Constitutive modeling and stress prediction method of particle reinforced metal matrix composites based on data-driven

Abstract

The present invention belongs to the technical field of data-driven computational mechanics and material constitutive model, and discloses a constitutive modeling method and stress prediction method of a particle-reinforced metal matrix composite material based on data-driven, the method comprising: establishing a representative volume unit model according to the structure of the particle-reinforced metal matrix composite material; inputting Young's modulus, Poisson's ratio, yield stress, and plastic strain of a plurality of particle-reinforced metal matrix composite materials of different components, and applying loads under different paths thereto, extracting and dividing data sets according to finite element calculation results; inputting the data sets into a BP neural network to complete an offline training process; and realizing stress prediction based on a neural network and updating of a consistent tangent modulus according to the training results, and obtaining a constitutive model of the particle-reinforced metal matrix composite material. The present invention can quickly and accurately establish a constitutive model of a particle-reinforced metal matrix composite material, more accurately describe its mechanical response behavior, and improve the accuracy of numerical simulation.

Description

Technical Field

[0001] The embodiments of the present invention belong to the technical field of data-driven computational mechanics and material constitutive model, and specifically relate to a constitutive modeling method and a stress prediction method of a particle-reinforced metal matrix composite material based on data-driven. Background Art

[0002] Particle Reinforced Metal Matrix Composite (PRMMC) has been successfully applied to aerospace, automobile and sports equipment fields due to its high specific strength, specific stiffness, good wear resistance and thermal stability. The mechanical properties and damage and failure laws of metal matrix composites depend on the microstructural characteristics of the composites, and the real microstructure of the composites often has the characteristics of complex structure and large amount of calculation, which causes researchers to use homogenization model and representative volume element model for finite element simulation and calculation. Because the constitutive relations of each component of the heterogeneous material under consideration are known, but the situation that the overall equivalent constitutive model is unknown is very common in engineering. Traditional methods generally use homogenization methods to deal with such problems, but traditional homogenization methods are less effective in dealing with nonlinear problems, especially elastoplastic problems. The constitutive model of particle reinforced metal matrix composites based on data-driven proposed in the present invention can effectively solve such problems, which is conducive to the law summary and development and utilization of the mechanical properties of particle reinforced metal matrix composites.

[0003] With the continuous emergence and widespread application of new metal matrix composites, there is an urgent need to develop more accurate and universal cross-scale constitutive models and design efficient and stable calculation methods for these models, so as to reveal the intrinsic relationship between microstructure and mechanical properties of materials from a mechanistic and quantitative perspective, and to be used for the design, analysis and advanced manufacturing of structural parts in practical engineering applications. Traditional constitutive modeling methods require the accumulation of a large amount of experimental data to summarize the deformation mechanism of materials. Generally, simplified assumptions and empirical relationships are used to construct explicit functions to fit experimental data to construct material constitutive relations. The mathematical structure is often very complex, and researchers are required to have a high level of mathematical derivation ability to describe the deformation mechanism and the relationship between stress and strain through explicit mathematical function expressions. Secondly, the fitted constitutive function will inevitably lose some information contained in the data, introduce errors and uncertainties, and may not meet the objectivity of the material model, such as the isotropy of the material. On the other hand, the traditional phenomenological constitutive model characterizes the mechanical behavior of materials as a whole from a macroscopic scale, and cannot describe the stress-strain evolution process of each phase component at a microscopic scale; on the other hand, the complex microstructure of composite materials determines that they often have obvious anisotropy and strong nonlinear characteristics at a macroscopic scale, and it is very difficult to construct a phenomenological constitutive model that can accurately describe their mechanical behavior. Therefore, it is urgent to develop a method that does not require the introduction of any empirical material model when constituting composite materials, and use this model to predict the stress of particle-reinforced metal matrix composites. Summary of the invention

[0004] In view of the above problems, an embodiment of the present invention provides a data-driven constitutive modeling method for a particle reinforced metal matrix composite material and a stress prediction method based on the model, which realizes rapid stress prediction of the particle reinforced metal matrix composite material.

[0005] According to one aspect of an embodiment of the present invention, a constitutive modeling method of a particle-reinforced metal matrix composite material based on data-driven is provided, the method comprising:

[0006] The RVE finite element model is established according to the structure of particle reinforced metal matrix composites;

[0007] Inputting Young's modulus, Poisson's ratio, yield stress, and plastic strain of particle-reinforced metal matrix composite materials of various components for finite element calculation, and extracting the true stress, strain, and increment data of the finite element model according to the finite element calculation results to form a data set;

[0008] The data set is input into the BP neural network to complete the training process, and the stress prediction based on the neural network and the update of the consistent tangent modulus are realized according to the training results to obtain the constitutive model of the particle reinforced metal matrix composite material.

