A material plasticity constitutive modeling method and device

Abstract

The application relates to a material plasticity constitutive modeling method and device, wherein the prediction data set in the method not only contains data obtained by performing a material plasticity deformation behavior experiment, but also contains prediction data obtained based on a phenomenological constitutive model, so that the prediction data can be combined with the experimental data, and then the material parameters are not limited to the scale of the experimental data; double optimization of a neural network model is realized by combining physical loss and data loss, so that when the model is iteratively optimized, the physical information is combined for constraint, the precision of the iterative optimization is improved, and in the optimization process, the parameters of the neural network model are iteratively optimized by combining a simulated annealing algorithm, so that the obtained target neural network model meets the high-precision requirement of material plasticity forming under multiple working conditions.

Description

Technical Field

[0001] This invention relates to the field of digital manufacturing technology for high-end equipment, and in particular to a method and apparatus for material plasticity constitutive molding. Background Technology

[0002] Traditional material plasticity constitutive equations are constructed through fitting experimental data or theoretical analysis of physical mechanisms and regression using linear methods. However, because these two types of constitutive models typically include many material parameters and are limited by the scale of experimental data, their prediction accuracy often falls short of the high-precision requirements for material plastic forming under various working conditions.

[0003] In recent years, data-driven methods have been introduced into the field of original modeling. However, traditional neural network models usually rely solely on experimental data for training and lack physical constraints. When the data scale is limited or the operating conditions vary greatly, problems such as overfitting and lack of interpretability are prone to occur, resulting in limited model prediction results.

[0004] Therefore, there is an urgent need to propose a material plasticity constitutive modeling method and device to solve the technical problems of existing constitutive models having a large number of parameters, strong dependence on experimental data, and the difficulty of traditional neural networks in balancing prediction accuracy and physical consistency. Summary of the Invention

[0005] In view of this, it is necessary to provide a material plasticity constitutive modeling method and apparatus to solve the technical problems of existing constitutive models having a large number of parameters, strong dependence on experimental data, and the difficulty of traditional neural networks in balancing prediction accuracy and physical consistency.

[0006] To address the aforementioned problems, in a first aspect, the present invention provides a method for constructing a material plasticity constitutive model, comprising: Obtain a predicted dataset of the plastic deformation behavior of the material; the predicted dataset includes true stress, true strain, material temperature, and strain rate; Based on the coupling relationship between the true strain, material temperature, strain rate, and true stress in the predicted dataset, a target constitutive model is constructed. The neural network model is optimized using both physical loss and data loss based on the predicted dataset and the target constitutive model. During the optimization process, the parameters of the neural network model are iteratively optimized using the simulated annealing algorithm to obtain the target neural network model.

[0007] In one possible implementation, obtaining the predicted dataset of the material's plastic deformation behavior includes: A basic dataset is constructed based on experimental data of the plastic deformation behavior of materials; the basic dataset includes stress, strain, material temperature and strain rate from experiments on the mechanical properties of materials under different working conditions; The stress and strain in the basic dataset are transformed to obtain a transformed dataset; the transformed dataset includes the true stress, the true strain, the material temperature, and the strain rate; The transformed dataset is normalized to obtain a standardized dataset; The standardized dataset is divided to obtain the prediction dataset.

[0008] In one possible implementation, constructing the target constitutive model based on the coupling relationship between the true strain, the material temperature, the strain rate, and the true stress in the predicted dataset includes: Construct the initial JC constitutive model; The initial JC constitutive model is transformed according to the coupling relationship between the true strain, the material temperature, the strain rate and the true stress in the predicted dataset to obtain the first constitutive model; Based on the mechanical behavior under extreme conditions in the predicted dataset, the first constitutive model is transformed into a formula to obtain the target constitutive model.

[0009] In one possible implementation, the step of performing dual optimization of the neural network model based on the predicted dataset and the target constitutive model using both physical loss and data loss, and iteratively optimizing the parameters of the neural network model through simulated annealing during the optimization process to obtain the target neural network model, includes: The target constitutive model is iteratively optimized to obtain the optimal parameter set; The physical loss and data loss are calculated based on the optimal parameter set, the initial hyperparameters, and the target constitutive model to obtain the initial total loss error; Noise data is generated based on the current annealing temperature; Based on the noise data, candidate values ​​are obtained; The physical loss and data loss are calculated based on the optimal parameter set, the candidate values, and the target constitutive model to obtain the candidate total loss error; When the candidate total loss error is greater than or equal to the initial total loss error, the parameters of the neural network model are iteratively optimized using the simulated annealing algorithm to obtain the target neural network model.

[0010] In one possible implementation, after calculating the physical loss and data loss based on the optimal parameter set, the candidate values, and the target constitutive model to obtain the candidate total loss error, the method further includes: When the candidate total loss error is less than the initial total loss error, the candidate total loss error is determined as the initial total loss error. If the preset number of training iterations has not been reached, a new candidate value is generated and iterative optimization is performed again.

