Inversion method for multiple constitutive parameters of material and related equipment
By using surrogate models and intrinsic orthogonal decomposition techniques, the problem of high computational cost in traditional inversion methods is solved, and efficient multi-constitutive parameter inversion of materials is achieved, which is suitable for parameter calibration of complex constitutive models.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-15
- Publication Date
- 2026-03-27
AI Technical Summary
Traditional inversion methods are inefficient due to the strong coupling between multiple constitutive parameters of materials and the high computational cost of solving the forward problem, making it difficult to effectively solve the parameter calibration problem of complex constitutive models.
Using a pre-trained surrogate model, the candidate constitutive parameter combination is transformed into a dimensionality-reduced representation through physical information neural network and intrinsic orthogonal decomposition technology. The mechanical response curve is reconstructed by combining the basis function set, and parameter inversion is achieved through matching degree calculation.
It significantly reduces computation time and resource requirements, improves the efficiency and stability of parameter inversion, and can quickly search the parameter space while ensuring the accuracy of the response curve. It is suitable for complex constitutive models with multiple field coupling.
Smart Images
Figure CN121744770A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the interdisciplinary field of computational mechanics and artificial intelligence, and specifically relates to a method and related equipment for inverting multiple constitutive parameters of materials. Background Technology
[0002] Accurately obtaining the constitutive parameters of materials is fundamental for engineering structural design, performance evaluation, and life prediction. As high-end equipment expands into extreme environments, materials often exhibit multiple coupled mechanical behaviors under complex service conditions such as high temperature and strong impact, including plastic flow, loading rate sensitivity, and high-temperature softening. To accurately describe these behaviors, researchers have developed complex constitutive models that simultaneously consider factors such as temperature, strain rate, and plastic internal variables. These complex constitutive models have numerous constitutive parameters with strong coupling, making them difficult to directly separate and calibrate through traditional experiments. Therefore, based on the material's mechanical response curves under specific loads, solving the inverse problem to invert its complete set of constitutive parameters has become an important technical approach.
[0003] However, material multi-constitutive parameter inversion is a typical nonlinear, high-dimensional, ill-conditioned inverse problem. The strong coupling between parameters and the high computational cost of solving the forward problem (such as finite element simulation) make traditional inversion methods generally inefficient when dealing with such complex models. Summary of the Invention
[0004] To address the problems existing in the prior art, this invention provides an inversion method and related equipment for multiple constitutive parameters of materials. Its purpose is to overcome the inefficiency caused by the strong coupling between parameters and the high computational cost of solving the forward problem in traditional inversion methods.
[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: According to a first aspect of the present invention, a method for inverting multiple constitutive parameters of a material is provided, comprising: S1. Input the candidate constitutive parameter combination into the pre-trained surrogate model to obtain the dimensionality reduction representation of the mechanical response corresponding to the candidate constitutive parameter combination; S2. Based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and the pre-determined set of basis functions, the predicted mechanical response curve corresponding to the candidate constitutive parameter combination is reconstructed. S3. Calculate the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve. S4. Determine whether the convergence condition is met based on the matching degree: if it is met, output the current candidate constitutive parameter combination as the inversion result; if it is not met, update the candidate constitutive parameter combination and return to step S1.
[0006] In one possible implementation of the first aspect, the proxy model is a physical information neural network model, the mechanical response dimensionality reduction characterization is an intrinsic orthogonal decomposition mode coefficient, and the basis function set is an intrinsic orthogonal decomposition mode basis function set; The training method for the physical information neural network model is as follows: Obtain a training dataset, which includes multiple sets of constitutive parameters and the corresponding mechanical response curves obtained by finite element simulation for each set of constitutive parameters; The corresponding mechanical response curves obtained by finite element simulation for all constitutive parameters are subjected to intrinsic orthogonal decomposition to obtain the set of intrinsic orthogonal decomposition mode basis functions, the cumulative energy contribution rate of intrinsic orthogonal decomposition modes, and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters. The number of intrinsic orthogonal decomposition modes is determined based on the cumulative energy contribution rate of the intrinsic orthogonal decomposition modes; Based on the number of intrinsic orthogonal decomposition modes, a physical information neural network model is constructed. The number of fully connected layers in the physical information neural network model is equal to the number of intrinsic orthogonal decomposition modes. Each set of constitutive parameters is used as input, and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters are used as output. The physical information neural network model is trained using the training dataset, wherein the loss function used for training includes constraint terms based on the physical laws of mechanical response.
