A material flow stress prediction method and system based on a physical information neural network under a complex stress state

Abstract

This invention relates to a method and system for predicting material flow stress under complex stress states based on a physical information neural network. The method includes: acquiring material mechanics sample data; inputting the material mechanics sample data into a flow stress prediction model to obtain predicted flow stress values; the flow stress prediction model is obtained through iterative optimization training using a mini-batch traversal of the training set; during training, the model parameters are optimized using a training loss function; the basis function stress is calculated using the analytical constitutive basis function module of the flow stress prediction model; and the predicted flow stress value is output based on the basis function stress combined with the original residual using a gated residual coupling module. This invention significantly improves the prediction accuracy and stress state discrimination capability under different stress states and composite loading conditions, while maintaining consistency with the preset physical trend and the baseline state.

Description

Technical Field

[0001] This invention relates to the fields of material constitutive modeling, computational solid mechanics and machine learning integration, and in particular to a method and system for predicting material flow stress under complex stress states based on physical information neural networks. Background Technology

[0002] The plastic flow behavior of metallic materials under high strain rate, variable temperature, and complex stress states (compression, tension, shear, and their combined loading) exhibits significant nonlinearity and is highly sensitive to stress state. Existing analytical constitutive models, including phenomenological empirical models (such as Johnson–Cook, JC) and physical fundamental models (such as Zerilli–Armstrong, ZA), can describe basic laws such as strain hardening, strain rate hardening, and thermal softening. However, they still have shortcomings in uniformly characterizing the differences in plastic response under different stress states, and they usually rely on a large number of multiaxial experiments for parameter calibration, which is costly and time-consuming, thus limiting their rapid application under complex working conditions.

[0003] On the other hand, although pure data-driven neural network models can learn the complex mapping from input parameters to flow stress, they often suffer from problems such as insufficient physical consistency, weak extrapolation ability, difficulty in ensuring consistency of baseline state degradation, and sensitivity to noise and data sparsity. When called in engineering simulations, they may cause unstable or unreasonable material responses, posing a reliability risk.

[0004] Physical Information Neural Networks (PINNs) can achieve a balance between fitting accuracy and physical consistency by embedding physical constraints such as boundary conditions, conservation relations, or constitutive consistency into the optimization objective in the form of residuals. However, in plastic constitutive modeling that considers stress state effects, there is still a lack of mature and reusable unified solutions for how to achieve an "explicit and controllable" expression of stress state effects and strict degradation consistency under key baseline states, thereby simultaneously satisfying prediction accuracy, physical rationality, and engineering deployability.

[0005] Within the JC framework, to enhance the ability to describe stress state effects, existing techniques often introduce stress triaxiality. and Lode angle parameters The relevant correction terms form the modified Johnson-Cook (MJC) form. This type of method typically treats the influence of stress state as a multiplicative correction to the JC response: stress triaxiality is constructed separately. Correction terms and Lode angle parameters The correction term is then multiplied to introduce the effect, thereby enabling a description of the stress state effect of material flow stress.

[0006] However, the MJC-type decoupled correction still has limitations in engineering applications: firstly, the implicit stress triaxiality is constructed separately and multiplied. With Lode angle parameters First, the assumption of approximate separability makes it difficult to fully characterize the nonlinear coupling and interaction that may exist between the two under multiaxial loading. Second, in order to maintain the closed form, the expression of the correction term is often limited to a low-order empirical form, which makes it difficult to balance accuracy and physical rationality when the stress state effect is highly nonlinear or when it is coupled with temperature and strain rate. Third, when it is required to be consistent with the JC response under reference states such as shear, it often relies on parameter calibration to make the correction term "close" to 1, which is a soft constraint and it is difficult to ensure strict consistency from a structural point of view, thus affecting the numerical stability and repeatability of the finite element iteration process.

[0007] Therefore, there is an urgent need for a method that can express stress triaxiality in a more general and controllable manner while maintaining the interpretability of analytical constitutive basis functions. With Lode angle parameters A technical solution that couples stress state effects and achieves strict structural degradation consistency under baseline shear conditions, and can be directly deployed in UMAT / VUMAT material subroutines to achieve reliable flow behavior prediction. Summary of the Invention

[0008] To address the problems existing in the prior art, the present invention aims to provide a method and system for predicting material flow stress under complex stress states based on a physical information neural network. This method achieves high-precision prediction of material flow stress under complex stress states, ensures that the shear reference state strictly degenerates into the JC response through structural constraints, and maintains the preset constitutive evolution trend by introducing boundary soft constraints and other mechanisms, thereby improving the reliability of the model in engineering simulation and constitutive identification applications.

