Finite element simulation-oriented elastomer constitutive model parameter machine learning optimization method and system

Abstract

The invention relates to the technical field of artificial intelligence, and provides a finite element simulation-oriented elastomer constitutive model parameter machine learning optimization method, which comprises the following steps of: obtaining stress data and strain data in an elastomer mechanics experiment through steps S1-S4, and respectively carrying out standardization processing on the stress data and the strain data to obtain a training data set; constructing a plurality of parallel physical information neural networks, wherein each physical information neural network is provided with a loss function; and inputting the stress data and the strain data of the to-be-analyzed material into the physical information neural networks, and performing parallel calculation by each physical information neural network to obtain material parameters. Based on the triaxial tensile strain energy stability and prediction precision index, an optimal constitutive model is screened out, and the optimal constitutive model and model parameters are packaged into a callable module. The invention discloses a system applying the method, and the method and the system adopt a multi-physical information neural network parallel prediction and intelligent screening architecture to realize efficient and automatic analysis of the elastomer constitutive model.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence technology, and in particular to a machine learning optimization method and system for constitutive model parameters of elastic bodies for finite element simulation. Background Technology

[0002] In modern engineering design and scientific research, finite element simulation technology has become a core tool for analyzing the mechanical behavior of complex structures and optimizing product performance. Its accuracy directly depends on the accurate description of the mechanical properties of materials. Among these, the selection and parameter calibration of the material constitutive model are crucial to the reliability of the simulation, especially for typical hyperelastic materials such as rubber and biological soft tissues, where the complexity of this process is even more pronounced. Hyperelastic materials exhibit significant nonlinear mechanical behavior and unique elastic recovery characteristics under large deformation conditions; their constitutive relations often require characterization through complex mathematical models.

[0003] CN112182928B discloses a software system for analyzing and optimizing the mechanical properties of rubber products. It includes the following modules: 1. Parametric Modeling Module: This module automates the modeling of changes in key design parameters of rubber products. Using a reference geometric model as a sample, it generates and updates the geometric and finite element models by changing parameter variables, driving parameter linkage between the parameter variables, geometric model, and mesh model. This ensures that the geometric and mesh models of the analyzed object are automatically generated as the input parameters change. 2. Constitutive Model Development Module: This module develops constitutive models suitable for rubber products, constructs a material library of constitutive models for various rubber products, identifies constitutive model parameters, and enables nested calls of constitutive model sub-modules in finite element numerical simulations. 3. Solution Result Analysis Module: Based on the parametric modeling and constitutive model development modules, this module provides multi-condition numerical simulations for predicting and evaluating the mechanical properties of rubber products. 4. Multi-Parameter Optimization Module: This module optimizes the performance of rubber products by performing multi-parameter optimizations on top of the parametric modeling and constitutive model development modules. Based on the generation module and the solution result analysis module, a multidisciplinary optimization mechanism is introduced to build an integrated ABAQUS and Isight optimization calculation module to realize the creep resistance and stress relaxation resistance optimization design analysis of rubber products. The operation steps of the parameterized modeling module include: ① Based on the geometric model of the rubber shock absorber, extract the key geometric feature parameters of the structure and establish a parameterized geometric model: First, the user inputs the key geometric parameter values, and the system will automatically search for parameter labels using the marker letters of the key geometric parameters to find the position of the parameter labels in the XXXFunction.py file; then, after finding the position, replace these marker letter parameter labels in the XXXFunction.py file with the parameter values ​​input by the user to create a new re-encoded XXXFunction.py file; finally, run the re-encoded XXXFunction.A Python file can be used to easily create a rubber shock absorber model with the following key geometric parameters: ① Specifying the height h, spacing d, and included angle a; ② Contact settings for the rubber shock absorber model: Based on actual application conditions, the upper end of the rubber shock absorber is connected to an analytical rigid body; to prevent mutual penetration between the rigid body and the rubber material, surface-to-surface contact is set in the contact area; using Python, the surface-to-surface contact relationship described above is integrated into the rubber shock absorber mechanical performance analysis and optimization design software system; ③ Boundary condition settings for the rubber shock absorber model: Based on actual application conditions, the bottom of the rubber damping pad is set to a fully constrained condition, and the upper end is a free boundary; based on the symmetry of the model, To improve computational efficiency, only one-quarter of the model was built, and symmetric constraints were applied in the X and Z directions. The boundary conditions described above were integrated into the rubber damper mechanical performance analysis and optimization design software system using Python. ④ Load condition settings for the rubber damper model: Based on actual application conditions, the load acts vertically on the analytical rigid body and is transmitted to the rubber damper through degree-of-freedom coupling. The load conditions described above were integrated into the rubber damper mechanical performance analysis and optimization design software system using Python. ⑤ Mesh generation settings for the rubber damper model: After setting the numerical simulation environment, element type, and material model for the rubber damper... Considering both the convergence consistency characteristics and computational cost, different mesh generation schemes with varying densities are proposed: Coarse, Medium, and Fine. The implementation method of the constitutive model development module includes the following steps: (1) Conducting mechanical tests on rubber product materials according to national standards and industry specifications; (2) Developing a constitutive model submodule material library for rubber product materials using FORTRAN language based on the user-defined subroutine interface provided by ABAQUS; (3) Using Python for integrated programming and applying intelligent optimization algorithms, identifying constitutive model parameters of rubber product materials based on mechanical test results; (4) A wizard-driven material input module was established, and a self-compiled user subroutine plugin was constructed to enable nested calls to the constitutive model submodule in finite element numerical simulations. The development of the constitutive model submodule material library for rubber products includes the following steps: First, using the built-in hyperelastic material constitutive model in ABAQUS, a hyperelastic constitutive model submodule was established. Second, considering the nonlinear hyperelastic characteristics and the time-varying degradation mechanism, a time-varying stress relaxation and creep constitutive model submodule was established. Finally, based on the established time-varying stress relaxation and creep constitutive model, the plastic damage effect was introduced to establish a time-varying relaxation-damage and time-varying creep-damage constitutive model submodule considering the residual deformation effect of damage.