[0011] In one possible implementation, the step of iteratively optimizing the parameters of the neural network model using the simulated annealing algorithm to obtain the target neural network model includes: Calculate the difference between the candidate total loss error and the initial total loss error; The acceptance probability is obtained based on the difference and the current annealing temperature; When the acceptance probability is not greater than a preset threshold, the current annealing temperature is updated based on the adaptive cooling rate strategy to obtain a new current annealing temperature, and if the preset number of training times has not been reached, iterative optimization is performed again based on the new current annealing temperature. When the acceptance probability is greater than a preset threshold, smoothing is performed based on the candidate value, the initial hyperparameter, and the preset smoothing coefficient to obtain the target hyperparameter; The current annealing temperature is updated based on an adaptive cooling rate strategy to obtain a new current annealing temperature; When the preset number of training iterations is reached, the physical loss and data loss are optimized simultaneously based on the optimal parameter set, the target hyperparameters, and the target constitutive model to obtain the target total loss error. The target neural network model is obtained by updating the weights and bias parameters in the neural network model based on the target total loss error, the new current annealing temperature, and the target hyperparameters.

[0012] In one possible implementation, the iterative optimization solution of the target constitutive model to obtain the optimal parameter set includes: The dimensionless temperature is obtained based on the material temperature in the predicted dataset; Substitute the strain, the dimensionless temperature, and the initial material parameters from the basic dataset into the target constitutive model for calculation to obtain all predicted stress values. Based on all the predicted stress values, the mean square error is obtained; The optimal parameter set is obtained by iterative optimization based on the mean square error.

[0013] In one possible implementation, the calculation of physical loss and data loss based on the optimal parameter set, initial hyperparameters, and the target constitutive model to obtain the initial total loss error includes: The optimal parameter set is input into the target constitutive model to obtain the physical true stress; The mean square error between the true stress and the physical true stress in the predicted dataset is determined as the physical loss; The predicted dataset is input into the phenomenological constitutive model to obtain the true stress of the phenomenon; The mean square error between the true stress in the predicted dataset and the true stress of the phenomenon is determined as the data loss. The initial total loss error is obtained based on the physical loss, the data loss, and the initial hyperparameters.

[0014] Secondly, the present invention also provides a method for constructing a material plasticity constitutive model, comprising: The plastic deformation behavior of the material is predicted based on the target neural network model obtained by the material plasticity constitutive modeling method.

[0015] Thirdly, the present invention also provides a material plasticity constitutive molding apparatus, comprising: The data acquisition module is used to acquire a predicted dataset of the plastic deformation behavior of materials; the predicted dataset includes true stress, true strain, material temperature, and strain rate. The model building module is used to construct a target constitutive model based on the coupling relationship between the true strain, the material temperature, the strain rate and the true stress in the predicted dataset. The dual optimization module is used to perform dual optimization of the neural network model based on the prediction dataset and the target constitutive model, using both physical loss and data loss. During the optimization process, the parameters of the neural network model are iteratively optimized using a simulated annealing algorithm to obtain the target neural network model.

[0016] The beneficial effects of this invention are as follows: the predicted dataset of this invention not only includes the material temperature and strain rate obtained from experiments on the plastic deformation behavior of materials, but also includes the predicted true stress and true strain, thereby combining the predicted data with the experimental data, so that the material parameters are not limited by the scale of the experimental data; it also combines physical loss and data loss to achieve dual optimization of the neural network model, so that the model is constrained by physical information during iterative optimization, thereby improving the accuracy of iterative optimization; and in the optimization process, the simulated annealing algorithm is combined to iteratively optimize the parameters of the neural network model, so that the obtained target neural network model can meet the high-precision requirements of material plastic forming under multiple working conditions. Attached Figure Description

[0017] Figure 1 A schematic flowchart of an embodiment of the material plasticity constitutive molding method provided by the present invention; Figure 2 For the present invention Figure 1 A schematic flowchart of an embodiment of step S103; Figure 3 A coordinate diagram illustrating an embodiment of the comparison results of predicted values ​​from the phenomenological material plasticity constitutive model provided by this invention; Figure 4 A coordinate diagram illustrating an example of the comparison results of the target constitutive model predictions provided in this invention; Figure 5 A coordinate diagram illustrating an embodiment of the prediction results of the constitutive model provided in this invention; Figure 6 A coordinate diagram illustrating another embodiment of the prediction results of the constitutive model provided in this invention; Figure 7 A schematic diagram of an embodiment of the material plasticity constituent molding device provided by the present invention. Detailed Implementation

[0018] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0019] like Figure 1 As shown, a specific embodiment of the present invention discloses a method for constructing a material plasticity constitutive model, comprising: S101. Obtain a prediction dataset of the material's plastic deformation behavior; the prediction dataset includes true stress, true strain, material temperature, and strain rate.