[0009] To achieve the above objectives, the present invention provides the following solution: A method for predicting material flow stress under complex stress states based on a physical information neural network includes: Obtain material mechanics sample data, input the material mechanics sample data into the flow stress prediction model, and obtain the flow stress prediction value; the flow stress prediction model is obtained by iterative optimization training using mini-batch traversal of the training set; during the training process, the model parameters are optimized through the training loss function; The basis function stress is calculated by the analytical constitutive basis function module of the flow stress prediction model, and the flow stress prediction value is output by the gated residual coupling module based on the basis function stress and the original residual.

[0010] Optionally, the material mechanics sample data includes: strain, strain rate, temperature, stress triaxiality, Lode angle parameter, and corresponding flow stress.

[0011] Optionally, the flow stress prediction model includes: The analytical constitutive basis function module is used to calculate the basis function stresses; The neural network residual module is used to obtain the original residual based on the normalization matrix; the normalization matrix is ​​obtained by linearly normalizing the material mechanics sample data. The gated residual coupling module is used to combine the original residual with the stress triaxiality to obtain the residual term, and combine it with the basis function stress to obtain the predicted value of the flow stress.

[0012] Optionally, calculating the basis function stress includes: ; ; in, For the basis function stress, In response, For strain rate, Let A represent temperature, and let B, C, n, and m represent the reference yield stress, hardening modulus, strain rate sensitivity coefficient, strain hardening exponent, and temperature softening exponent, respectively. These are Johnson–Cook basis functions.

[0013] Optionally, obtaining the residual term includes: ; in, The residual strength coefficient is... It is a bounded function. For the original residual, For stress triaxiality, For Lode angle parameters.

[0014] Optionally, obtaining the predicted flow stress value includes: ; in, To predict flow stress values, For the basis function stress, In response, For strain rate, For temperature, For stress triaxiality, For Lode angle parameters, This is the residual term.

[0015] Optionally, the residual term is controlled by a gating function, which is used as a multiplicative factor of the residual term to activate the original residual, i.e., when... When this occurs, it proves that the current material is in a pure shear state, and the gate function... ,and then The predicted flow stress value strictly degenerates to ,when If the current material is under compression or other complex stress state, the correction value learned by the network is introduced into the predicted flow stress value; where, It is triaxial. For Lode angle parameters.

[0016] Optionally, the training loss function includes: ; in, , , , These are the weighting coefficients. For data fitting loss, For soft constraint loss at the boundary, This is a regularization term.

[0017] To achieve the above objectives, the present invention also provides a material flow stress prediction system based on a physical information neural network under complex stress states, comprising: The data acquisition unit is used to acquire material mechanics sample data; The stress prediction unit is used to input the material mechanics sample data into the flow stress prediction model to obtain the flow stress prediction value; the flow stress prediction model is obtained by iterative optimization training through mini-batch traversal of the training set; during the training process, the model parameters are optimized through the training loss function. The basis function stress is calculated by the analytical constitutive basis function module of the flow stress prediction model, and the flow stress prediction value is output by the gated residual coupling module based on the basis function stress and the original residual.

[0018] The beneficial effects of this invention are as follows: (1) Structural physical degradation guarantee: due to exist When the time is 0, the residual term g is strictly 0. This invention enables the model output to strictly degenerate into the basis function response in the shearing reference state, avoiding the instability caused by relying solely on the "soft constraint" of the loss term.

[0019] (2) Integrated coupling expression of stress state effect: This invention expresses the stress triaxiality With Lode angle parameters Using it as input and achieving controllable representation through gated residuals, more complex coupling relationships can be learned, thus overcoming the expression bottleneck of the MJC decoupled product structure.

[0020] (3) Controllable physical trend: The present invention maintains the preset evolution trend of compression / tension / shear and other states by experimentally observing the constructed boundary soft constraints, thereby improving the engineering credibility.

[0021] (4) High deployability: The output stress of this invention maintains the dimension of MPa, which is convenient for UMAT / VUMAT calls and error index (MAE, RMSE) interpretation. The consistency of the reference state improves the stability of finite element iteration.