[0009] In some implementations, the updating of the stress prediction and the consistent tangent modulus based on the neural network according to the training results includes:

[0010] Based on the secondary development interface framework, the trained neural network parameters are converted into the computer language corresponding to the secondary development interface;

[0011] Neural network-based stress prediction and consistent tangent modulus updating are implemented according to the neural network parameters and embedded into the corresponding secondary development interface framework.

[0012] In some implementations, extracting the true stress, strain, and increment data of the finite element model according to the finite element calculation results includes:

[0013] Apply multiple different displacement boundary conditions to the RVE finite element model and obtain the corresponding average volume stress through finite element calculation; and

[0014] Displacement loads of different proportions are applied in the three main stress directions of the cell X, Y, and Z. The selected load state should be evenly distributed in the three-dimensional space, and the average volume strain of the RVE finite element model in the three main stress directions of the cell X, Y, and Z is calculated.

[0015] In some implementations, the average volume strain and average volume stress in the three main stress directions are calculated using the formula:

[0016]

[0017]

[0018] in, and are the average volume stress and average volume strain in the three directions of x, y, and z on the finite element model,

[0019] is the infinitesimal volume in RVE, is the total volume of the RVE, and They are the true stress and true strain in the x, y, and z directions on the infinitesimal element in RVE.

[0020] In some implementations, the step of inputting the data set into a BP neural network to complete a training process includes:

[0021] Dividing the data set into a training set, a validation set, and a test set;

[0022] Normalizing the data set;

[0023] Initialize weights and biases;

[0024] dividing the data set into an input set and an output set;

[0025] Offline training of ANN model.

[0026] In some implementations, the training process further includes:

[0027] The average volume strain and average volume stress in the three main directions are used as input to define the constraints, objective function and learning rate for updating network parameters during training.

[0028] The agent neural network is iteratively trained until all objective functions are satisfied.

[0029] In some implementations, the step of performing offline training on the ANN model specifically includes:

[0030] S1. Calculate the output of the neuron nodes of each hidden layer in the neural network using an activation function;

[0031] S2. Calculate the output of the neuron nodes in the output layer of the neural network according to the activation function;

[0032] S3. Calculate the error between the actual output and the expected output of the output layer;

[0033] If the error can meet the preset requirements, the trained neural network parameters are converted into a computer language corresponding to the secondary development interface.

[0034] In some implementations, the step of performing offline training on the ANN model further includes:

[0035] If the error cannot meet the preset requirements, the hidden layer error is calculated, the error gradient is solved, the weight and bias are adjusted according to the learning function, and steps S1, S2 and S3 are repeated.

[0036] In some implementations, after the data set is formed, the method of exchanging the order of components is further included to expand the data set, and the specific expansion method is:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] in, is the volume stress in a single stress direction, is the volume strain in a single stress direction; superscript Indicates the numbers of different arrangement orders; W and B are the weight matrix and bias matrix of the trained neural network respectively;

[0044] The final average volume stress in the three main stress directions is calculated from the stresses obtained in different input orders using the following formula: .

[0045] In some implementations, the particle-reinforced metal matrix composite material includes a matrix material and a spherical particle material, the matrix material is Al, the spherical particle material is SiC, and the particle volume fraction is calculated as follows:

[0046]

[0047] in, is the particle volume fraction of the granular material, N is the number of particles, R is the radius of the spherical particle, and L, M and H are the length, width and height of the matrix material model respectively.

[0048] In some implementations, the initializing weights and biases further includes:

[0049] Initialize the neural network and determine the hyperparameters of the neural network by multiple tests on the data set, including the number of training times, the learning rate, the minimum error of the training target, the number of hidden layers, and the number of neurons in the hidden layer;

[0050] According to the specific task and the characteristics of the dataset, the number of neurons in each layer is determined, and the weights and bias of the initial network are set.

[0051] In some implementations, the activation function uses a hyperbolic tangent function, and the transfer function from the hidden layer to the output layer uses a linear activation function.

[0052] In some implementations, the consistent tangent modulus is updated by:

[0053] In the linear elastic deformation stage, the Poisson's ratio and Young's modulus of the composite material can be approximately solved based on the finite element simulation data and the least square method;

[0054] During the plastic deformation stage, the consistent tangent modulus is updated based on the idea of ​​replacing differential with difference.