[0007] In one possible implementation of the first aspect, the loss function is specifically:
[0008] In the formula, The loss function; The mean square error of the intrinsic orthogonal decomposition mode coefficients; The mean square error of the mechanical response curve; The energy contribution error to the intrinsic orthogonal decomposition; To predict the intrinsic orthogonal decomposition mode coefficients; The target intrinsic orthogonal decomposition modal coefficients; The mechanical response curve is reconstructed based on the predicted intrinsic orthogonal decomposition mode coefficients and the intrinsic orthogonal decomposition mode basis function set; The mechanical response curve is reconstructed based on the target intrinsic orthogonal decomposition modal coefficients and the intrinsic orthogonal decomposition modal basis function set.
[0009] In one possible implementation of the first aspect, the inversion method is implemented through a visual user interface, including: Import the target experimental mechanical response curve into the visual user interface; The candidate constitutive parameter combination is input through the parameter adjustment control provided by the visual user interface, and the mechanical response prediction curve corresponding to the reconstructed candidate constitutive parameter combination is displayed in real time in the visual user interface based on the output of the surrogate model. When the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve meets the convergence condition, the current candidate constitutive parameter combination is output as the inversion result through the visual user interface.
[0010] In one possible implementation of the first aspect, the parameter adjustment control is a slider; The updated candidate constitutive parameter combination specifically refers to changing the candidate constitutive parameter combination in real time in response to the user's drag operation command on the slider.
[0011] In one possible implementation of the first aspect, the reconstructing of the predicted mechanical response curve corresponding to the candidate constitutive parameter combination based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and a pre-determined set of basis functions specifically involves: The mechanical response prediction curve corresponding to the candidate constitutive parameter combination is obtained by multiplying the dimensionality reduction representation of the mechanical response corresponding to the basis function in the basis function set and summing the results.
[0012] In one possible implementation of the first aspect, the matching degree is obtained by calculating the error norm between the predicted mechanical response curve and the target experimental mechanical response curve; The convergence condition is that the error norm is less than a preset threshold.
[0013] According to a second aspect of the present invention, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the aforementioned method for inverting multiple constitutive parameters of a material.
[0014] According to a third aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing a computer program, which, when executed by a processor, implements the aforementioned method for inverting multiple constitutive parameters of a material.
[0015] According to a fourth aspect of the present invention, a computer program product is provided that, when executed by a processor, implements the aforementioned method for inverting multiple constitutive parameters of a material.
[0016] Compared with the prior art, the present invention has at least the following beneficial effects: This invention provides an inversion method for multiple constitutive parameters of materials. By employing a pre-trained surrogate model to replace the computationally expensive finite element simulation and other direct problem-solving processes, it significantly reduces the time and computational resources required for a single parameter evaluation. This allows for faster completion of multiple rounds of parameter iteration and optimization under the same conditions, effectively solving the inefficiency problem caused by the high computational cost of traditional methods. By transforming the mechanical response curve into a dimensionality-reduced representation and reconstructing it based on a set of basis functions, this method reduces the dimensionality of the parameter optimization space while preserving key response features. Based on near real-time computational efficiency, the parameter inversion process can search the parameter space more densely, resulting in more stable numerical values. The surrogate model, after thorough training, can accurately capture the mapping relationship between constitutive parameters and mechanical response. Combined with the basis function reconstruction strategy, it can perform matching degree calculations while ensuring the overall shape and key feature accuracy of the response curve, thus ensuring that the inverted parameters conform to physical laws and match well with actual experimental curves. This method does not rely on specific optimization algorithms or a large number of forward problem solving calls. It is applicable to various complex constitutive models that consider multiple field couplings such as temperature and strain rate. By constructing a surrogate model and a dimensionality reduction and reconstruction mechanism, it reduces the dependence on high-performance computing environments while ensuring inversion accuracy. Attached Figure Description
[0017] To more clearly illustrate the technical solutions in the specific embodiments of the present invention, the drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.
