Research On Hybrid Numerical Method For Uncertain Parameter Identification Of Nonlinear Materials

The finite element method is widely used in the analysis of solid structures,in which the explicit finite element algorithm is mainly used to simulate the high-speed collision problems in the fields of automobile and aerospace.As the core module of the finite element solver,the material constitutive module determines the relationship between the internal deformation and the internal force.Among them,a large number of metal materials used in engineering can be calculated by plastic constitutive law,while most rubber materials with large deformation can be summarized by the behavior of superelastic materials.In order to meet the needs of practical engineering applications,we need to develop a plastic and hyperelastic constitutive calculation program based on explicit finite element method,and calibrate with foreign commercial software to verify the correctness of the algorithm.In addition,in practical engineering,the parameter calibration of material constitutive model has also attracted much attention.The calibration of material parameters can be regarded as an inverse problem.When the observation response of the system is provided,the parameters can be identified and calibrated by reverse technology.In fact,this inverse problem is often morbid.The uncertainty method regards the input and output variables of the system as random variables,and uses the existing prior information and the constructed likelihood function to model the posterior distribution of the parameters.In many cases,the uncertainty method can effectively solve the ill-conditioned inverse problems in practical engineering.Among them,the approximate Bayesian method is widely used in inverse problem solving because it does not need to construct the specific likelihood function form directly.In view of the above,the main work of this paper is as follows:(1)Based on the updated Lagrangian scheme of nonlinear finite element method,the equivalent integral form of equilibrium differential equation of finite deformation solid is derived,and the specific flow of explicit finite element algorithm is introduced.Then,the stress renewal algorithms of J2 plasticity,Johnson-Cook constitutive model and Mooney-Rilvlin superelasticity are derived,and the corresponding explicit finite element programs are developed according to the numerical calculation theory.Compared with the results of commercial software,the accuracy of the nonlinear material constitutive model established in this paper is verified.(2)Based on the above Mooney-Rilvlin hyperelasticity and Johnson-Cook constitutive model,this paper uses the inverse method based on approximate Bayesian framework to estimate the uncertainty of constitutive parameters.In this paper,the self-encoder is used to extract the reduced-dimensional features of the data,and the neural network model is used to construct the mapping relationship between the undetermined material parameters and sufficient statistics,and the ANSM sampling method is used to obtain the posterior distribution features of the materials.The results show that when the sufficient statistics of appropriate dimensions are used,the approximate model with high accuracy can be constructed and the estimated values of material parameters close to the real value can be obtained.(3)In order to reduce the amount of calculation and the number of samples in constructing the approximate model,this paper introduces the transfer learning method to train the network model,and explores the feasibility of transfer learning in the above reverse methods.Initialize the network model in the new case with the weight of the neural network model trained in the previous case,and then construct a new approximate model through fewer data samples and the number of iterations of training.The results show that the model constructed by transfer learning can be effectively used to approximate the Bayesian sampling process,and the parameter estimation results with high accuracy can be obtained.(4)In order to identify the Johnson-Cook damage failure parameters,this paper proposes a weighted feature space distance measurement method and uses the responses under various loading conditions to construct the output of the approximate model.At the same time,the two super parameters added by the improved method can identify the material parameters with high accuracy by giving an appropriate set of distance weight parameters.The results show that the reverse algorithm after adjusting the distance metric still has high stability under different noise levels,and a posteriori mean estimation which is very close to the real value can be obtained,which shows the effectiveness of the improved method proposed in this paper.