| Multi-scale finite element methods are required to perform parallel computations between the macroscopic and microscopic scales when dealing with composite material problems.This method utilizes homogenization theory to consider the influence of microstructure on macroscopic properties and can obtain the macroscopic constitutive model of composite materials.This method has accelerated the analysis of mechanical problems of composite materials to some extent.However,when dealing with nonlinear composite material problems,it is necessary to repeatedly perform full-field finite element iterative analysis on several finely resolved microscopic finite element models,resulting in high computational costs.In order to overcome this difficulty,scholars have begun to focus on data-driven constitutive replacement models,and the data-driven algorithms used to train models have evolved from early artificial neural networks(ANN)to current recurrent neural networks(RNN).The trained data-driven model has certain efficiency advantages compared with traditional methods in dealing with complex problems,and the model can be reused with almost no follow-up training cost.This thesis establishes an RNN data-driven model to replace the constitutive analysis of microscopic scale,in order to accelerate the multiscale simulation of nonlinear two-dimensional particle-reinforced composite materials.A database is generated through finite element analysis of microstructures subjected to randomly applied loading paths,which is used to train the RNN model.By setting different material properties,the issues of historical dependence and non-historical dependence are separately studied,and the model accuracy is improved by discussing the modeling effect of RNN unit types and the database sample selection in the RVE.Regarding the RNN unit types,the modeling effects of three commonly used RNN units are studied.Regarding the database sample selection,the influence of the number of samples and the output variable dimension on the model performance is discussed,as well as the generalization ability of the model trained by the samples generated from the randomly applied loading paths to other loading paths.Finally,the idea of transfer learning is introduced,and the samples corresponding to other loading paths are used for secondary training of the model to enhance its generalization ability to other loading paths.The research conclusions of this thesis are as follows:(1)In this study,RNN data-driven models were established to replace the microscale constitutive analysis,in order to accelerate the multiscale simulation of nonlinear two-dimensional particle-reinforced composite materials.The database for training the RNN model was generated by conducting finite element analysis on microstructures under random loading paths.The model accuracy was improved by discussing the model type for RVE units and sample selection for the database with different material properties,as well as the effects of sample quantity and output variable dimension on the model accuracy.Finally,transfer learning was introduced to enhance the model’s generalization ability to other loading paths.The research results show that all RNN models can accurately predict the microstructure’s constitutive relationship for both historical and non-historical dependency problems.The prediction effect for non-historical dependency problems is better than that for historical dependency problems,indicating that historical state information affects the model’s effectiveness to some extent.(2)Comparing the three RNN data-driven models established for historical and non-historical dependency problems,it was found that regardless of the problem type,the training time for the Tanh-RNN unit model was much shorter than that for the LSTM unit model and GRU unit model,but its model error was much larger than the other two models.The LSTM and GRU unit models performed similarly in terms of model efficiency and calculation accuracy.Although the Tanh-RNN unit model has a great advantage in computing efficiency,considering that the training time for all three models is not long,LSTM and GRU units are the best choices for modeling.(3)The study investigated the effect of the sample size in the database used for training the data-driven model.The results showed that as the sample size increased,the model’s performance improved,but the improvement was not linear and gradually diminished.Therefore,it is possible to reduce the sample size as much as possible to save time and cost while ensuring the model’s accuracy.(4)The study also examined the effect of the model’s output variable dimension on its performance.The results indicated that increasing the output variable dimension would reduce the model’s performance,but as long as the dimension increase is not too much,the error remains within an acceptable range.(5)The study verified the generalization ability of the trained model using the loading path generated in this paper.The specific method was to input other unknown loading paths generated samples into the trained model for prediction and compare the prediction results with the results of finite element calculation.The results showed that the trained data-driven model also had a certain recognition effect on other unknown loading paths,and the error was within the ideal range.(6)The idea of transfer learning was introduced to perform secondary training on the trained data-driven model by adding new samples generated by other loading paths.After comparing the errors,it was found that transfer learning can significantly improve the model’s ability to generalize to other paths. |
