A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

被引:2
作者
Chen, Ce [1 ,2 ,3 ]
Wu, Liujun [1 ,2 ,3 ]
Fu, Jiaqi [1 ,2 ]
Xin, Chenyang [1 ,2 ,3 ]
Liu, Wenbin [1 ,2 ,4 ]
Duan, Huiling [1 ,2 ,3 ]
机构
[1] Peking Univ, Dept Mech & Engn Sci, State Key Lab Turbulence & Complex Syst, Coll Engn,BIC ESAT, Beijing 100871, Peoples R China
[2] Peking Univ, HEDPS, CAPT, Beijing 100871, Peoples R China
[3] Peking Univ, Collaborat Innovat Ctr, IFSA, MoE, Beijing 100871, Peoples R China
[4] City Univ Hong Kong, Dept Mech Engn, Lab Nanomat & Nanomech, Hong Kong, Peoples R China
基金
中国国家自然科学基金;
关键词
Nonlinear homogenization; Neural network; Micromechanics; Interface effects; Mori-Tanaka method; PARTICLE-REINFORCED COMPOSITES; ELASTIC FIELD; STRAIN; MODEL; HOMOGENIZATION; BEHAVIOR; STRESS; RUBBER; FRAMEWORK; SOLIDS;
D O I
10.1016/j.jmps.2024.105681
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics -guided neural network. In particular, the nonlinear Mori-Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori-Tanaka method in the condition of the small deformation. Notably, this neural -network -based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.
引用
收藏
页数:22
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