[0004] In existing technologies, constitutive model parameters for elastomeric materials are typically fitted using traditional optimization algorithms such as the least squares method. While these experimental data-based parameter identification methods are computationally fast, they have significant limitations. They require pre-selection of a specific constitutive model form and cannot automatically assess the applicability of different constitutive models. When faced with complex mechanical behaviors, a single constitutive model often fails to accurately describe all the characteristics of the material. These purely mathematical optimization methods rely entirely on experimental data and lack consideration for the physical laws governing materials. Summary of the Invention

[0005] Long-term practice has revealed that while traditional data-driven methods such as the least squares method have advantages in parameter fitting speed, their fitting results often violate the fundamental physical laws of materials. For example, they may produce negative elastic moduli with no physical meaning or cause the strain energy function to lose its convexity. This physical inconsistency can seriously affect the reliability of subsequent finite element simulations. On the other hand, although optimization methods based on physical constraints can ensure the physical rationality of parameters, their computational efficiency is often significantly lower than that of purely data-driven methods, making it difficult to meet the needs of rapid modeling in engineering practice.

[0006] It is necessary to simultaneously consider: 1) the computational efficiency advantages of traditional data-driven methods; 2) the rationality guarantee of physical constraint methods; and 3) the intelligent features of automatic multi-model selection. In particular, it is necessary to resolve the inherent contradiction between rapid computation and physical rationality. In view of this, this invention aims to propose a machine learning optimization method for the parameters of elastic body constitutive models for finite element simulation, including:

[0007] Step S1: Obtain stress and strain data from the elastic body mechanics experiment, and standardize the stress and strain data respectively to obtain the training dataset;

[0008] Step S2: Construct multiple parallel physical information neural networks, each of which is configured with a loss function; train the physical information neural networks using a training dataset to obtain trained physical information neural networks;

[0009] Step S3: Input the stress and strain data of the material to be analyzed into the trained physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation.

[0010] Step S4: Based on the stability and prediction accuracy of triaxial tensile strain energy, the optimal constitutive model is selected, and the optimal constitutive model and model parameters are encapsulated into a callable module.

[0011] Preferably, in step S2, the loss function includes the experimental data fitting error and the physical constraint terms of the constitutive equation.

[0012] Preferably, the physical constraints include at least the stress-strain differential relationship constraint, the material incompressibility constraint, and the strain energy function convexity constraint.

[0013] Preferably, in step S4, the stability of triaxial tensile strain energy is verified by calculating the non-negativity of strain energy of material parameters under a triaxial tensile virtual working condition.