[0022] (5) Improved robustness and generalization ability: This invention improves noise resistance and suppresses overfitting through Huber loss, weight decay and training stabilization strategies.

[0023] (6) Improved prediction accuracy and stress state discrimination capability: Compared with the basis function model (JC, ZA) and its traditional form, the improved model of this invention can more clearly distinguish stress states such as uniaxial compression, uniaxial tension, shear and compression-shear / tension-shear combination on multi-condition data; on this basis, PINN further improves the overall fitting accuracy and stress state discrimination capability. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a flowchart of a material flow stress prediction method based on a physical information neural network under complex stress conditions, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the flow stress prediction model structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the description of the plastic rheological stress of TA1 material using the MJC model in an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the description of the plastic rheological stress of TA1 material using the MZA model in an embodiment of the present invention. Figure 5 This is a schematic diagram illustrating the description of the plastic rheological stress of TA1 material using the PINN model in an embodiment of the present invention. Figure 6 This is a schematic diagram of the experimental test results of TA1 material under different stress states according to an embodiment of the present invention; Figure 7The following diagrams illustrate the predictive capabilities of different models for TA1 plastic rheological stress in the embodiments of the present invention: (a) is the error diagram under the condition of 10⁻³ / s and 25°C, (b) is the error diagram under the condition of 2000 / s and 25°C, and (c) is the error diagram under the condition of 2000 / s and -196°C. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] This embodiment discloses a method for predicting material flow stress under complex stress states based on a physical information neural network, including: acquiring material mechanics sample data; inputting the material mechanics sample data into a flow stress prediction model to obtain predicted flow stress values; obtaining the flow stress prediction model through iterative optimization training using a mini-batch traversal of the training set; optimizing model parameters through a training loss function during training; calculating basis function stresses through the analytical constitutive basis function module of the flow stress prediction model; and outputting predicted flow stress values ​​based on the basis function stresses combined with the original residuals using a gated residual coupling module.

[0029] Specifically, this embodiment discloses a method for predicting material flow stress under complex stress states based on a physical information neural network, including: S1, acquiring material mechanics sample data, wherein the sample data includes at least strain. strain rate ,temperature Stress triaxiality Lode angle parameters and the corresponding flow stress ; S2, For the input feature vector Perform linear normalization to obtain the normalized input matrix; maintain the output flow stress. The physical dimensions are not normalized; S3. Construct a prediction model: like Figure 2 The prediction model includes: The analytical constitutive basis function module is used to calculate the basis function stresses. ; The neural network residual module is used to output the original residual based on the normalized matrix. The neural network residual module is a specially designed sub-network whose core function is to calculate and output the original residual value based on the input normalized feature matrix.

[0030] Specifically, this module receives normalized five-dimensional input features, including strain, strain rate, temperature, stress triaxiality, and Lode angle parameters. These features are first scaled to a uniform numerical range to ensure the stability of network training. After entering this module, the input features undergo nonlinear transformations through multiple fully connected layers, each using tanh as the activation function, enabling the network to learn the complex mapping relationship between input and output.

[0031] Essentially, this module is a function approximator that learns patterns in the training data to establish a nonlinear mapping from the normalized input space to the original residual space. Ultimately, the module outputs a scalar value, namely the original residual. This value represents the degree of deviation of the material's actual stress response from the benchmark JC constitutive model under the current input conditions, but it is still in its "raw" state and has not yet undergone subsequent gating modulation and scaling processing; Gated residual coupling module, used to convert the original residual With stress triaxiality Lode angle parameters Combine to obtain the residual term and output predicted flow stress ,satisfy: ; S4. Construct the training loss function The training loss function includes at least the data fitting loss. Boundary soft constraint loss and regularization terms Two or three of the following, and optionally including baseline consistency loss. ; S5. The prediction model is trained using mini-batch iterative optimization to obtain the trained model. The training process is as follows: Training the prediction model is an iterative optimization process based on mini-batch gradient descent, the core of which is to adjust the network parameters by constructing and minimizing the loss function. Before training begins, data preparation is required, including dividing the experimental data into training and test sets, and normalizing the input features (strain, strain rate, temperature, stress triaxiality, and Lode angle parameters). The training loss function consists of several parts: first, the data fitting loss, which uses mean squared error to measure the difference between the network-predicted stress and the experimentally measured stress, which is the main driving force for model learning; second, the boundary soft constraint loss, which applies physical constraints that compressive stress is greater than tensile stress and tensile stress is greater than shear stress; and finally, the regularization term, which prevents overfitting by applying L2 penalty to the network weights. In addition, a baseline consistency loss can be optionally included, but since the network structure guarantees automatic degradation to a JC model when shearing the baseline state, this term can be set to zero. During training, at the beginning of each round, the training data is randomly shuffled and then divided into mini-batches of a fixed size (e.g., 64 samples per batch). For each mini-batch, forward propagation is performed to obtain the predicted stress. The various losses are calculated and weighted to obtain the total loss. Then, backpropagation is used to calculate the gradient of the loss with respect to the network parameters, and the Adam optimizer is used to update the parameters based on the gradient. This process is repeated for each batch until all batches are completed, thus completing one training epoch. During training, model performance is periodically evaluated on the validation set, monitoring metrics such as R², and the learning rate is adjusted according to a preset strategy. If validation performance does not improve for an extended period, an early stopping mechanism is triggered. After thousands of iterations of optimization, the network parameters gradually converge, and the model can accurately predict flow stress under different stress states while satisfying physical consistency constraints. The final trained prediction model is then used for subsequent applications. S6. Apply the trained model to a given input. Output the corresponding predicted flow stress value .