[0020] The prediction dataset in this embodiment of the invention originates from experimental mechanical properties of materials under different working conditions or from validated numerical simulation data. The data should cover the strain, temperature, strain rate range, etc., that the target material may experience in actual processes. Necessary preprocessing is performed on the raw data, such as outlier removal, noise smoothing, and normalization.

[0021] S102. Based on the coupling relationship between true strain, material temperature, strain rate and true stress in the predicted dataset, construct the target constitutive model.

[0022] In this embodiment of the invention, the target constitutive model is a mathematical model based on physical mechanisms, used to describe the intrinsic relationship between flow stress and various deformation parameters. The construction process includes: determining the material constants in the target constitutive model through regression analysis based on the prediction dataset. This model, as a mathematical expression of physical laws, will be used to apply physical constraints to the neural network model in subsequent steps.

[0023] S103. Based on the prediction dataset and the target constitutive model, the neural network model is optimized by both physical loss and data loss. During the optimization process, the parameters of the neural network model are iteratively optimized by the simulated annealing algorithm to obtain the target neural network model.

[0024] In this embodiment of the invention, the neural network model is constructed based on a feedforward neural network, a recurrent neural network, or a deep feedforward network architecture. The input layer nodes of the model correspond to experimental data such as true strain, and the output layer nodes are the predicted values ​​of true stress. The loss function of the neural network model is constructed to perform dual optimization of physical loss and data loss, and the simulated annealing algorithm is used to globally optimize the weights and bias parameters of the neural network model.

[0025] Furthermore, the prediction dataset can be divided into a training set and a test set according to a predetermined method. After the neural network model is trained on the training set, the network parameters that result in the minimum loss and the best prediction performance after n iterations of optimization are saved, thus obtaining the physical model for the task of predicting the plastic deformation behavior of materials. Finally, the obtained target neural network model is applied to the task of predicting the plastic deformation behavior of materials.

[0026] Compared with existing technologies, the prediction dataset provided in this embodiment not only includes data obtained from experiments on the plastic deformation behavior of materials, but also includes prediction data obtained based on the target constitutive model. This ensures that material parameters are not limited by the scale of experimental data. Furthermore, it combines physical loss and data loss to achieve dual optimization of the neural network model, thereby improving the accuracy of iterative optimization by incorporating physical information as a constraint during iterative optimization. In addition, the simulated annealing algorithm is used to iteratively optimize the parameters of the neural network model during the optimization process, so that the obtained target neural network model can meet the high-precision requirements of material plastic forming under multiple working conditions.

[0027] In some embodiments of the present invention, step S101 includes: The basic dataset is constructed based on experimental data of the plastic deformation behavior of materials. The basic dataset includes stress, strain, material temperature and strain rate in the mechanical property experiments of materials under different working conditions.

[0028] To obtain experimental data on the plastic deformation behavior of materials in this embodiment of the invention, it is necessary to build a material mechanical property experimental platform, conduct mechanical property experiments under different experimental conditions and obtain experimental data, which will serve as the basic dataset for subsequent model training and validation.

[0029] The stress and strain in the base dataset are transformed to obtain the transformed dataset; the transformed dataset includes true stress, true strain, material temperature and strain rate.

[0030] To accurately characterize the plastic deformation behavior of materials under extreme working conditions, this invention can perform data conversion on the stress and strain data from mechanical property experiments under different working conditions in the basic dataset, converting engineering stress-strain data into true stress-true strain data, and constructing a material plastic deformation behavior prediction dataset. The prediction dataset includes: true stress, true strain, material temperature, and strain rate. The conversion formulas are shown in formulas (1) and (2), respectively: (1) In the formula, This represents the actual stress during the stretching process; This refers to the engineering stress during the tensile process; This refers to the engineering strain during the tensile process.

[0031] (2) In the formula, This represents the actual strain during the stretching process; This refers to the engineering strain during the tensile process.

[0032] The transformed dataset is normalized to obtain a standardized dataset.

[0033] In order to eliminate the influence of different units on the prediction data, the present invention normalizes the prediction dataset to form a standardized dataset suitable for neural network training. The formula is shown in formula (3): (3) In the formula, The data is after normalization; This is the original input data; and These correspond to the maximum and minimum values ​​of the original input data, respectively.

[0034] The standard dataset is divided to obtain the prediction dataset.

[0035] In this embodiment of the invention, the standard dataset can be divided into a training set and a test set according to a set method (such as a 7:3 ratio) to form a material plastic deformation behavior prediction dataset.

[0036] Furthermore, after constructing the data set for predicting the plastic deformation behavior of materials, the data type of the prediction dataset is converted to improve the efficiency of neural network training; the specific conversion process and the data type of the conversion can be set according to the actual situation, and this embodiment of the invention does not impose any restrictions here.

[0037] In some embodiments of the present invention, step S102 includes: Construct the initial JC constitutive model.

