An unsupervised machine learning approach to reduce nonlinear FE2 multiscale calculations using macro clustering

被引:12
作者
Chaouch, Souhail [1 ]
Yvonnet, Julien [1 ]
机构
[1] Univ Gustave Eiffel, MSME, CNRS, UMR 8208, F-77454 Marne La Vallee, France
关键词
Multi-scale modeling; Unsupervised learning; k-means FE2; Finite Elements Method; COMPUTATIONAL HOMOGENIZATION; HETEROGENEOUS MATERIALS; HYPER-REDUCTION; PREDICTION; BEHAVIOR;
D O I
10.1016/j.finel.2023.104069
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Solving nonlinear multiscale methods with history-dependent behaviors and fine macroscopic meshes is a well-known challenge. In this work, an unsupervised machine learning-based clustering approach is developed to reduce nonlinear Multilevel Finite Element-FE2 calculations. In contrast with most available techniques which aim at developing Reduced Order Models (ROM) or AI-based surrogate models for the microscale nonlinear problems, the present technique reduces the problem from the macro scale by creating clusters of macro Gauss points which are assumed to be in close mechanical states. Then, a single micro nonlinear Representative Volume Element (RVE) calculation is performed for each cluster. A linear approximation of the macro stress is used in each cluster. Handling internal variables is carried out by using anelastic macro strains in the clustering vectors in addition to the macro strains components. Finally, some convergence issues related to the use of clusters at the macro scale are addressed through a cluster freezing algorithm. The technique is applied to nonlinear hyperelastic, viscoelastic and elastoplastic composites. In contrast to available ROM or machine-learning-based acceleration techniques, the present method does not require neither preliminary off-line calculations, nor training, nor data base, nor reduced basis at the macro scale, while maintaining typical speed-up factors about 20 as compared to classical FE2.
引用
收藏
页数:26
相关论文
共 51 条
[21]   Computational homogenization of nonlinear elastic materials using neural networks [J].
Le, B. A. ;
Yvonnet, J. ;
He, Q. -C. .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2015, 104 (12) :1061-1084
[22]   Multiscale computation on feedforward neural network and recurrent neural network [J].
Li, Bin ;
Zhuang, Xiaoying .
FRONTIERS OF STRUCTURAL AND CIVIL ENGINEERING, 2020, 14 (06) :1285-1298
[23]   A Clustering Method Based on K-Means Algorithm [J].
Li, Youguo ;
Wu, Haiyan .
INTERNATIONAL CONFERENCE ON SOLID STATE DEVICES AND MATERIALS SCIENCE, 2012, 25 :1104-1109
[24]   Microstructural material database for self-consistent clustering analysis of elastoplastic strain softening materials [J].
Liu, Zeliang ;
Fleming, Mark ;
Liu, Wing Kam .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 330 :547-577
[25]   Self-consistent clustering analysis: An efficient multi-scale scheme for inelastic heterogeneous materials [J].
Liu, Zeliang ;
Bessa, M. A. ;
Liu, Wing Kam .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2016, 306 :319-341
[26]   A Stochastic FE2 Data-Driven Method for Nonlinear Multiscale Modeling [J].
Lu, Xiaoxin ;
Yvonnet, Julien ;
Papadopoulos, Leonidas ;
Kalogeris, Ioannis ;
Papadopoulos, Vissarion .
MATERIALS, 2021, 14 (11)
[27]   A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites [J].
Lu, Xiaoxin ;
Giovanis, Dimitris G. ;
Yvonnet, Julien ;
Papadopoulos, Vissarion ;
Detrez, Fabrice ;
Bai, Jinbo .
COMPUTATIONAL MECHANICS, 2019, 64 (02) :307-321
[28]  
MacQueen J., 1967, P 5 BERKELEY S MATH, V1, P281
[29]   Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN) [J].
Masi, Filippo ;
Stefanou, Ioannis .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 398
[30]   Nonuniform transformation field analysis [J].
Michel, JC ;
Suquet, P .
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2003, 40 (25) :6937-6955