[0032] Furthermore, the analytical constitutive basis functions Johnson-Cook basis functions : ; In the formula: A, B, C, n, and m represent the reference yield stress, hardening modulus, strain rate sensitivity coefficient, strain hardening index, and temperature softening index, respectively.

[0033] Furthermore, the residual term satisfy: ; in, The residual strength coefficient is... It is a bounded function.

[0034] Furthermore, the gate function , making when hour, ,and then The Strictly degenerated into .

[0035] The gating function acts as a physical state identifier in the entire residual mechanism: 1) Quantifying the degree of deviation: by calculating the stress triaxiality And Lode angle parameters The sum of squares quantifies the degree to which the current stress state deviates from the pure shear reference state. When the material is in a pure shear state, ,at this time When the material is under compression or other stress, and Not zero, 2) Controlled residual activation: The gate function is used as a residual term. The multiplicative factor controls the original residual. To what extent is it activated? Only when deviating from the shear reference state does the gating function allow the correction learned by the network to be applied to the final stress. 3) Physical meaning mapping: This design embodies the physical idea of ​​"taking the shear state as the reference and superimposing corrections on it with other stress states", so that the network structure itself contains physical prior knowledge.

[0036] Strict degradation of the shear reference state refers to when At that time, regardless of how the network is trained, the final residual term The stress must be zero, thus ensuring that the stress is strictly equal to the JC model prediction. This design plays the following key roles: 1) Physical consistency guarantee: Ensures that the network will not violate the physical law that "the material response under pure shear conditions should conform to the JC model" under any circumstances, avoiding non-physical interpretations that may arise from data-driven methods. 2) Extrapolation reliability: For shear state regions that may be missing in the training data, the network will automatically degenerate into the JC model, ensuring the reliability of the model's predictions under unseen shear conditions. 3) Reduced overfitting risk: Using the shear baseline state as an "anchor point" constrains the network's behavior under this key physical state, effectively reducing the risk of overfitting in sparse data regions. 4) Interpretability basis: Provides a clear physical baseline for the network's predictions, giving the model correction (residual term) a clear physical meaning, i.e., the degree of deviation from the JC model.

[0037] Relationship with flow stress calculation: The formula for calculating the final flow stress is: .

[0038] This design reflects a multi-layered relationship: 1) Multiplication correction relationship: residual term The residuals are applied multiplicatively to the JC basis functions, meaning that the residuals act as a relative rather than an absolute correction; that is, the deviation from the JC model is proportional to the JC reference stress itself. This design is more consistent with the physical characteristics of material constitutive behavior, as material hardening effects often have multiplicative characteristics. 2) Gated modulation relationship: The gate function acts as... The modulator determines the amount of correction the network learns. To what extent does it affect the final stress? When the material is under compression or other stress states, ,allow The JC model is modified; when in a shearing state, gate=0, completely shielded. The effect of tanh. 3) The limiting relationship of tanh: the tanh function will The residual correction is limited to the range [-1, 1] to ensure that the correction is not too drastic and to maintain numerical stability. Meanwhile, the smoothing property of tanh makes the correction process continuously differentiable. 4) Scaling relationship of gscale: The gscale parameter controls the overall magnitude of the residual correction, balancing the relative importance of the JC baseline term and the network learning term.