[0018] Figure 1 This is a flowchart of a method for inverting multiple constitutive parameters of a material according to the present invention; Figure 2 This is a schematic diagram of the overall architecture for real-time mechanical response prediction that combines intrinsic orthogonal decomposition and physical information neural network model in the implementation method. Figure 3 These are schematic diagrams illustrating two loading paths in the embodiment; Figure 4 This is a schematic diagram illustrating the prediction effects of two loading paths in the embodiment; Figure 5 This example demonstrates the inversion process using three curves from the first set of experimental data, based on a visual user interface. Figure 6 This serves as a verification of the constitutive parameter inversion results based on the first set of experimental data in the embodiments; Figure 7 This example demonstrates the inversion process using three curves from the second set of experimental data, based on a visual user interface. Figure 8 This serves as a verification of the constitutive parameter inversion results based on the second set of experimental data in the embodiments. Detailed Implementation
[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions 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, 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.
[0020] like Figure 1 and Figure 2 As shown, this invention provides a method for inverting multiple constitutive parameters of a material, specifically including the following steps: S1. Input the candidate constitutive parameter combination into the pre-trained surrogate model to obtain the dimensionality reduction representation of the mechanical response corresponding to the candidate constitutive parameter combination.
[0021] Specifically, the surrogate model needs to be constructed and trained. In this embodiment, a physical information neural network is preferably used as the surrogate model, and the dimensionality reduction representation of the mechanical response adopts intrinsic orthogonal decomposition of mode coefficients, with the basis function set being the intrinsic orthogonal decomposition of mode basis function set.
[0022] The specific training method for the physical information neural network model is as follows: (1) Obtain the training dataset, which includes multiple sets of constitutive parameters and the corresponding mechanical response curves obtained by finite element simulation for each set of constitutive parameters.
[0023] In other words, finite element simulation software is used to sample a large number of parameters within the parameter space covered by the material constitutive model. For each set of sampled constitutive parameter combinations, a complete finite element simulation is performed to obtain its corresponding mechanical response curve, such as a stress-strain curve. This creates a training dataset containing multiple sets of correspondences between "constitutive parameter combinations and mechanical response curves".
[0024] (2) Perform intrinsic orthogonal decomposition on the corresponding mechanical response curves obtained by finite element simulation for all constitutive parameters to obtain the set of intrinsic orthogonal decomposition mode basis functions, the cumulative energy contribution rate of intrinsic orthogonal decomposition modes and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters.
[0025] In other words, a snapshot matrix is constructed from all the mechanical response curves in the training dataset. Eigenorthogonal decomposition (EOD) analysis is then performed on this snapshot matrix to extract an optimal set of EOD mode basis functions. This set of EOD mode basis functions can describe the characteristics of all mechanical response curves to the maximum extent with the fewest basis functions. Simultaneously, the EOD mode coefficient vector corresponding to each mechanical response curve, as well as the cumulative energy contribution rate of each order of EOD mode, are calculated.
[0026] (3) Determine the number of intrinsic orthogonal decomposition modes based on the cumulative energy contribution rate of the intrinsic orthogonal decomposition modes. Specifically, based on the preset energy cutoff standard, for example, to make the cumulative energy contribution rate of the selected modes reach more than 99.5%, determine the number of intrinsic orthogonal decomposition modes to be retained based on the cumulative energy contribution rate calculated in the previous step.
[0027] (4) Based on the number of intrinsic orthogonal decomposition modes, construct a physical information neural network model. The number of fully connected layers in the physical information neural network model is equal to the number of intrinsic orthogonal decomposition modes. Take each set of constitutive parameters as input and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters as output.
[0028] In other words, a fully connected neural network is constructed where the number of nodes in the input layer equals the number of constitutive parameters, and the number of nodes in the output layer equals the determined number of intrinsic orthogonal decomposition modes, n. The output of this network is the predicted intrinsic orthogonal decomposition mode coefficients. It should be noted that the network structure, such as the number of hidden layers and nodes, can be designed according to the complexity of the specific problem.