[0014] Preferably, the physical information neural network includes at least a parallel network structure with a shared bottom feature extraction layer and an independent output layer.

[0015] Preferably, a physical information neural network is constructed for each constitutive function, and each physical information neural network includes at least an unfolding layer, a linear layer, a normalization layer, and an activation layer; the main body of the physical information neural network adopts a fully connected neural network.

[0016] Preferably, a loss calculation module is constructed based on the constitutive function to calculate the strain energy residual Loss.

[0017]

[0018]

[0019] Among them, L δ For Huber loss The function, where y is stress, x is strain, and W true The true strain energy, W, is calculated by integrating the stress-strain curve. pred δ is the predicted value, and δ is the hyperparameter of the threshold, which controls the switching point between MSE and MAE.

[0020] Preferably, if the output of the physical information neural network is,

[0021] α1,α2,α3,μ1,μ2,μ3

[0022] So,

[0023]

[0024] Where λ1, λ2, and λ3 are the stretch ratio coefficients, α1, α2, and α3 are the nonlinear strain hardening characteristic parameters of the material, and μ1, μ2, and μ3 are the shear modulus parameters of the material.

[0025] This invention also discloses a system for machine learning optimization of parameters of elastic body constitutive models for finite element simulation, as described above, the system comprising:

[0026] The data preprocessing unit is used to acquire stress and strain data from the elastic body mechanics experiment, and to standardize the stress and strain data to obtain the training dataset.

[0027] The model building unit is used to build multiple physical information neural networks in parallel, each of which is configured with a loss function; the physical information neural networks are trained using a training dataset to obtain trained physical information neural networks;

[0028] The model calculation unit is used to input the stress and strain data of the material to be analyzed into the trained physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation.

[0029] The output unit is used to select the optimal constitutive model based on the stability and prediction accuracy of triaxial tensile strain energy, and encapsulate the optimal constitutive model and model parameters into a callable module.

[0030] This invention provides an electronic device, comprising at least one processor; and

[0031] A memory communicatively connected to the at least one processor; wherein,

[0032] The memory stores instructions that can be executed by the at least one processor, which enables the at least one processor to perform the above-described machine learning optimization method for elastic body constitutive model parameters for finite element simulation.

[0033] The present invention provides a machine-readable storage medium storing instructions for causing a machine to execute the machine learning optimization method for elastic body constitutive model parameters for finite element simulation as described above.

[0034] This invention discloses a machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation. Through steps S1-S4, the method first acquires stress and strain data from the elastic body mechanical experiment, standardizes the stress and strain data to obtain a training dataset, and then constructs multiple parallel physical information neural networks (PINs), each with a loss function. The PINs are trained using the training dataset to obtain trained PINs. The stress and strain data of the material to be analyzed are input into the trained PINs, and each PIN calculates the material parameters in parallel. Based on the stability and prediction accuracy of triaxial tensile strain energy, the optimal constitutive model is selected, and the optimal constitutive model and its parameters are encapsulated into a callable module. This invention also discloses a system applying the above-mentioned machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation. This method and system employ a multi-physical information neural network parallel prediction and intelligent selection architecture to achieve efficient and automated analysis of elastic body constitutive models. The resulting technical effects include at least the following:

[0035] First, it can simultaneously process parameter predictions for multiple constitutive models. By embedding physical constraints and stability verification mechanisms, it ensures that the results strictly conform to the laws of mechanics, significantly improving the efficiency and reliability of parameter identification. Compared with traditional methods, it greatly shortens the analysis cycle and avoids human error.

[0036] Second, it provides complete industrial application solutions, which can seamlessly integrate the optimized model parameters into mainstream finite element software, ensuring the accuracy of analysis results and simplifying the simulation process in actual engineering, providing efficient and reliable technical support for the design and performance evaluation of elastomer materials.

[0037] Meanwhile, this invention possesses excellent versatility and scalability, and can be widely applied to determining the constitutive relations of various elastomer materials. Through an innovative architecture of multi-physics information neural networks, this invention achieves automated analysis of elastomer constitutive models. Its features, such as simultaneous processing of multiple model parameters, embedded mechanical constraints to ensure reliability, and seamless integration with industrial software, not only overcome the efficiency and error problems of traditional methods but also possess broad applicability, providing efficient and reliable technical support for the design and performance evaluation of elastomer materials.

