Recent progress on mechanics investigations of heterogeneous materials based on physical information neural networks
Heterogeneous materials are a widely utilized concept in the field of engineering.The explosive development of deep learning methods in recent years has introduced new approaches for addressing many complex problems within heterogeneous material systems.However,deep learning,due to its high degree of parallelism,nonlinearity,and numerous complex parameter operations,is difficult to interpret intuitively.In the application of deep learning to heterogeneous materials,challenges such as generating physically meaningless solutions,low generalization,and reliance on high-quality and large datasets are often encountered.Physics-informed neural networks(PINNs)effectively address these issues by integrating physical knowledge with deep learning methods.Consequently,PINNs have gradually become a popular method in the fields of solid mechanics and structural engineering,offering new ideas for predicting and designing heterogeneous material systems.To better understand the related research work,this paper provides a systematic review of the application of PINNs in the field of heterogeneous materials and summarizes the improvements of PINNs adapted to the characteristics of the problems of heterogeneous materials,including the use of the idea of domain decomposition,the use of reducing the order of derivatives to cope with the poor training accuracy of the network resulting from the higher-order partial differential equations which describe the problem,the combination of physical information and large models to cope with the increasingly complex physical problems in practice and other types of physical neural networks such as deep material networks.Subsequently,the practical applications of PINNs in heterogeneous materials are systematically introduced,with the most extensive applications in composites,concrete,alloy microstructures,and elastography of heterogeneous materials,etc.,and are mainly focused on thermodynamic problems and material properties(strength,fatigue damage,etc.),as a large number of theoretical models of partial differential equations(PDEs)have already been accumulated in the research of these areas.On this basis,we look forward to further research directions and highlight the prospects for more in-depth and extensive applications of PINNs to heterogeneous materials.Three main points are mentioned:(1)Different types of problems cannot be directly migrated to use PINNs trained for other types of problems,which limits the generalization of PINNs to a certain extent.Is it possible to develop a generalized framework for PINNs,so that arbitrary partial differential equations can be solved under this framework?(2)Nowadays,the application of PINNs mainly focuses on the mature heterogeneous material systems,while the emerging materials,such as meta-materials and nano-materials,have fewer applications.On the one hand,it may need the development of related theories,and on the other hand,it can be used for the construction of new network structures according to the new characteristics of the new materials.(3)At present,the training of PINNs on heterogeneous materials mainly uses single-source data,but some scholars use multi-source data to train PINNs.Research on training PINNs with multi-source data can be carried out to optimize the network structure of PINNs,and further improve the PINNs in terms of reducing the cost of data acquisition,accelerating the convergence,and improving the prediction accuracy.
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