[0038] The initial JC constitutive model in this embodiment of the invention is used to characterize the flow stress behavior of materials under high strain, high strain rate, and high temperature conditions, while comprehensively considering the effects of strain hardening, strain rate sensitivity, and thermal softening. Its expression is shown in formula (4): (4) In the formula, , , All are material parameters; The strain hardening index; Equivalent plastic strain; This represents the actual strain rate; Reference strain rate; This is the actual temperature; For reference temperature; The melting point of the material; This is the thermal softening index.

[0039] Based on the coupling relationship between true strain, material temperature, strain rate and true stress in the predicted dataset, the initial JC constitutive model is transformed to obtain the first constitutive model.

[0040] In order to make the first correction to the initial JC constitutive model, this invention proposes an empirical thermo-mechanical coupled constitutive equation. Unlike the Johnson-Cook model, it focuses more on the coupling relationship between microscopic mechanisms and temperature and strain rate. The formula is shown in equation (5): (5) In the formula, , , These are the material parameters for strain hardening; Equivalent plastic strain; The strain rate sensitivity coefficient; It is a dimensionless strain rate obtained from the reference strain rate and the actual strain rate; , The thermal sensitivity coefficient; The value is a dimensionless temperature.

[0041] Based on the mechanical behavior under extreme conditions in the predicted dataset, the first constitutive model is transformed into a formula to obtain the target constitutive model.

[0042] To perform a second modification to the initial JC constitutive model, this invention proposes an empirical model that combines polynomial strain hardening and exponential thermal softening effects. This model is more concise in form, with the fourth-order polynomial describing the flow stress as a function of plastic strain. The variation law is applicable to characterizing the mechanical behavior of materials under extreme working conditions. The target constitutive model is shown in formula (6): (6) In the formula, 、 、 、 、 、 、 All are material parameters; Equivalent plastic strain; It is a dimensionless strain rate obtained from the reference strain rate and the actual strain rate; The value is a dimensionless temperature.

[0043] Furthermore, after obtaining the target constitutive model, its accuracy can be evaluated, specifically by defining the optimization function as mean squared error (MSE). The acquired prediction dataset is imported, and the defined dimensionless temperature is calculated based on this dataset, the reference temperature, and the material's melting point temperature.

[0044] In each solution process, the initial guessed material parameters are first input, and the optimization function is solved by iterative optimization. Through iterative optimization, the material parameters are finally obtained.

[0045] After obtaining the material parameters of each target constitutive model, the accuracy of the target constitutive model is evaluated. The evaluation includes: assessing the accuracy of the constitutive model based on evaluation coefficients; the evaluation coefficients include at least one of the following: , MAE As shown in formulas (7) and (8): (7) (8) when , MAE When all preset conditions are met, it can be determined that the target constitutive model meets the accuracy requirements. The preset conditions can be reaching the corresponding preset threshold or being in the corresponding preset interval. The specific conditions can be set according to the actual situation, and the embodiments of the present invention do not impose any limitations here.

[0046] Furthermore, the neural network loss function framework of this embodiment of the invention performs dual optimization through data loss and physical loss to obtain better prediction results. Specifically, in the loss function framework based on physical information, the stress data used for physical information prediction is calculated outside the framework by the target constitutive model. After completing the above data calculation, the same normalization process and data type conversion are required as described above.

[0047] Since the prediction dataset is divided into training and test sets according to a set method, in order to maintain consistency with the prediction dataset, the calculated true stress data also needs to be divided in the same way, corresponding to the training and test sets respectively.

[0048] In some embodiments of the present invention, such as Figure 2 As shown, step S103 includes: S201. Iteratively optimize the target constitutive model to obtain the optimal parameter set.

[0049] In this embodiment of the invention, the data from the training set in the prediction dataset can be substituted into the target constitutive model for iterative optimization and solution, thereby obtaining the optimal parameter set.

[0050] In some embodiments of the present invention, step S201 includes: Dimensionless temperatures are obtained based on the material temperatures in the predicted dataset.

[0051] In this embodiment of the invention, dimensionless temperature can be calculated based on the material temperature in the predicted dataset, as well as the room temperature and melting point temperature of the material obtained from actual conditions and historical data. The calculation of dimensionless temperature is shown in formula (9): (9) In the formula, The temperature is dimensionless. For material temperature, This refers to room temperature. This is the melting point temperature of the material.

[0052] The strain, dimensionless temperature, and initial material parameters from the basic dataset are substituted into the target constitutive model for calculation to obtain all predicted stress values.

[0053] In order to enable the loss function of a neural network to have both high accuracy and physical information constraints during the optimization process, this invention constructs a loss function framework based on physical information. This framework can simultaneously calculate the data loss obtained based on the prediction dataset and the physical loss obtained based on the target constitutive model.

[0054] The mean square error is obtained based on all predicted stress values.

[0055] The optimal parameter set is obtained by iterative optimization based on the mean square error.

[0056] In the constitutive model parameter fitting process of this invention, the objective function is used as the optimization result. The objective function is set as the mean square error (MSE). By iteratively solving the material parameters of the target constitutive model, the material parameters of the target constitutive model can be obtained, that is, the optimal parameter set is obtained.

