[33]	DONG H, LINGHU J, NIE Y. Integrated wavelet-learning method for macroscopic mechanical properties prediction of concrete composites with hierarchical random configurations[J]. Composite Structures, 2023, 304(1): 116357.
[34]	杜修力, 金浏. 混凝土材料宏观力学特性分析的细观单元等效化模型[J]. 计算力学学报, 2012, 29(5): 654-661. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201205004.htm DU Xiuli, JIN Liu. Analysis of macroscopic mechanical properties of concrete materials meso-unit equivalence model[J]. Chinese Journal of Computational Mechanics, 2012, 29(5): 654-661. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201205004.htm
[35]	陈青青, 张煜航, 张杰, 等. 含孔隙混凝土二维细观建模方法研究[J]. 应用数学和力学, 2020, 41(2): 182-194. doi: 10.21656/1000-0887.400058 CHEN Qingqing, ZHANG Yuhang, ZHANG Jie, et al. Study on a 2D mesoscopic modeling method for concrete with voids[J]. Applied Mathematics and Mechanics, 2020, 41(2): 182-194. (in Chinese) doi: 10.21656/1000-0887.400058
[36]	陈青青. 含孔隙混凝土细观建模方法与数值研究[D]. 太原: 太原理工大学, 2020. CHEN Qingqing. Meso-scale modeling and numerical investigation of concrete with pores[D]. Taiyuan: Taiyuan University of Technology, 2020. (in Chinese)
[37]	金浏, 余文轩, 杜修力, 等. 低应变率下混凝土动态拉伸破坏尺寸效应细观模拟[J]. 工程力学, 2019, 36(8): 59-78. https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201908006.htm JIN Liu, YU Wenxuan, DU Xiuli, et al. Meso-scale simulation of size effect of dynamic tensile strength of concrete under low strain rates[J]. Engineering Mechanics, 2019, 36(8): 59-78. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201908006.htm
[38]	吴震. EPS多孔混凝土力学性能试验及三维数值模拟研究[D]. 上海: 上海交通大学, 2012. WU Zhen. Experimental research and 3D modeling of EPS cellular concrete[D]. Shanghai: Shanghai Jiao Tong University, 2012. (in Chinese)
[39]	金浏. 细观混凝土分析模型与方法研究[D]. 北京: 北京工业大学, 2014. JIN Liu. Study on meso-scopic model and analysis method of concrete[D]. Beijing: Beijing University of Technology, 2014. (in Chinese)