[0055] In some implementations, the plastic deformation stage specifically includes:

[0056] Add disturbance increments to the components of the three main stress directions in turn, and predict the corresponding stress components through the trained neural network model;

[0057] The stress increment before and after the disturbance is added is calculated, combined with the strain increment, based on the definition of the consistent tangent modulus, and the Jacobian matrix of the current incremental step is updated according to the idea of ​​replacing differentials with differences.

[0058] According to another aspect of an embodiment of the present invention, a data-driven method for predicting stress of a particle-reinforced metal matrix composite material is provided. The method predicts stress based on a model obtained by the above-mentioned constitutive modeling method of the data-driven particle-reinforced metal matrix composite material.

[0059] In some implementations, the method uses the above-mentioned method to model the constitutive structure of the particle reinforced metal composite material.

[0060] Compared with the prior art, the present invention has the following beneficial effects:

[0061] The present invention proposes a data-driven method for isotropic elastic-plastic material constitutive model, which can be used for constitutive modeling of metal matrix composite materials and can effectively learn the constitutive model of homogeneous materials and heterogeneous materials. In addition, the BP neural network used can infinitely approximate any continuous function, so it can be used to construct a constitutive model of nonlinear elastic-plastic materials. The method is achieved by using a neural network to establish a mapping between principal strains and principal stresses in the main direction. This method has the following advantages: (1) The constitutive model can be established directly through data automation without human intervention in the intermediate process, thus getting rid of the interference of human experience and avoiding the use of a large amount of knowledge reserves and the derivation of complex formulas to obtain the constitutive model of the material. Therefore, it can greatly improve the efficiency of establishing the constitutive model of new materials; (2) The BP neural network constitutive model does not require the calculation of material parameters. Compared with the traditional constitutive model, the neural network constitutive model is simpler, more effective and more robust; (3) It can be integrated into the user-defined interface of commercial finite element software and is easy to use; (4) Data-driven constitutive modeling can be performed based on finite element calculations and experimental data. The BP neural network constitutive model can store and train more comprehensive information related to material properties, such as the service temperature of the material, the microscopic characteristics of the material at different positions, etc., thereby further improving the generalization ability of the neural network model.

[0062] The above description is only an overview of the technical solution of the embodiment of the present invention. In order to more clearly understand the technical means of the embodiment of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the embodiment of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] The accompanying drawings are only used to illustrate the embodiments and are not to be considered as limiting the present invention. In addition, the same reference symbols are used to represent the same components throughout the accompanying drawings. In the accompanying drawings:

[0064] Figure 1 is a schematic diagram of a representative volume unit in the embodiment;

[0065] Figure 2 Schematic diagram of BP neural network in the embodiment;

[0066] Figure 3 A flow chart for constitutive modeling of particle reinforced metal matrix composites based on data-driven;

[0067] Figure 4 To compare the data-driven constitutive prediction results of particle-reinforced metal matrix composites with direct calculation results and experimental results;

[0068] Figure 5 It is the equivalent stress cloud diagram under the instant configuration of the direct calculation method and neural network constitutive calculation. DETAILED DESCRIPTION

[0069] Data-driven computational mechanics method is an emerging numerical solution paradigm that does not rely on material constitutive models. It has been rapidly developed and improved in recent years. The main reason is that it can make full use of a large amount of experimental data and numerical simulation data to improve the accuracy and efficiency of computational mechanics analysis. Artificial Neural Network (ANN) method is a type of machine learning and artificial intelligence technology inspired by biological neural systems, which is used to handle complex pattern recognition, classification, prediction and other tasks. It has the characteristics of strong nonlinear mapping ability, high generalization ability and good ductility. The powerful mapping and fitting ability of neural networks enables it to describe more complex material behaviors. A sufficiently deep neural network can infinitely approximate any continuous function in any closed interval. Therefore, the equivalent constitutive model of composite materials can be established based on the ANN method through offline stress-strain data, and then its macroscopic mechanical response can be predicted through online calculation.

[0070] Embodiment 1:

[0071] This embodiment provides a constitutive modeling method of a particle reinforced metal matrix composite material based on data driving, which is implemented by the following steps:

[0072] The RVE finite element model is established according to the structure of particle reinforced metal matrix composites;

[0073] Inputting Young's modulus, Poisson's ratio, yield stress, and plastic strain of particle-reinforced metal matrix composite materials of various components for finite element calculation, and extracting the true stress, strain, and increment data of the finite element model according to the finite element calculation results to form a data set;

[0074] Step 100: Establish an RVE finite element model according to the structure of the particle reinforced metal matrix composite material. The RVE finite element model can be obtained by conventional means, which will not be described in detail in this application.