[0057] S202. Calculate the physical loss and data loss based on the optimal parameter set, initial hyperparameters, and target constitutive model to obtain the initial total loss error.

[0058] This invention allows for the setting of initial hyperparameters, which can be configured according to actual conditions; this invention does not impose any limitations on this setting. Physical loss and data loss are calculated using the optimal parameter set, initial hyperparameters, and the target constitutive model. Based on the physical loss and data loss, the initial total loss error is then calculated.

[0059] In some embodiments of the present invention, step S202 includes: The optimal parameter set is input into the target constitutive model to obtain the physical true stress.

[0060] In this embodiment of the invention, the data from the obtained optimal parameter set can be input one by one into the target constitutive model, and the physical true stress can be output.

[0061] The mean square error between the true stress in the predicted dataset and the physical true stress is defined as the physical loss.

[0062] In this embodiment of the invention, the mean square error between the true stress in the predicted dataset and the physical true stress can be calculated, and the mean square error can be determined as the physical loss. The physical loss is calculated as shown in formula (10): (10) In the formula, The first one obtained based on the constitutive model The predicted value for each sample.

[0063] The predicted dataset is input into the phenomenological constitutive model to obtain the true stress of the phenomenon.

[0064] The phenomenological constitutive model in this embodiment of the invention can be a fitting of the macroscopic deformation behavior of materials based on experimental data. Therefore, data from the predicted dataset can be substituted one by one into the phenomenological constitutive model to obtain the true stress of the phenomenon.

[0065] The mean square error between the true stress in the predicted dataset and the true stress of the observed phenomena is defined as the data loss.

[0066] After obtaining the true stress of all phenomena in this embodiment of the invention, the mean square error can be calculated based on the true stress of the phenomena. The mean square error is determined as the data loss, and the data loss is calculated as shown in formula (11): (11) In the formula, To determine the data loss; The total number of samples; For the first Predicted values ​​for each sample; For the first The true value of each sample.

[0067] The initial total loss error is obtained based on physical loss, data loss, and initial hyperparameters.

[0068] In this embodiment of the invention, under the default configuration, data loss and physical loss have the same weight. This invention introduces an initial hyperparameter. This is used to adjust the contribution weight of physical loss in the total loss function. Initial hyperparameters are introduced. Then, the physical loss term is shown in formula (12): (12) Calculating the initial total loss error using a loss function framework based on physical information As shown in formula (13): (13) S203. Generate noise data based on the current annealing temperature.

[0069] This invention provides an optimizer based on the simulated annealing algorithm for collaborative optimization of neural network parameters. The optimizer based on the simulated annealing algorithm begins by initializing the model parameters.

[0070] For hyperparameters The optimization process generates noise data based on the annealing temperature.

[0071] In the neural network training iteration, new values ​​are obtained based on the current annealing temperature. Candidate values ​​are shown in formula (14): (14) In the formula, This represents the normally distributed noise produced by the annealing temperature parameter; Indicates the current annealing temperature; Indicates the minimum permissible annealing temperature; This indicates the initial annealing temperature.

[0072] S204. Based on the noise data, obtain candidate values.

[0073] This invention simulates large-scale disturbances by mapping normally distributed noise to a logarithmic distribution, while avoiding the generation of positive and negative values. Therefore, after obtaining the noise data, it can generate [the necessary data]. candidate values As shown in formula (14): (14) In the formula, as candidates value; For the current value; The noise is obtained from a normal distribution.

[0074] Furthermore, the candidates If the value constraint is within a reasonable range, and the candidate If the value is not a valid number, it will be rolled back to the current value. The value, or correction, is made when it is within the boundary range.

[0075] S205. Calculate the physical loss and data loss based on the optimal parameter set, candidate values, and target constitutive model to obtain the candidate total loss error.

[0076] In this embodiment of the invention, the steps in step S202 above are repeated to calculate the physical loss and data loss based on the optimal parameter set, candidate values ​​and target constitutive model, and to obtain the candidate total loss error. The specific process is the same as above, and will not be repeated here.

[0077] In some embodiments of the present invention, after step S205, the method further includes: When the candidate total loss error is less than the initial total loss error, the candidate total loss error is determined as the initial total loss error. If the preset number of training iterations has not been reached, a new candidate value is generated and iterative optimization is performed again.

[0078] In this embodiment of the invention, a material annealing process is performed once in each round of neural network training iteration. Based on the current loss value and the annealing temperature, an acceptance decision is made: if the candidate total loss error is less than the initial total loss error, a new candidate value is generated and iterative optimization is performed again before the preset number of training iterations is reached.

[0079] S206. When the candidate total loss error is greater than or equal to the initial total loss error, the parameters of the neural network model are iteratively optimized using the simulated annealing algorithm to obtain the target neural network model.