[0038] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0039] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0040] In the attached diagram:

[0041] Figure 1 This is a schematic diagram of the physical information neural network model framework in a machine learning optimization method for parameters of an elastic body constitutive model for finite element simulation, according to one embodiment of the present invention.

[0042] Figure 2 This is a schematic diagram of the physical information neural network training process of a machine learning optimization method for parameters of an elastic body constitutive model for finite element simulation, according to one embodiment of the present invention.

[0043] Figure 3 This is a flowchart illustrating the optimization process of elastic body constitutive model parameters in a machine learning optimization method for finite element simulation, according to one embodiment of the present invention. Detailed Implementation

[0044] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0045] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. 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 should fall within the scope of protection of the present invention.

[0046] It should be noted that the terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of the invention described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0047] To address the technical problems existing in current technologies, while traditional data-driven methods such as the least squares method have advantages in parameter fitting speed, their fitting results often violate the fundamental physical laws of materials. For example, they may produce negative elastic moduli with no physical meaning or cause the strain energy function to lose convexity. This physical inconsistency seriously affects the reliability of subsequent finite element simulations. On the other hand, although optimization methods based on physical constraints can ensure the physical rationality of parameters, their computational efficiency is often significantly lower than that of purely data-driven methods, making it difficult to meet the needs of rapid modeling in engineering practice. This invention provides a schematic diagram of a physical information neural network model framework in a machine learning optimization method for parameters of elastic body constitutive models for finite element simulation, as shown below. Figure 1-3 As shown, the machine learning optimization method for the constitutive model parameters of elastic bodies for finite element simulation includes,

[0048] Step S1: Obtain stress and strain data from the elastic body mechanics experiment, and standardize the stress and strain data respectively to obtain the training dataset;

[0049] Step S2: Construct multiple parallel physical information neural networks, each of which is configured with a loss function; train the physical information neural networks using a training dataset to obtain trained physical information neural networks;

[0050] Step S3: Input the stress and strain data of the material to be analyzed into the trained physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation.

[0051] Step S4: Based on the stability and prediction accuracy of triaxial tensile strain energy, the optimal constitutive model is selected, and the optimal constitutive model and model parameters are encapsulated into a callable module.

[0052] This invention discloses a machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation. Through steps S1-S4, the method first acquires stress and strain data from the elastic body mechanical experiment, and then standardizes the stress and strain data to obtain a training dataset. Multiple parallel physical information neural networks are constructed, each with a loss function. The training dataset is used to train the physical information neural networks, resulting in trained physical information neural networks. The stress and strain data of the material to be analyzed are input into the trained physical information neural networks, and each physical information neural network calculates the material parameters in parallel. Based on the stability and prediction accuracy of triaxial tensile strain energy, the optimal constitutive model is selected, and the optimal constitutive model and its parameters are encapsulated into a callable module. This invention also discloses a system applying the above-mentioned machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation. This method and system employ a multi-physical information neural network parallel prediction and intelligent selection architecture to achieve efficient and automated analysis of elastic body constitutive models. This innovative architecture, utilizing a multi-physics neural network, enables automated analysis of constitutive models of elastic bodies. It can simultaneously process parameter predictions for multiple constitutive models and ensures that the results conform to mechanical laws through embedded physical constraints and stability verification mechanisms. This significantly improves the efficiency and reliability of parameter identification, greatly shortens the analysis cycle compared to traditional methods, and avoids human error. Furthermore, it provides a complete industrial application solution, seamlessly integrating optimized model parameters into mainstream finite element software. In practical engineering, this ensures the accuracy of analysis results while simplifying the simulation process. It possesses good versatility and scalability, applicable to the determination of constitutive relations for various elastomer materials, providing efficient and reliable technical support for elastomer material design and performance evaluation.

[0053] The Physics-Informed Neural Network (PINN) is a deep learning model that incorporates constraints from physical laws. Strain energy is the elastic energy stored in a material during deformation. The triaxial tensile strain energy stability index is an indicator of the error between the predicted strain energy curve and the actual experimental curve, obtained by fitting the stress-strain curve of a single tensile method to the process material parameters. A smaller value indicates higher stability; a larger value indicates lower stability. The index also considers the ability to predict curves for two other tensile methods based on the process material parameters. If the predicted curves have small errors compared to the experimental curves, the triaxial tensile strain energy stability is considered high. The same applies to the curves for the other two tensile methods.