[0075] Step 110. Input the Young's modulus, Poisson's ratio, yield stress, and plastic strain of particle-reinforced metal matrix composites of various components for finite element calculation, and extract the real stress, strain, and incremental data of the finite element model according to the finite element calculation results to form a data set. That is, through the elastic-plastic mechanical response of the RVE finite element model, the data set required for training the BP neural network is established. Take a representative area in the material to establish a finite element model. This area can be homogeneous or contain microstructures (non-homogeneous). For the convenience of calculation, a cubic area is generally taken to calculate its elastic-plastic mechanical response. Then, different displacement boundary conditions are applied to the finite element model for establishing RVE, and the corresponding average stress is obtained through finite element calculation. Displacement loads of different proportions are applied to the three main stress directions of the cell X, Y, and Z. The selected load state should be evenly distributed in the three-dimensional space, and the average volume stress of the three main directions of RVE is calculated. A set of displacement loads is regarded as a loading path, and each loading path is evenly divided into the same number of incremental steps. During the entire loading process, the average volume stress and average volume strain of the RVE at each incremental step in the X, Y, and Z directions are calculated in real time.

[0076] In this embodiment, the material involved in step 110 is a particle-reinforced metal matrix composite material, the matrix material is Al, the spherical particle material is SiC, and the calculation formula of the particle volume fraction is as follows:

[0077]

[0078] in, is the particle volume fraction of the granular material, N is the number of particles, R is the radius of the spherical particle, and L, M, and H are the length, width, and height of the matrix material model.

[0079] In the description of this embodiment, the load path distribution in step 110 uses a spherical coordinate system generation method to obtain a uniformly distributed three-dimensional vector, which obeys the independent and identically distributed condition. Different path loads are applied to the finite element model to obtain stress-strain data of the composite material under different loads, thereby improving the generalization ability of the neural network.

[0080] As a further description of this embodiment, in step 110, the average volume strain and average volume stress in the three main directions of the finite element model are extracted according to the finite element calculation results, and the calculation formula is as follows:

[0081]

[0082]

[0083] in, and are the average volume stress and average volume strain in the three directions of x, y, and z on the finite element model,

[0084] is the infinitesimal volume in RVE, is the total volume of the RVE, and are the true stress and true strain in the three directions of x, y, and z on the microelement in RVE. and Unless otherwise specified, they refer to the average volume stress and average volume strain.

[0085] Step 120: Build a BP neural network model to learn the mechanical elastic-plastic behavior of composite materials, that is, complete the offline training process of the data-driven particle-reinforced metal matrix composite constitutive model; divide the data set obtained in step 110 into an input set and an output set. First, the ANN model is trained offline, taking the average volume strain in the three main directions as input and the average volume stress in the three directions as input. Then, define the constraints, objective functions and learning rates for updating the network parameters during the training process, and iteratively train the proxy neural network until all objective functions are met, and end the training of the network.

[0086] The data set is input into the BP neural network to complete the training process, and the stress prediction based on the neural network and the update of the consistent tangent modulus are realized according to the training results to obtain the constitutive model of the particle reinforced metal matrix composite material. Specifically, the following steps are included:

[0087] Step 130: Considering the objectivity of isotropic materials, the data points obtained after the stress and strain components in the data set are exchanged at the same time can still be described by the constitutive model. Therefore, the data set can be expanded by exchanging the order of components, that is, to build a neural network structure (isotropic ANN) whose output results are independent of the input order. It is necessary to arrange and combine the three stresses of a set of inputs, that is, a set of inputs can be expanded to six sets of inputs, and the corresponding order of the six sets of inputs is recorded. The specific expansion method is as follows:

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] in, Superscript Indicates the number of different arrangement orders. The final average volume stress in the three directions can be calculated from the stress obtained in different input orders using the following formula:

[0095]

[0096] Step 140: The format of the divided input and output data sets is InputData=[ ]; OutputData=[ ], the total training data is divided into training set, validation set and test set, accounting for 70%, 15% and 15% respectively.

[0097] Step 150: Normalize the data set and convert the data to the range of [-1,1]. The calculation method is as follows:

[0098]

[0099] in, is the input and output data set, is the maximum value in the input and output data sets, is the minimum value in the input and output data sets.

[0100] Step 160: Initialize the neural network and determine the hyperparameters of the neural network through multiple tests on the data set. Including the number of training times, learning rate, minimum error of the training target, number of hidden layers, number of neurons in the hidden layer, etc. According to the characteristics of the specific task and data set, determine the number of neurons in each layer, and initialize the weights and bias of the network. Use an activation function for activation. Preferably, the hidden layer activation function uses the hyperbolic tangent (tanh) function, and the transfer function from the hidden layer to the output layer uses the linear activation (purelin) function. The function is specifically expressed as follows:

[0101]

[0102]

[0103] Step 170: When the neural network trained in step 160 reaches a predetermined threshold, the relationship between the true strain and the true stress of the training network survival RVE model is recorded, and the corresponding weight matrix and bias matrix, normalization and denormalization parameters are recorded.