[0080] In this embodiment of the invention, when the candidate total loss error is greater than or equal to the initial total loss error, the set of parameters is accepted with a certain probability according to the Metropolis criterion. The acceptance probability depends on the current annealing temperature and the loss value.

[0081] In some embodiments of the present invention, step S206 includes: Calculate the difference between the candidate total loss error and the initial total loss error.

[0082] This invention calculates the candidate total loss error. Compared with the initial total loss error The difference is shown in formula (15): (15) The acceptance probability is obtained based on the difference and the current annealing temperature.

[0083] In this embodiment of the invention, the acceptance probability can be calculated as shown in formula (16): (16) In the formula, The probability of accepting a solution according to the criterion; The candidate total loss error; This represents the initial total loss error; The current annealing temperature; It is the Boltzmann constant.

[0084] When the acceptance probability is not greater than the preset threshold, the current annealing temperature is updated based on the adaptive cooling rate strategy to obtain the new current annealing temperature. If the preset number of training iterations has not been reached, the iteration optimization is performed again based on the new current annealing temperature.

[0085] The update process in this embodiment of the invention is the same as the process described later in the "updating the current annealing temperature based on the adaptive cooling rate strategy to obtain the new current annealing temperature". This embodiment of the invention is described in detail below. After the update, if the preset number of training times has not been reached, iterative optimization is performed again based on the new current annealing temperature.

[0086] When the acceptance probability is greater than the preset threshold, smoothing is performed based on the candidate value, the initial hyperparameter, and the preset smoothing coefficient to obtain the target hyperparameter.

[0087] This invention embodiment can compare the acceptance probability with a preset threshold. When the acceptance probability is greater than the preset threshold, the current, worse set of parameters is accepted. The preset threshold is generated as follows: .

[0088] Furthermore, when the acceptance probability is not greater than a preset threshold, the weights and biases of the neural network are updated simultaneously while updating the optimal loss.

[0089] Based on the current hyperparameters in this embodiment of the invention The corresponding loss value is used to determine acceptance based on the current annealing temperature: if the perturbed loss value is better than the historical best loss, then the λ value is directly accepted and updated; if the perturbed loss value is not improved, then the new λ value is accepted with a certain probability according to the Metropolis criterion. The value, the specific formula is the same as above. If accepting the new... The value is then further smoothed using the EMA method, as shown in formula (17): (17) In the formula, For the updated ; The smoothing coefficient is set.

[0090] The current annealing temperature is updated based on an adaptive cooling rate strategy to obtain a new current annealing temperature.

[0091] In this embodiment of the invention, temperature updates are performed at the final stage of each material annealing process. This embodiment introduces an adaptive cooling rate strategy that dynamically adjusts the temperature based on the quality of the current solution and the performance of neighboring solutions, effectively improving search efficiency. New current annealing temperature. The update is shown in formula (18): (18) In the formula, The annealing cooling rate; This represents the current number of training iterations. This represents the total number of training sessions. This is the current annealing temperature.

[0092] Without performing gradient calculations, the model parameters of the neural network are saved and copied into the model, and the best loss value recorded during the current optimization process is returned for external monitoring of the optimization process.

[0093] When the preset number of training iterations is reached, the physical loss and data loss are optimized simultaneously based on the optimal parameter set, target hyperparameters, and target constitutive model to obtain the target total loss error.

[0094] In this embodiment of the invention, after the update, it can determine whether the current number of training iterations has reached the preset number of training iterations. If so, it performs dual optimization of physical loss and data loss based on the updated target hyperparameters, the optimal parameter set, the target hyperparameters, and the target constitutive model to obtain the target total loss error.

[0095] The weights and bias parameters in the neural network model are updated based on the total loss error of the target, the new current annealing temperature, and the target hyperparameters to obtain the target neural network model.

[0096] After obtaining the target total loss error, the new current annealing temperature, and the target hyperparameters, this invention can update the weights and bias parameters of the neural network, thereby obtaining the trained target neural network model.

[0097] Furthermore, in order to obtain good training results and achieve the expected prediction accuracy, a complete neural network learning architecture is constructed, which integrates the physical information-based neural network loss function framework and the optimizer based on the simulated annealing algorithm from the above steps.

[0098] After the neural network initialization is completed, its basic structure is set. The number of nodes in each hidden layer is determined according to an empirical formula, and the calculation formula is shown in formula (19): (19) In the formula, , These represent the number of nodes in the input layer and the number of nodes in the output layer, respectively. For parameters within a certain range, ; All networks use linear layers; the activation function is the hyperbolic tangent function Tanh, and its specific expression is shown in formula (20): (20) The weights of the neural network are initialized using the Xavier initialization method, which randomly samples the weights within a suitable range. The calculation formula for Xavier initialization is shown in formula (21): (twenty one) In the formula, U It is a uniform distribution; This represents the number of input nodes in the previous layer. This represents the number of output nodes for the next layer.