[0054] To embed the constitutive equation and stability conditions, ensuring that the prediction results conform to the laws of mechanics, in a more preferred embodiment of the present invention, in step S2, the loss function includes the experimental data fitting error and the physical constraint terms of the constitutive equation. The physical laws are enforced through the PINN loss function. Stress data and corresponding strain data of the elastic body are obtained through uniaxial tensile experiments. Normalization and noise filtering are performed on the stress and strain data to obtain training and testing sets. For each candidate constitutive function, such as Mooney-Rivlin, Ogden, and Yeoh, a PINN is independently constructed. The training set is input into the PINN to train the model, and the testing set is used to test the PINN model. The PINN model is output when it meets the prediction accuracy requirements. Material parameters are predicted using this PINN model, and the predicted strain energy is calculated based on the material parameters. The optimal constitutive model is selected and integrated into the finite element software. Global linear normalization, such as Min-Max normalization, is performed on the stress data, with a range of [0,1].

[0055]

[0056] Where x is the original data value, x min x is the minimum value of the feature. max x is the maximum value of the feature. norm These are the normalized data values.

[0057] Calculate the corresponding inputs for the constitutive model. For example, some constitutive model inputs are shown in Table 1 below:

[0058] Table 1 Input parameters corresponding to the constitutive model

[0059]

[0060]

[0061] The tensile ratio coefficient is obtained based on strain data. In uniaxial tensile loading, the tensile ratio coefficients for λ1, λ2, and λ3 are...

[0062] λ = strain - 1

[0063] λ1=λ

[0064]

[0065]

[0066] The strain tensors I1 and I2 are obtained based on the stretch ratio, specifically as follows:

[0067]

[0068]

[0069] The multi-physics information neural network is constructed as follows:

[0070] Step S21: Using PyTorch, a physical information neural network is independently constructed for each constitutive function, such as Mooney-Rivlin, Ogden, Yeoh, etc. The main body of the network adopts a fully connected neural network, which includes unfolding layers, linear layers, normalization layers, activation layers, etc.

[0071] Step S22: The shape of the input-output layer of the physical information neural network needs to be determined by the constitutive function. For example, Yeoh's input layer consists of stress, strain, and the strain tensor I1.

[0072] The output layer size is determined based on the number of parameters in the constitutive model. Some output parameters of the constitutive model are shown in Table 2 below:

[0073] Table 2 Output parameters corresponding to the constitutive model

[0074]

[0075]

[0076] Where α1, α2, and α3 are the nonlinear strain hardening characteristic parameters of the material, and μ1, μ2, and μ3 are the shear modulus parameters of the material, which are output parameters of the Ogden model. 10 C 20 C 30 C represents the output parameters of the Yeoh model. 10 C 01 These are the output parameters of Mooney-Rivlin. They are all material parameters, used to calculate and predict strain energy, thus enabling the selection of the optimal constitutive model for integration into the finite element software.

[0077] To ensure that the prediction results strictly adhere to the inherent mathematical relationship between stress and strain in elastomer mechanics, and closely match the physical properties of most elastomer materials, this invention prevents the model from outputting erroneous parameters that do not conform to the material's volume change laws. It also ensures the energy stability of the material during stress, avoiding the prediction of non-physical solutions that lead to abnormal material mechanical behavior. In a more preferred embodiment of this invention, the physical constraints include at least stress-strain differential relationship constraints, material incompressibility constraints, and strain energy function convexity constraints. This reduces the potential biases of purely data-driven models, ensuring that the parameter prediction results both conform to theoretical derivations and closely match the actual mechanical performance of the material, thus improving the accuracy of subsequent constitutive models.

[0078] Strict control over the physical rationality of material parameters from an energy perspective ensures that the selected optimal constitutive model can still meet basic mechanical stability requirements under complex stress conditions. Specifically, strain energy non-negativity is a core indicator for maintaining the mechanical stability of elastomeric materials under triaxial tension. This verification effectively eliminates unreasonable parameters that may exhibit energy anomalies under extreme stress conditions, avoiding distortion of material mechanical properties in engineering simulations due to model parameter defects. In a more preferred embodiment of this invention, in step S4, the triaxial tensile strain energy stability is verified by calculating the non-negativity of strain energy of material parameters under triaxial tensile virtual conditions. This improves the reliability and safety of the final output model in practical engineering applications.