[0029] In one embodiment, the neural network parameters are shown in Table 1.
[0030] Table 1
[0031] (5) Train the physical information neural network model with the training dataset, wherein the loss function used for training includes a constraint term based on the physical laws of mechanical response.
[0032] In other words, the neural network is trained using the constitutive parameter combinations obtained from sampling as input features and their corresponding intrinsic orthogonal decomposition mode coefficient vectors as training targets. To ensure that the surrogate model's predictions not only fit the data but also conform to fundamental physical laws, this implementation method incorporates a physical constraint term into the loss function, specifically in the following form:
[0033] In the formula, The loss function; The mean square error of the intrinsic orthogonal decomposition mode coefficients; The mean square error of the mechanical response curve; The energy contribution error to the intrinsic orthogonal decomposition; To predict the intrinsic orthogonal decomposition mode coefficients; The target intrinsic orthogonal decomposition modal coefficients; The mechanical response curve is reconstructed based on the predicted intrinsic orthogonal decomposition mode coefficients and the intrinsic orthogonal decomposition mode basis function set; The mechanical response curve is reconstructed based on the target intrinsic orthogonal decomposition modal coefficients and the intrinsic orthogonal decomposition modal basis function set.
[0034] By optimizing the composite loss function, a well-trained surrogate model is finally obtained. This surrogate model can quickly and accurately predict the corresponding intrinsic orthogonal decomposition mode coefficients based on the combination of input constitutive parameters.
[0035] During the inversion process, the candidate constitutive parameter combination to be evaluated is directly input into the trained surrogate model, and its corresponding intrinsic orthogonal decomposition mode coefficients can be output instantaneously, which is the dimensionality reduction characterization of the mechanical response.
[0036] S2. Based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and the pre-determined set of basis functions, the predicted mechanical response curve corresponding to the candidate constitutive parameter combination is reconstructed.
[0037] In one possible implementation, the reconstructing of the predicted mechanical response curve corresponding to the candidate constitutive parameter combination based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and a pre-determined set of basis functions specifically involves: The mechanical response prediction curve corresponding to the candidate constitutive parameter combination is obtained by multiplying the dimensionality reduction representation of the mechanical response corresponding to the basis function in the basis function set and summing the results.
[0038] In other words, this step maps the reduced-dimensional space back to the original response space. Specifically, it maps the predicted intrinsic orthogonal decomposition mode coefficients obtained in step S1. With the set of eigenorthogonal decomposition modal basis functions obtained during the model training phase Perform linear combinations.
[0039] S3. Calculate the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve.
[0040] It should be understood that the target experimental mechanical response curve is the material target mechanical response curve obtained through real physical experiments.
[0041] In one specific implementation, the matching degree is obtained by calculating the error norm between the predicted mechanical response curve and the target experimental mechanical response curve. For example, root mean square error or mean absolute error is used as a measure of the matching degree.
[0042] S4. Determine whether the convergence condition is met based on the matching degree: if it is met, output the current candidate constitutive parameter combination as the inversion result; if it is not met, update the candidate constitutive parameter combination and return to step S1.
[0043] That is, it determines whether the matching degree calculated in step S3 meets the preset convergence condition. Typically, the convergence condition is set to the error norm being less than a preset threshold.
[0044] If the convergence condition is met, i.e. the error norm is less than a pre-set threshold, then the current candidate constitutive parameter combination is considered to be able to reproduce the experimental curve with high accuracy, and it is output as the final inversion result.
[0045] If the convergence condition is not met, i.e. the error norm is not less than the preset threshold, then the candidate constitutive parameter combination needs to be updated, and the process returns to step S1 to start a new round of prediction, reconstruction, matching and judgment.
[0046] In one possible implementation, the inversion method is implemented through a visual user interface, including: Import the target experimental mechanical response curve into the visual user interface; The candidate constitutive parameter combination is input through the parameter adjustment control provided by the visual user interface, and the mechanical response prediction curve corresponding to the reconstructed candidate constitutive parameter combination is displayed in real time in the visual user interface based on the output of the surrogate model. When the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve meets the convergence condition, the current candidate constitutive parameter combination is output as the inversion result through the visual user interface.