[0104] Step 180 is to perform denormalization and calculate the true average volume stress. The calculation formula is as follows:

[0105]

[0106] Step 200: Based on the secondary development interface framework provided in the commercial finite element software, the parameters of step 170 are converted into the computer language corresponding to the secondary development interface, the stress prediction of the proxy neural network and the update of the consistent tangent modulus are realized, and embedded into the corresponding interface framework to complete the numerical implementation of the data-driven calculation method of the constitutive model of metal matrix composite materials.

[0107] In the description of this embodiment, for step 200, the updating steps of the consistent tangent modulus are as follows: In the initial incremental step, that is, the linear elastic deformation stage, the Poisson's ratio and Young's modulus of the composite material can be approximately solved based on the finite element simulation data and the least squares method. Due to the linear elastic stage, the calculated Poisson's ratio and Young's modulus are basically constant. When the relative error of the Poisson's ratio and Young's modulus calculated in adjacent incremental steps exceeds 20%, it is considered that the material has entered plastic deformation. In the plastic deformation stage, the consistent tangent modulus can be updated based on the idea of ​​replacing differential with differential. The three components of are added with disturbance increments in sequence ( ), the disturbance increment is 10% of the current strain component, and then the corresponding stress component is predicted by the trained ANN model, and the stress increment before and after the disturbance is calculated. Combined with the strain increment (the applied disturbance increment), based on the definition of the consistent tangent modulus, according to the difference Substitution Differentiation The Jacobian matrix of the current incremental step is updated based on the idea of ​​.

[0108] Furthermore, in step 200, commercial finite element software includes software such as ABAQUS and ANSYS that can provide a user secondary development interface. This embodiment uses the user-defined material program UMAT provided by ABAQUS to perform finite element calculations.

[0109] Embodiment 2:

[0110] This embodiment 2 is implemented by using the method provided in embodiment 1. Specifically, it includes the following steps:

[0111] Step 100: Based on the idea of ​​homogenization, a constitutive model of composite materials is constructed. The following example demonstrates the equivalent constitutive modeling and macroscopic response prediction of metal matrix composite materials using neural networks. First, the RVE model is established by selecting a typical region of the composite material, such as Figure 1 As shown, its elastic-plastic mechanical response is calculated to verify the accuracy of the neural network method.

[0112] Further, consider The composite material is a particle-reinforced composite material. The matrix material is AL, and the spherical particle material is SiC. The spherical particles account for 14% of the total RVE volume. According to formula (1), the corresponding spherical particle diameter is 0.64. The mesh type is C3D4, and the mesh size is 0.1. The parameters of the two materials are shown in Table 1:

[0113]

[0114] Table 1 Composite material parameters

[0115]

[0116] Step 200: extracting a data set for neural network training based on finite element calculation, and using average volume stress and average volume strain as output and input of ANN.

[0117] In order to train the isotropic elastic-plastic mechanical response behavior of the RVE model, boundary conditions and displacement loads are first applied to the RVE model. The three RVE surfaces coincident with the YOZ, XOZ and XOY planes are fixed in the X, Y and Z directions respectively, and the other three surfaces parallel to the YOZ, XOZ and XOY planes are applied with uniformly distributed displacements, such as Figure 1 The selection of displacement load path obeys random uniform distribution in three-dimensional space, and 14 uniformly distributed three-dimensional vectors are obtained by using spherical coordinate system generation method. The loading path is generated by the following formula.

[0118]

[0119] in ， ； ， 。

[0120] The displacement load u applied to the RVE in the present invention can be expressed by the following formula:

[0121]

[0122] in, is the loading direction in the principal stress space, is the load path number, and the specific value is listed in Table 2. is the increment step number, is the coefficient defining the displacement load applied, and is taken as 0.15. and are the total number of loading paths and the total number of incremental steps, which are 14 and 500 respectively (i.e., 14 different displacement loads are applied to the RVE model in turn in ABAQUS, with a fixed step size and 500 increments). Finally, the finite element simulation data is post-processed, and the average volume stress at each incremental step during the entire loading process is extracted according to the following formulas (4) and (5): ) and the average volumetric strain ( ).