[0079] To balance the efficiency of feature extraction with the flexibility of model output, this approach aims to reduce redundant computations, improve processing speed, and ensure the specificity and accuracy of each parallel network when processing different constitutive models. For example... Figure 1 As shown, in a more preferred embodiment of the present invention, the physical information neural network includes at least a parallel network structure with a shared bottom-level feature extraction layer and independent output layers. The shared bottom-level feature extraction layer can efficiently extract universal basic mechanical features from stress and strain data, avoiding redundant calculations and significantly improving model training and inference efficiency. Simultaneously, it ensures consistency in the understanding of basic features among different parallel networks, providing a unified feature foundation for subsequent independent calculations. The independent output layers allow each network to perform personalized parameter learning and output based on the characteristics of a specific constitutive model, meeting the differentiated needs of different models for parameter prediction and enhancing the network's adaptability to diverse constitutive models. ELU (Exponential Linear Unit) is a non-linear activation function; when the input is greater than 0, the output is equal to the input itself. When the input is less than or equal to 0, the output is α(e^(-1 / 2)). x-1), α is usually taken as 1. Compared to ReLU, ELU solves the neuron death problem caused by the gradient being 0 in the negative input region by introducing an exponential function, enabling the model to learn smoother features and accelerating convergence. LayerNorm (LayerNormalization) is a normalization technique that standardizes the inputs of all neurons in a layer of a neural network. It calculates the mean and variance of all input data in that layer, then subtracts the mean from each input and divides by the standard deviation, adding scaling and translation parameters to keep the data distribution within a range of mean 0 and variance 1. Unlike BatchNorm, which depends on batch data, LayerNorm is batch-independent and suitable for small batch or sequential data scenarios. It can effectively alleviate internal covariate bias and make network training more stable. When used in combination, LayerNorm is usually applied for normalization after the linear layers of the network, and then ELU is used to introduce nonlinear transformation. This combination can stabilize the data distribution, accelerate training, and retain effective information in the negative input region, improving the model's ability to fit complex features. It is commonly used in fully connected networks and deep learning models.

[0080] LeakyReLU and LayerNorm are techniques used in deep learning to improve network performance. Combining them effectively optimizes the model's training process and prediction results. LeakyReLU is a leaky linear rectified unit, also an activation function designed to address the problem of dead neurons in the ReLU activation function. When the input is greater than 0, the output equals the input itself; when the input is less than or equal to 0, the output is the input multiplied by a very small slope, typically 0.01. This design allows for small gradient flows even in negative input regions, preventing neurons from permanently failing due to long-term negative input, enhancing the network's ability to capture negative features, while retaining the computationally efficient nature of ReLU.

[0081] To assign an independent network to each constitutive function, unique features of specific constitutive relations can be captured, avoiding feature interference between different functions and improving the accuracy of parameter prediction for a single constitutive model. In a more preferred embodiment of the invention, a physical information neural network is constructed for each constitutive function. Each physical information neural network includes at least an unfolding layer, a linear layer, a normalization layer, and an activation layer; the main body of the physical information neural network adopts a fully connected neural network. The fully connected neural network can fully exploit the nonlinear correlation between the input stress and strain data and the output parameters. Combined with the unfolding layer's adjustment of data dimensions, the linear layer's feature mapping, the normalization layer's optimization of data distribution, and the activation layer's nonlinear transformation, it can efficiently handle complex mapping relationships in elasticity mechanics, ensuring the model has a good fitting ability for high-dimensional, strongly coupled mechanical data. Each layer has a clear function and works synergistically. The normalization layer reduces the impact of data scale differences on training, and the activation layer gives the model the ability to handle nonlinear problems. The overall structure allows the network to converge faster and the prediction results to be more stable during the learning process, providing a reliable foundation for subsequent parameter selection. For example, the input stress and strain data can be expanded into one-dimensional feature vectors to unify the data dimension and adapt to the input requirements of fully connected networks. Multiple linear transformation layers, such as 3-5 layers, can be set up in the linear layers. High-dimensional mapping of the features is performed using a weight matrix, and the number of neurons in each layer is adjusted according to the constitutive function complexity, for example, gradually decreasing from 256 to match the dimension of the output parameters.