[0099] During model training iterations, the Adam optimizer is set as the basic optimizer, and the optimizer is improved using the simulated annealing algorithm. Annealing parameters, including initial temperature and cooling rate, are also set.

[0100] When there is an error between the actual value corresponding to the prediction dataset and the output value of the neural network model, the prediction model parameters are adjusted based on this error. The specific adjustment methods are shown in formulas (22) and (23): (twenty two) (twenty three) In the formula, These are the weight parameters updated after the nth iteration. For the first n The weight parameters after -1 iteration update For learning rate, For the loss function with respect to weights (gradient), The bias parameters are updated after the nth iteration. For the first n The bias parameter after -1 iteration update For the loss function with respect to bias The gradient.

[0101] Based on experimental values ​​of D1800HFD steel, this invention has made predictions according to different constitutive models. The comparison results of the predicted values ​​of the phenomenological material plasticity constitutive model are as follows: Figure 3 As shown, a comparison of the predicted values ​​of the material plasticity constitutive model based on the physical information neural network is presented. Figure 4 As shown. Figure 3 and Figure 4 The left figure shows a temperature of 700°C and a strain rate of 0.01 / 0.1 s. -1 The curve graph, Figure 3 and Figure 4 The left figure shows the temperature at 800 / 900°C and the strain rate at 0.01 s⁻¹. -1 The curves show that the predictions of the constitutive model based on the physical information neural network of this application have a high overlap rate, indicating that the prediction accuracy of the embodiments of this invention is high.

[0102] Based on the experimental values ​​of the test sample titanium alloy TC11, the embodiments of the present invention made predictions according to the physical information neural network material plasticity constitutive model. Figure 5 With a current density of 30 A / mm 2 A schematic diagram comparing the experimental curve and the fitted curve with a duty cycle of 1 and a power-on cycle of 20s. Figure 6 This diagram illustrates the comparison between the experimental curve and the fitted curve for a current density of 10 A / mm², a duty cycle of 0.4, and a energizing period of 10 s. The solid line represents the experimental curve, and the circular solid line represents the fitted curve. The predicted values ​​obtained by the constitutive model based on the physical information neural network of this application show a high overlap rate, indicating high prediction accuracy in this embodiment.

[0103] Depend on Figure 3 The predicted values ​​obtained from the phenomenological constitutive model of material plasticity indicate that the parameter solution method can accurately describe the plastic deformation behavior of materials.

[0104] Depend on Figures 4-6The predicted values ​​obtained from the material plastic constitutive model based on the physical information neural network show that the constructed constitutive model can accurately describe the plastic deformation behavior of materials and has the characteristics of strong generalization. It can characterize the prediction of complex deformation behavior of different materials under extreme working conditions.

[0105] To better implement the material plasticity constitutive molding method in the embodiments of the present invention, correspondingly, the embodiments of the present invention also provide a material plasticity constitutive molding apparatus, such as... Figure 7 As shown, the material plasticity constitutive molding apparatus 700 includes: The data acquisition module 701 is used to acquire a predicted dataset of the plastic deformation behavior of materials; the predicted dataset includes true stress, true strain, material temperature and strain rate; Model building module 702 is used to build the target constitutive model based on the coupling relationship between true strain, material temperature, strain rate and true stress in the prediction dataset; The dual optimization module 703 is used to perform dual optimization of physical loss and data loss on the neural network model based on the prediction dataset and the target constitutive model. During the optimization process, the parameters of the neural network model are iteratively optimized through the simulated annealing algorithm to obtain the target neural network model.

[0106] The material plasticity molding apparatus 700 provided in the above embodiments can realize the technical solutions described in the above material plasticity molding method embodiments. The specific implementation principles of each module or unit can be found in the corresponding content in the above material plasticity molding method embodiments, which will not be repeated here.

[0107] The above provides a detailed description of the material plasticity constituent molding method and apparatus provided by the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for constructing a material plasticity constitutive model, characterized in that, include: Obtain a dataset predicting the plastic deformation behavior of materials; The predicted dataset includes true stress, true strain, material temperature, and strain rate; Based on the coupling relationship between the true strain, material temperature, strain rate, and true stress in the predicted dataset, a target constitutive model is constructed. The neural network model is optimized using both physical loss and data loss based on the predicted dataset and the target constitutive model. During the optimization process, the parameters of the neural network model are iteratively optimized using the simulated annealing algorithm to obtain the target neural network model.

2. The material plasticity constitutive molding method according to claim 1, characterized in that, The dataset for predicting the plastic deformation behavior of materials includes: A basic dataset is constructed based on experimental data of the plastic deformation behavior of materials; the basic dataset includes stress, strain, material temperature and strain rate from experiments on the mechanical properties of materials under different working conditions; The stress and strain in the basic dataset are transformed to obtain a transformed dataset; the transformed dataset includes the true stress, the true strain, the material temperature, and the strain rate; The transformed dataset is normalized to obtain a standardized dataset; The standardized dataset is divided to obtain the prediction dataset.