[0039] Furthermore, the training loss function for: ; in , , , These are the weighting coefficients.

[0040] The Huber loss or Smooth L1 loss is employed to improve robustness to noisy samples. Constructed based on experimental observations, used to constrain the same , , Under different stress states, the flow stresses satisfy a preset order relationship or proportional relationship, wherein the order relationship includes at least one or more of the following: the compression state is greater than the tension state, and the tension state is greater than the shear state.

[0041] Furthermore, at least one of the following is employed during training: segmented learning rate decay, gradient pruning, early stopping strategy, and L2 weight decay regularization.

[0042] Furthermore, the feedforward fully connected network backbone has an input dimension of 5 and an output dimension of 1, and the hidden layers adopt a multi-layer fully connected structure and use... Activation function.

[0043] Furthermore, the training employs the Adam optimizer and performs one or more of the following strategies: gradient pruning, segmented learning rate decay, and early stopping based on validation set metrics.

[0044] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] In one embodiment, this embodiment discloses a method for predicting material flow stress under complex stress states based on a physical information neural network, including: Data Acquisition and Preprocessing: Sample data should contain at least the following: The input is linearly normalized (e.g., mapped to [0,1]), while the output stress remains unnormalized in MPa to ensure that MAE and RMSE have direct physical meaning. Data is randomly divided into training and testing sets in a 4:1 ratio to ensure that each stress state is representative during both training and testing phases. Figure 1 As shown.

[0046] PINN model structure: A feedforward fully connected network is constructed to learn the residual mapping: the input dimension is 5, and the output is a 1-dimensional scalar. The example hidden layer configuration is 256–256–128–128, with each layer using tanh activation. The model has approximately 1.17 × 10⁵ parameters, suitable for characterizing complex stress state effects with finite samples.

[0047] Constitutive representation: basis functions + gated residuals: Johnson–Cook plastic constitutive model is preferred as the basis function. ; Introducing multiplicative residual structure: The residual term is: .

[0048] Since tanh is bounded and exist The time is zero, therefore under the shear reference state ,ensure Strictly equal to This avoids relying on soft constraints to achieve baseline consistency.

[0049] Loss function design: The overall loss can be expressed as: It consists of the following parts: (1) Data fitting loss Used for constraints The difference between the actual stress and the actual stress. Huber (Smooth L1) is preferred to enhance robustness.

[0050] (2) Shear reference state consistency loss : Input the stress triaxiality from the sample With Lode angle parameters Replace with shear reference state parameters ( ), constraint model output and Consistency; since the structure of this invention has guaranteed strict degradation, this item can be selectively assigned a smaller weight or set to zero to verify / enhance the consistency of the baseline state degradation.

[0051] (3) Boundary soft constraint loss Based on experimental observations, stress sequence / proportional relationships are constructed for different stress states to maintain constitutive evolution trends and physical rationality.

[0052] (4) Regular terms We employ weight decay (L2 regularization) to suppress overfitting and improve generalization.

[0053] Training strategy: Mini-batch training is used to iteratively update the training set. The Adam optimizer is selected first. The training rate is reduced in stages, gradient pruning is performed, and an early stopping mechanism based on validation set metrics is used to improve training stability and generalization ability.

[0054] Multi-model comparison and stress state effect expression analysis: On the example dataset, the classic JC and ZA models, as well as three improved models MJC, MZA, and the present invention PINN are compared. (1) In terms of overall predictive ability, compared with the MZA model, the MJC model has a significantly lower overall error in predicting the plastic flow behavior of TA1 under complex stress conditions, such as Figure 3-4 As shown; the overall prediction accuracy of PINN under various stress states is basically equivalent to that of MJC, such as... Figure 5 As shown.

[0055] (2) Regarding the ability to distinguish stress states, compared with the classical JC and ZA models, MJC, MZA, and the PINN of this invention show more obvious differences in flow stress between different stress states. They can clearly distinguish the stress levels of uniaxial compression, uniaxial tension, simple shear, and combined compression / shear / tension / shear loading conditions, demonstrating stronger stress state sensitivity. This indicates that explicitly introducing a stress state term into the classical constitutive framework can significantly improve the ability to characterize stress state effects. On this basis, the PINN of this invention, combined with physical constraints and training with limited experimental data, further improves the overall fitting accuracy and stress state distinguishability.