[0082] To transform the physical constraints corresponding to the constitutive function, such as the stress-strain differential relationship, into the regularization term of the loss function during network training, and to optimize network parameters through backpropagation to ensure that the output parameters satisfy the mechanical laws of the constitutive model, in a more preferred embodiment of this invention, a loss calculation module is constructed based on the constitutive function to calculate the strain energy residual Loss.

[0083]

[0084]

[0085] Among them, L δ For Huber loss The function, where y is stress, x is strain, and W true The true strain energy, W, is calculated by integrating the stress-strain curve. pred δ is the predicted value, and δ is a hyperparameter of the threshold that controls the switching point between MSE and MAE. δ is preferably set to 1.0.

[0086] Among them, W true This is the true strain energy calculated by integrating the stress-strain curve.

[0087]

[0088] Based on the model output parameters, f(x) is calculated using the constitutive function formula. Taking Ogden as an example, the model output parameters are:

[0089] α1,α2,α3,μ1,μ2,μ3

[0090] The formula for calculating f(x) is as follows:

[0091]

[0092] Where λ1, λ2, and λ3 are the stretch ratios, α1, α2, and α3 are the nonlinear strain hardening characteristic parameters of the material, and μ1, μ2, and μ3 are the shear modulus parameters of the material.

[0093] Each dedicated network is trained individually using a training dataset. By adjusting hyperparameters such as the learning rate and number of iterations, the network is made to focus on fitting the parameter mapping rules of the corresponding constitutive function. This ultimately forms a set of physical information neural networks with consistent structure but independent parameters, designed for different constitutive models. The specific method for selecting the optimal constitutive model based on performance metrics such as prediction accuracy and stability is as follows:

[0094] Step S41: The prediction accuracy is obtained by calculating the strain energy residual, which is the same as the network residual calculation method.

[0095] Step S42, the stability of triaxial tensile strain energy is determined by whether the calculated strain energy of triaxial tension matches the true value. During the calculation process, there may be situations where uniaxial tensile predictions are accurate, but multiaxial tensile predictions are unstable. By adjusting the calculation method of the tensile ratio, the strain energy for different loading methods can be obtained. The adjustment method is shown in Table 3 below:

[0096] Table 3: Adjusted stretch ratio for different loading methods

[0097]

[0098] The optimal constitutive model and model parameters are encapsulated into a callable module, for example, embedded in finite element software.

[0099] Step S43, taking Abaqus as an example, implements a closed-loop calculation in the finite element software to read stress-strain curves in real time, call neural network prediction parameters, and update the material model.

[0100] Step S44: Obtain the strain data of the current element through the user subroutine UMAT. Write the strain data to a text file within UMAT. Then, call a Python script to read the data. The Python script calls a neural network for prediction and saves the name of the optimal constitutive function and its parameters. Finally, UMAT reads the saved data and performs simulation calculations.

[0101] This invention also discloses a system for machine learning optimization of parameters of elastic body constitutive models for finite element simulation, as described above, the system comprising:

[0102] The data preprocessing unit is used to acquire stress and strain data from the elastic body mechanics experiment, and to standardize the stress and strain data to obtain the training dataset.

[0103] The model building unit is used to build multiple physical information neural networks in parallel, each of which is configured with a loss function; the physical information neural networks are trained using a training dataset to obtain trained physical information neural networks;

[0104] The model calculation unit is used to input the stress and strain data of the material to be analyzed into the trained physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation.

[0105] The output unit is used to select the optimal constitutive model based on the stability and prediction accuracy of triaxial tensile strain energy, and encapsulate the optimal constitutive model and model parameters into a callable module.

[0106] In this system, the data preprocessing unit acquires stress and strain data from elastomer mechanics experiments and standardizes it to form a training dataset. The model building unit constructs multiple parallel physical information neural networks, configuring a loss function for each network, and then uses the training dataset to train the model. The model calculation unit inputs the stress and strain data of the material to be analyzed into the trained physical information neural network, and obtains the material parameters through parallel computation of each network. The output unit selects the optimal constitutive model based on the stability and prediction accuracy of triaxial tensile strain energy, and encapsulates the model and its corresponding parameters into a callable module. This innovative architecture of parallel prediction and intelligent selection using multi-physical information neural networks enables efficient and automated analysis of elastomer constitutive models. It can simultaneously process parameter predictions for multiple constitutive models, and by embedding physical constraints and stability verification mechanisms, it ensures that the results conform to mechanical laws. Compared with traditional trial-and-error methods, it significantly shortens the analysis cycle and avoids human error. It also provides complete industrial application solutions, which can seamlessly integrate the optimized model parameters into mainstream finite element software. It has significant advantages in practical engineering applications, ensuring the accuracy of analysis results and simplifying the simulation process. It provides efficient and reliable technical support for the design and performance evaluation of elastomer materials. Its versatility and scalability are applicable to the determination of constitutive relations of various elastomer materials.