[0123]

[0124]

[0125] Table 2 Mechanical loading path direction

[0126]

[0127] Step 300: Repeat the above steps until all load paths in Table 2 are calculated, and summarize all data sets and divide them into input sets and output sets.

[0128] Step 400: Expand the data set, considering that the ANN model is an output and input order-independent model, to ensure the objectivity of the constitutive model prediction results. The specific expansion method is as follows:

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135] in, Superscript Indicates the number of different arrangement orders. The final average volume stress in the three main stress directions can be calculated from the stresses obtained in different input orders using the following formula:

[0136]

[0137] Step 500: Set the input data set InputData=[ ] and output data set OutputData=[ ] is divided into training set, validation set and test set, with the training set accounting for 70%, the validation set accounting for 15%, and the test set accounting for 15%.

[0138] Step 600: Normalize the data set and convert the data to the range of [-1,1]. The calculation method is as follows:

[0139]

[0140] in, is the input and output data set, is the maximum value in the input and output data sets, is the minimum value in the input and output data sets.

[0141] Step 700: Initialize the neural network, which consists of an input layer, 6 hidden layers, and an output layer. The number of neurons in the input layer is 3, the number of neurons in the hidden layer is 10, 20, 20, 20, 20, and 10 respectively, and the number of neurons in the output layer is 3; the hidden layer weights are initialized using the He initialization method, and the bias term is initialized using random distribution initialization; the hidden layer activation function uses the hyperbolic tangent (tanh) function, and the transfer function from the hidden layer to the output layer uses the linear activation (purelin) function; the number of training times is 10,000, the learning rate is 1e-5, and the training target minimum error is 1e-10.

[0142] Step 800: Using the training set to train the constitutive model of the metal matrix composite material, Figure 2 The learning process of the neural network, the final training mean square error reached 1e-10, and the accuracy of the network training set reached 85.3%. The accuracy of the test set of the ANN constitutive model obtained after training reached 84.2%. After the network training is completed, the weight moment term, bias term and normalization parameter of the network are output.

[0143] Step 900: Denormalize and calculate the true average volume stress. The calculation formula is as follows:

[0144]

[0145] Step 1000: Based on the neural network model parameters in step 800, the material constitutive subroutine UMAT is written in Fortran language to update the stress and Jacobian matrix (consistent tangent modulus) of the proxy neural network, and is embedded in the ABAQUS framework to complete the numerical implementation of the constitutive model calculation method of particle reinforced metal matrix composites based on data-driven, such as Figure 3 As shown in the figure. In the ABAQUS implicit algorithm, the objective rate of the constitutive relationship used by the software is the Jaumann rate, and the consistent tangent modulus is the derivative of the Cauchy stress Jaumann rate to the programming tensor rate under the current configuration.

[0146] Furthermore, the updating process of the subroutine UMAT in step 1000 is as follows:

[0147] Step 1001: Linear elastic deformation stage, for the data set summarized in step 400, since there are 14 different load paths, a fixed step size is used for the application of each load, and 500 incremental steps are divided, so the data set has a total of 70,000 groups. The data set is expressed as [ ]=[ ].

[0148] Step 1002: In the initial increment step, define an initial consistent tangent modulus. Assuming that the material deformation is very small, the mechanical behavior of the composite material satisfies Hooke's law, and the relationship between the principal stress increment and the principal strain increment of the material can be expressed by the following formula:

[0149] .

[0150] in:

[0151]

[0152]

[0153]

[0154] in and are two independent material constants. Combining the above expressions, Young's modulus E and Poisson's ratio ν can be obtained and It is expressed as follows:

[0155]

[0156]

[0157] and It can be obtained by fitting the data of the elastic stage by the least square method (to ensure that the data is in the elastic stage, only the equal to 1 and 2):

[0158] .

[0159] In summary, the consistent tangent modulus under the initial incremental step can be obtained. The specific expression is as follows:

[0160]

[0161] in, is the second-order unit tensor, is the fourth unit tensor.

[0162] Step 1003: For subsequent incremental steps, the principal strain at the end of the current incremental step is read from UMAT, and the stress is updated through prediction by the trained ANN model. Based on the stress increment and strain increment at the beginning and end of the corresponding incremental step, three sets of overdetermined equations are solved by the least squares method to solve C11 and C12 in formula (16), and then the consistent tangent modulus under the current incremental step is updated.

[0163] Step 1004: In the linear elastic stage, the calculated Poisson's ratio and Young's modulus are basically constant. When the relative error of the Poisson's ratio and Young's modulus calculated in adjacent incremental steps exceeds 20%, it is considered that the material enters plastic deformation.