[0056] (3) From the perspective of analytical constitutive model, both MJC and MZA add a stress state correction term on the basis of the JC / ZA framework, so that the flow stress can change with the stress triaxiality. With Lode angle parameters The changes exhibit a regular pattern. Taking MZA as an example, its predictions reproduce the trend of "increased shear component - decreased flow stress": the stress-strain curves of CS45 and CS30 under combined compression and shear conditions lie between uniaxial compression and simple shear, while the curves of TS60 and TS30 under combined tension and shear conditions lie between uniaxial tension and simple shear, reflecting the transitional behavior between dominant stress states. MJC further improves the quantitative accuracy based on this, especially under combined stress conditions, providing key characteristics such as the CS30 curve being lower than the uniaxial tension curve, which is closer to the actual plastic rheological response. Figure 6 As shown.

[0057] (4) However, since MJC / MZA still uses a product structure that separates the main term "strain-strain rate-temperature" from the stress state correction term, its ability to express higher-order coupling relationships between stress triaxiality, Lode angle parameters, and parameters such as strain rate and temperature is still limited. In contrast, the PINN of this invention expresses stress triaxiality... Lode angle parameters By directly using these features as input and learning the coupling relationship within a data-driven and physical constraint framework, it can more stably capture the differences in work hardening rates under different stress states and the transitional hardening characteristics of composite conditions. It further consolidates and strengthens the key phenomena revealed by MJC in the prediction process, exhibiting higher resolution and predictive stability, such as... Figure 7 As shown in (a)-(c).

[0058] In summary, the PINN of this invention can serve as an important supplement to analytical constitutive models for refined modeling and engineering evaluation of stress state-related plastic responses of materials such as TA1.

[0059] Physical consistency verification: A shear baseline consistency test and a boundary trend test were employed. Under the shear baseline state, the model strictly degenerates into a basis function response; the boundary soft constraint satisfaction rate meets the preset requirements. These results demonstrate that the present invention can maintain the preset constitutive evolution trend and physical rationality while improving prediction accuracy.

[0060] UMAT / VUMAT Deployment: After training, the model parameters and normalized parameters are exported and encapsulated as callable material model functions, then integrated into UMAT / VUMAT. At each integration point of the finite element method, an input vector is constructed based on the current strain, strain rate, and temperature information, as well as the stress triaxiality and Lode angle parameters obtained from the stress update algorithm. After normalization, the model inference is called to obtain the flow stress (or equivalent stress) response, which is used for stress update and material response prediction. Because the output of this invention maintains the MPa dimension and the reference state strictly degenerates consistently, it facilitates the improvement of numerical stability and result repeatability in finite element iteration.

[0061] Example and Performance Verification (Taking TA1 material as an example): An experimental dataset containing stress states such as uniaxial compression, simple shear, and uniaxial tension was selected for training and testing. The model's performance on the test set was: R²=0.8640, RMSE=89.00 MPa, MAE=50.54 MPa; the performance on the validation / test set was: R²=0.8978, RMSE=76.14 MPa, MAE=46.32 MPa.

[0062] Comparing the results using only the JC basis function: Test set R²=0.3377, RMSE=196.44 MPa, MAE=160.32 MPa; Validation / Test set R²=0.3916, RMSE=185.78 MPa, MAE=160.32 MPa. The results show that PINN, by introducing stress-state-gated residuals, significantly improves the characterization ability of the material's plastic flow behavior and its stress-state effects.

[0063] The physical consistency test shows that the consistency of the shear baseline state and the boundary constraint satisfaction rate are both 100%, indicating that while significantly improving the prediction accuracy, the model can maintain the preset constitutive evolution trend and physical rationality.

[0064] like Figure 5 As shown, the model of this invention can accurately predict the flow stress-strain relationship under uniaxial compression, uniaxial tension and simple shear stress conditions, and can reflect the flow stress difference caused by the change of the dominant stress state under combined load conditions.