[0107] This invention provides an electronic device, comprising at least one processor; and

[0108] A memory communicatively connected to the at least one processor; wherein,

[0109] The memory stores instructions that can be executed by the at least one processor, which enables the at least one processor to perform the above-described machine learning optimization method for elastic body constitutive model parameters for finite element simulation.

[0110] The present invention provides a machine-readable storage medium storing instructions for causing a machine to execute the machine learning optimization method for parameters of elastic body constitutive model for finite element simulation as described above.

[0111] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0112] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0113] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0114] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation, characterized in that, The machine learning optimization method for elastic body constitutive model parameters for finite element simulation includes: Step S1: Obtain stress and strain data from the elastic body mechanics experiment, and standardize the stress and strain data respectively to obtain the training dataset; Step S2: Construct multiple parallel physical information neural networks, each of which is configured with a loss function; train the physical information neural networks using a training dataset to obtain trained physical information neural networks; Step S3: Input the stress and strain data of the material to be analyzed into the physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation. Step S4: Based on the stability and prediction accuracy of triaxial tensile strain energy, the optimal constitutive model is selected, and the optimal constitutive model and model parameters are encapsulated into a callable module.

2. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation according to claim 1, characterized in that, In step S2, the loss function includes the experimental data fitting error and the physical constraint terms of the constitutive equation.

3. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation according to claim 2, characterized in that, The physical constraints include at least the stress-strain differential relationship constraint, the material incompressibility constraint, and the strain energy function convexity constraint.

4. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation according to claim 1, characterized in that, In step S4, the stability of triaxial tensile strain energy is verified by calculating the non-negativity of strain energy under the triaxial tensile virtual working condition of material parameters.

5. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation according to any one of claims 1-4, characterized in that, The physical information neural network includes at least a parallel network structure with a shared bottom feature extraction layer and an independent output layer.

6. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation as described in claim 5, characterized in that, A physical information neural network is constructed for each constitutive function, and each physical information neural network includes at least an unfolding layer, a linear layer, a normalization layer, and an activation layer; the main body of the physical information neural network adopts a fully connected neural network.

7. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation as described in claim 6, characterized in that, A loss calculation module is constructed based on the constitutive function to calculate the strain energy residual loss, which is: Among them, L δ For Huber loss The function, where y is stress, x is strain, and W true The true strain energy, W, is calculated by integrating the stress-strain curve. pred δ is the predicted value, and δ is the hyperparameter of the threshold, which controls the switching point between MSE and MAE.

8. The machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation as described in claim 6, characterized in that, If the output of the physical information neural network is... α1, α2, α3, μ1μ2, μ3 So, Where λ1, λ2, λ3 are the stretch ratio coefficients, α1, α2, α3 are the nonlinear strain hardening characteristic parameters of the material, and μ1, μ2, μ3 are the shear modulus parameters of the material.

9. A system for machine learning optimization of constitutive model parameters of elastic bodies for finite element simulation as described in any one of claims 1-8, characterized in that, The system includes, The data preprocessing unit is used to acquire stress and strain data from the elastic body mechanics experiment, and to standardize the stress and strain data to obtain the training dataset. The model building unit is used to build multiple physical information neural networks in parallel, each of which is configured with a loss function; the physical information neural networks are trained using a training dataset to obtain trained physical information neural networks; The model calculation unit is used to input the stress and strain data of the material to be analyzed into the physical information neural network, and the material parameters are obtained by each physical information neural network in parallel calculation. The output unit is used to select the optimal constitutive model based on the stability and prediction accuracy of triaxial tensile strain energy, and encapsulate the optimal constitutive model and model parameters into a callable module.

10. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores instructions for causing the machine to execute the machine learning optimization method for constitutive model parameters of elastic bodies for finite element simulation as described in any one of claims 1-8.

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