[0164] Step 1005: In the plastic deformation stage, the consistent tangent modulus can be updated based on the idea of ​​replacing differential with differential. The three components of are added with disturbance increments in sequence ( ), the disturbance increment is 10% of the current strain component, and then the corresponding stress component is predicted by the trained ANN model, and the stress increment before and after the disturbance is calculated. Combined with the strain increment (the applied disturbance increment), based on the definition of the consistent tangent modulus, according to the difference Substitution Differentiation The consistent tangent modulus in the current increment is updated based on the idea of ​​.

[0165] Step 1006: In the ABAQUS implicit algorithm, the objective rate of the constitutive relationship used by the software is the Jaumann rate, and the consistent tangent modulus is the derivative of the Cauchy stress Jaumann rate to the programming tensor rate under the current configuration. The consistent tangent modulus of isotropic three-dimensional materials is expressed as follows:

[0166]

[0167] Step 1100: Verify the accuracy of the BP neural network constitutive model. Use the finite element software ABAQUS to simulate and analyze the RVE of the composite material, namely direct numerical simulation (DNS), and use its results as a benchmark. For the neural network method proposed in the present invention, the RVE macro constitutive model is replaced by the trained neural network, and only one grid needs to be divided, such as Figure 1 shown. Figure 4 The equivalent stress cloud diagrams of the simulation results of the two methods are shown. Figure 5The mechanical responses simulated by the DNS method and the ANN method are shown. The results predicted by the two methods are basically consistent; the simulation results of the two numerical methods are basically consistent with the experimental results. The errors between the ANN and DNS and the experimental results are within 3%. The sources of the numerical errors in the comparison between the simulation results and the experiment may be as follows: (1) The finite element model does not consider the interaction between particles, the interface between the matrix and particles, etc.; (2) The particle distribution does not strictly meet the statistical uniform distribution; (3) The neural network prediction error.

[0168] Embodiment 3:

[0169] This embodiment 3 provides a data-driven stress prediction method for particle-reinforced metal-based composite materials. The stress prediction method of this embodiment is based on the method described in embodiment 1 or embodiment 2 to perform modeling and stress prediction on the particle-reinforced metal-based composite materials.

[0170] In summary, this data-driven constitutive modeling method for particle-reinforced metal matrix composites shows high accuracy, can effectively learn the constitutive model of homogeneous materials and the constitutive model of heterogeneous materials, and at the same time ensure the objectivity, isotropy and stability of the constitutive model. Compared with the existing constitutive modeling method, the method in this embodiment can quickly and accurately establish various new types of particle-reinforced metal matrix composite constitutive models, improve the accuracy of numerical simulation, and help to obtain material life prediction and damage assessment in material stress prediction.

[0171] In the description provided herein, a large number of specific details are described. However, it is understood that embodiments of the present invention can be practiced without these specific details. Similarly, in order to simplify the present invention and help understand one or more of the various inventive aspects, in the above description of exemplary embodiments of the present invention, the various features of the embodiments of the present invention are sometimes grouped together into a single embodiment, figure, or description thereof. Wherein, the claims that follow the specific embodiment are hereby expressly incorporated into the specific embodiment, wherein each claim itself is a separate embodiment of the present invention.

[0172] It should be noted that the above embodiments illustrate the present invention rather than limit it, and that those skilled in the art may devise alternative embodiments without departing from the scope of the appended claims. In the claims, any reference symbol between brackets shall not be construed as a limitation on the claims. The word "comprising" does not exclude the presence of elements or steps not listed in the claims. The word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements. The present invention may be implemented by means of hardware comprising a number of different elements and by means of a suitably programmed computer. The steps in the above embodiments, unless otherwise specified, shall not be understood as limitations on the order of execution.