3. The material plasticity constitutive molding method according to claim 1, characterized in that, The step of constructing a target constitutive model based on the coupling relationship between the true strain, the material temperature, the strain rate, and the true stress in the predicted dataset includes: Construct the initial JC constitutive model; The initial JC constitutive model is transformed according to the coupling relationship between the true strain, the material temperature and the true stress in the predicted dataset to obtain the first constitutive model; Based on the mechanical behavior under extreme conditions in the predicted dataset, the first constitutive model is transformed into a formula to obtain the target constitutive model.

4. The material plasticity constitutive molding method according to claim 2, characterized in that, The process of performing dual optimization of the neural network model based on the predicted dataset and the target constitutive model, using both physical loss and data loss, and iteratively optimizing the parameters of the neural network model through simulated annealing during the optimization process to obtain the target neural network model, includes: The target constitutive model is iteratively optimized to obtain the optimal parameter set; The physical loss and data loss are calculated based on the optimal parameter set, the initial hyperparameters, and the target constitutive model to obtain the initial total loss error; Noise data is generated based on the current annealing temperature; Based on the noise data, candidate values ​​are obtained; The physical loss and data loss are calculated based on the optimal parameter set, the candidate values, and the target constitutive model to obtain the candidate total loss error; When the candidate total loss error is greater than or equal to the initial total loss error, the parameters of the neural network model are iteratively optimized using the simulated annealing algorithm to obtain the target neural network model.

5. The material plasticity constitutive molding method according to claim 4, characterized in that, After calculating the physical loss and data loss based on the optimal parameter set, the candidate values, and the target constitutive model to obtain the candidate total loss error, the method further includes: When the candidate total loss error is less than the initial total loss error, the candidate total loss error is determined as the initial total loss error. If the preset number of training iterations has not been reached, a new candidate value is generated and iterative optimization is performed again.

6. The material plasticity constitutive molding method according to claim 4, characterized in that, The step of iteratively optimizing the parameters of the neural network model using the simulated annealing algorithm to obtain the target neural network model includes: Calculate the difference between the candidate total loss error and the initial total loss error; The acceptance probability is obtained based on the difference and the current annealing temperature; When the acceptance probability is not greater than a preset threshold, the current annealing temperature is updated based on the adaptive cooling rate strategy to obtain a new current annealing temperature, and if the preset number of training times has not been reached, iterative optimization is performed again based on the new current annealing temperature. When the acceptance probability is greater than a preset threshold, smoothing is performed based on the candidate value, the initial hyperparameter, and the preset smoothing coefficient to obtain the target hyperparameter; The current annealing temperature is updated based on an adaptive cooling rate strategy to obtain a new current annealing temperature; When the preset number of training iterations is reached, the physical loss and data loss are optimized simultaneously based on the optimal parameter set, the target hyperparameters, and the target constitutive model to obtain the target total loss error. The target neural network model is obtained by updating the weights and bias parameters in the neural network model based on the target total loss error, the new current annealing temperature, and the target hyperparameters.

7. The material plasticity constitutive molding method according to claim 4, characterized in that, The iterative optimization solution of the target constitutive model to obtain the optimal parameter set includes: The dimensionless temperature is obtained based on the material temperature in the predicted dataset; Substitute the strain, the dimensionless temperature, and the initial material parameters from the basic dataset into the target constitutive model for calculation to obtain all predicted stress values. Based on all the predicted stress values, the mean square error is obtained; The optimal parameter set is obtained by iterative optimization based on the mean square error.

8. The material plasticity constitutive molding method according to claim 4, characterized in that, The calculation of physical loss and data loss based on the optimal parameter set, initial hyperparameters, and target constitutive model to obtain the initial total loss error includes: The optimal parameter set is input into the target constitutive model to obtain the physical true stress; The mean square error between the true stress and the physical true stress in the predicted dataset is determined as the physical loss; The predicted dataset is input into the phenomenological constitutive model to obtain the true stress of the phenomenon; The mean square error between the true stress in the predicted dataset and the true stress of the phenomenon is determined as the data loss. The initial total loss error is obtained based on the physical loss, the data loss, and the initial hyperparameters.

9. A method for predicting the plastic deformation behavior of materials, characterized in that, include: The target neural network model obtained by any one of the material plasticity constitutive modeling methods according to claims 1 to 8 is used to predict the plastic deformation behavior of the material.

10. A material plasticity constitutive molding device, characterized in that, include: The data acquisition module is used to acquire a predicted dataset of the plastic deformation behavior of materials; the predicted dataset includes true stress, true strain, material temperature, and strain rate. The model building module is used to construct a target constitutive model based on the coupling relationship between the true strain, the material temperature, the strain rate and the true stress in the predicted dataset. The dual optimization module is used to perform dual optimization of the neural network model based on the prediction dataset and the target constitutive model, using both physical loss and data loss. During the optimization process, the parameters of the neural network model are iteratively optimized using a simulated annealing algorithm to obtain the target neural network model.

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