[0065] In the embodiments, the present invention is compared and verified with the MJC model and the MZA model, and stress-strain curve fitting plots and error plots are given. The results show that compared with the MJC model, the present invention has a higher tolerance for stress triaxiality. Lode angle parameters The invention introduces the decoupling multiplicative method of the correction term by using a gated residual structure to control the stress triaxiality. With Lode angle parameters By performing end-to-end learning of the coupling effects, the differences in plastic response under different combined stress states can be more accurately distinguished. Compared with other models such as MZA, the present invention significantly reduces the overall error on complex stress state data and maintains a 100% satisfaction rate in terms of shear baseline consistency and boundary trend constraints, thereby achieving a unity of "prediction accuracy - physical consistency - engineering deployability".

[0066] This embodiment also discloses a flow stress prediction system for metallic materials under complex stress states, comprising: a data acquisition unit for acquiring material mechanics sample data; a stress prediction unit for inputting the material mechanics sample data into a flow stress prediction model to obtain flow stress prediction values; the flow stress prediction model is obtained by iterative optimization training using a mini-batch traversal of the training set; during the training process, the model parameters are optimized through a training loss function; the basis function stress is calculated through the analytical constitutive basis function module of the flow stress prediction model, and the flow stress prediction value is output based on the basis function stress combined with the original residual by the gated residual coupling module.

[0067] This embodiment also discloses a system for predicting the flow stress of metallic materials under complex stress states, including: a data processing module, a basis function module, a residual network module, a gating coupling module, a loss construction module, a training optimization module, and an inference output module, for executing method steps.

[0068] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for predicting material flow stress under complex stress states based on a physical information neural network, characterized in that, include: Obtain material mechanics sample data, input the material mechanics sample data into the flow stress prediction model, and obtain the flow stress prediction value; The flow stress prediction model is obtained by iterative optimization training using a small batch traversal of the training set. During training, the model parameters are optimized by training the loss function; The basis function stress is calculated by the analytical constitutive basis function module of the flow stress prediction model, and the flow stress prediction value is output by the gated residual coupling module based on the basis function stress and the original residual.

2. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 1, characterized in that, The material mechanics sample data includes: strain, strain rate, temperature, stress triaxiality, Lode angle parameters, and corresponding flow stress.

3. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 1, characterized in that, The flow stress prediction model includes: The analytical constitutive basis function module is used to calculate the basis function stresses; The neural network residual module is used to obtain the original residual based on the normalization matrix; the normalization matrix is ​​obtained by linearly normalizing the material mechanics sample data. The gated residual coupling module is used to combine the original residual with the stress triaxiality to obtain the residual term, and combine it with the basis function stress to obtain the predicted value of the flow stress.

4. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 3, characterized in that, Calculating the basis function stress includes: ； ； in, For the basis function stress, In response, For strain rate, Let A represent temperature, and let B, C, n, and m represent the reference yield stress, hardening modulus, strain rate sensitivity coefficient, strain hardening exponent, and temperature softening exponent, respectively. These are Johnson–Cook basis functions.

5. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 3, characterized in that, The residual terms are obtained as follows: ； in, The residual strength coefficient is... It is a bounded function. For the original residual, For stress triaxiality, For Lode angle parameters.

6. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 1, characterized in that, Obtaining the predicted flow stress value includes: ； in, To predict flow stress values, For the basis function stress, In response, For strain rate, For temperature, For stress triaxiality, For Lode angle parameters, This is the residual term.

7. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 6, characterized in that, The residual term is controlled by a gating function, which is used as a multiplicative factor of the residual term to activate the original residual, i.e., when... When this occurs, it proves that the current material is in a pure shear state, and the gate function... ,and then The predicted flow stress value strictly degenerates to ,when If the current material is under compression or other complex stress state, the correction value learned by the network is introduced into the predicted flow stress value; where, It is triaxial. For Lode angle parameters.

8. The method for predicting material flow stress under complex stress states based on a physical information neural network according to claim 1, characterized in that, The training loss function includes: ； in, , , , These are the weighting coefficients. For data fitting loss, For boundary soft constraint loss, This is a regularization term.

9. A material flow stress prediction system based on a physical information neural network under complex stress states, implemented by the method according to any one of claims 1-8, characterized in that, include: The data acquisition unit is used to acquire material mechanics sample data; The stress prediction unit is used to input the material mechanics sample data into the flow stress prediction model to obtain the flow stress prediction value; the flow stress prediction model is obtained by iterative optimization training through mini-batch traversal of the training set. During training, the model parameters are optimized by training the loss function; The basis function stress is calculated by the analytical constitutive basis function module of the flow stress prediction model, and the flow stress prediction value is output by the gated residual coupling module based on the basis function stress and the original residual.

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