Claims

1. A constitutive modeling method for particle reinforced metal matrix composites based on data-driven, characterized in that: The method comprises: The RVE finite element model is established according to the structure of particle reinforced metal matrix composites; Inputting Young's modulus, Poisson's ratio, yield stress, and plastic strain of particle-reinforced metal matrix composite materials of various components for finite element calculation, and extracting the true stress, strain, and increment data of the finite element model according to the finite element calculation results to form a data set; The data set is input into a BP neural network to complete a training process, and stress prediction based on the neural network and update of the consistent tangent modulus are implemented according to the training results to obtain a constitutive model of a particle reinforced metal matrix composite material; The method of extracting the true stress, strain and incremental data of the finite element model according to the finite element calculation results includes: applying a plurality of different displacement boundary conditions to the RVE finite element model, and obtaining the corresponding average volume stress through finite element calculation; and applying displacement loads of different proportions in the three main stress directions of the cell X, Y, and Z. The selected load state should be evenly distributed in the three-dimensional space, and the average volume strain of the RVE finite element model in the three main stress directions of the cell X, Y, and Z is calculated; The data set is input into the BP neural network to complete the training process, including: dividing the data set into a training set, a verification set and a test set; normalizing the data set; initializing weights and biases; dividing the data set into an input set and an output set; and training the ANN model offline; After the data set is formed, the data set is further expanded by exchanging the order of components. The specific expansion method is: in, is the volume stress in a single stress direction, is the volume strain in a single stress direction; superscript Indicates the numbers of different arrangement orders; W and B are the weight matrix and bias matrix in the trained neural network respectively; The final average volume stress in the three main stress directions is calculated from the stresses obtained in different input orders using the following formula: in The updating steps of the consistent tangent modulus are as follows: in the initial incremental step, that is, the linear elastic deformation stage, the Poisson's ratio and Young's modulus of the composite material can be approximately solved based on the finite element simulation data and the least squares method. Due to the linear elastic stage, the calculated Poisson's ratio and Young's modulus are constants. When the relative errors of the Poisson's ratio and Young's modulus calculated in adjacent incremental steps exceed 20%, it is considered that the material enters plastic deformation; in the plastic deformation stage, the consistent tangent modulus is updated based on the idea of ​​differential substitution, and disturbance increments are added to the three components in turn to form strain increments. The disturbance increment is 10% of the current strain component, and then the corresponding stress component is predicted by the trained ANN model, and the stress increment before and after the disturbance is added is calculated. Combined with the strain increment, based on the definition of the consistent tangent modulus, the Jacobian matrix in the current incremental step is updated according to the idea of ​​differential substitution.

2. The method according to claim 1, characterized in that The method of realizing stress prediction based on a neural network and updating the consistent tangent modulus according to the training results includes: Based on the secondary development interface framework, the trained neural network parameters are converted into the computer language corresponding to the secondary development interface; Neural network-based stress prediction and consistent tangent modulus updating are implemented according to the neural network parameters and embedded into the corresponding secondary development interface framework.

3. The method according to claim 1, characterized in that The average volume strain and average volume stress in the three main stress directions are calculated as follows: in in in, and are the average volume stress and average volume strain in the three directions of x, y, and z on the finite element model, is the infinitesimal volume in RVE, is the total volume of the RVE, and They are the true stress and true strain in the x, y, and z directions on the infinitesimal element in RVE.

4. The method according to any one of claims 1 to 3, characterized in that The step of inputting the data set into the BP neural network to complete the training process also includes: The average volume strain and average volume stress in the three main stress directions are used as input to define the constraints, objective function and learning rate for updating network parameters during training. The BP neural network is trained iteratively until all objective functions are satisfied.

5. The method according to claim 1, characterized in that: The steps of offline training of the ANN model specifically include: S1. Calculate the output of the neuron nodes of each hidden layer in the neural network using an activation function; S2. Calculate the output of the neuron nodes in the output layer of the neural network according to the activation function; S3. Calculate the error between the actual output and the expected output of the output layer; If the error can meet the preset requirements, the trained neural network parameters are converted into a computer language corresponding to the secondary development interface.

6. The method according to claim 5, characterized in that The step of performing offline training on the ANN model also includes: If the error cannot meet the preset requirements, the hidden layer error is calculated, the error gradient is solved, the weight and bias are adjusted according to the learning function, and steps S1, S2 and S3 are repeated.

7. The method according to claim 1, characterized in that The particle-reinforced metal matrix composite material comprises a matrix material and a spherical particle material, the matrix material is AL, the spherical particle material is SiC, and the particle volume fraction is calculated as follows: in, is the particle volume fraction of the granular material, N is the number of particles, R is the radius of the spherical particle, and L, M and H are the length, width and height of the matrix material model respectively.

8. The method according to claim 1, characterized in that The initialization of weights and biases further comprises: Initialize the neural network and determine the hyperparameters of the neural network by multiple tests on the data set, including the number of training times, the learning rate, the minimum error of the training target, the number of hidden layers, and the number of neurons in the hidden layer; According to the specific task and the characteristics of the dataset, the number of neurons in each layer is determined, and the weights and bias of the initial network are set.

9. The method according to claim 5, characterized in that The activation function adopts a hyperbolic tangent function, and the transfer function from the hidden layer to the output layer adopts a linear activation function.

10. A data-driven stress prediction method for particle-reinforced metal matrix composites, characterized in that: The method predicts stress based on a model obtained by a data-driven constitutive modeling method for particle-reinforced metal matrix composite materials as described in any one of claims 1 to 9.

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