[0047] In other words, users can import the experimental mechanical response curve of the target material into the system using the file import function provided in the interface. The main view area of the interface will then display the experimental mechanical response curve of the target material.
[0048] The interface provides an independent parameter adjustment control, such as a slider, for each constitutive parameter to be inverted. The value range of each slider is set based on prior knowledge. Users can intuitively change the values of candidate constitutive parameter combinations by dragging these sliders with the mouse.
[0049] Whenever a user adjusts any slider (i.e., updates the candidate parameter combination), the system background immediately performs the following operations: a. Input the current combination of candidate parameters into the loaded proxy model; b. Obtain the predicted intrinsic orthogonal decomposition coefficients and reconstruct the mechanical response prediction curves corresponding to the candidate constitutive parameter combinations.
[0050] c. The reconstructed mechanical response prediction curve is plotted in real time on the main view area of the interface and overlaid on the previously imported target experimental mechanical response curve. For example, the target experimental mechanical response curve is displayed in a specific color, while the mechanical response prediction curve is dynamically updated in another color.
[0051] While adjusting the parameters, users can visually observe the degree of agreement between the predicted mechanical response curve and the target experimental mechanical response curve. When the user deems the two curves to be in perfect agreement, they can stop adjusting. At this point, the user can use the output results button on the interface to export the candidate constitutive parameter combination corresponding to the current slider as the inversion result to a file.
[0052] This implementation combines efficient surrogate model prediction with intuitive human-computer interaction, enabling engineers to use their professional experience to guide the search direction, quickly lock in a reasonable range of parameters, avoid getting stuck in local optima, and even directly obtain satisfactory inversion results, greatly improving the flexibility and efficiency of the inversion process.
[0053] Example To verify the effectiveness of this invention, specific examples are provided below for explanation.
[0054] For the overall architecture such as Figure 2 As shown, it is divided into an offline phase and an online phase. The offline phase is achieved through... Figure 3 The method for constructing the training dataset is given. The training dataset is then constructed, and subsequently, intrinsic orthogonal decomposition (IOD) is used to reduce its dimensionality, obtaining the set of IOD mode basis functions and the corresponding IOD mode coefficients. Following this... Figure 2 In the online phase shown, the pre-trained physical information neural network model predicts the corresponding intrinsic orthogonal decomposition mode coefficients for the input constitutive parameter combination. These coefficients are then multiplied with the intrinsic orthogonal decomposition mode basis function set obtained in the offline phase to reconstruct the mechanical response prediction curve corresponding to the constitutive parameter combination in real time.
[0055] For numerical verification Figure 4 The prediction results of the method of this invention based on the constructed training dataset are presented under two loading paths. In the figure, the red line represents the constructed training dataset, the blue line represents the mechanical response prediction curve obtained using the method of this invention, and the surface formed by the black lines represents the target mechanical response curve. Figure 4It can be clearly observed that the curve interpolation smoothness and accuracy predicted by the method of the present invention in the process of temperature change and strain rate change are significantly improved.
[0056] For experimental verification, Figure 5 , Figure 7 The inversion process based on experimental data of 6061 aluminum and gamma-titanium aluminum alloy is presented respectively. The specific procedure is as follows: select three data points from the training dataset, use the constructed user interface to adjust the combination of material constitutive parameters so that the mechanical response prediction curve matches the target mechanical response curve, and use the matched combination of material constitutive parameters as the material parameters obtained by inversion. Figure 6 , Figure 8 The inversion results based on experimental data of 6061 aluminum and gamma-titanium aluminum alloy are presented for verification. The figures clearly show that the inverted parameters can definitively characterize the mechanical response of the corresponding materials under various loading conditions.
[0057] Regarding computation time, Table 1 compares the computation time of a single calculation using the standard constitutive model embedded in commercial software and the computation time of a single calculation using the present invention. The present invention is about 100,000 times faster than the standard computation model.
[0058] Table 1 compares the calculation time using the finite element method and the method of the present invention in the examples.
[0059] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions from the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of an inversion method for multiple constitutive parameters of materials.
[0060] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the operating system of the terminal. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be Random Access Memory (RAM) or non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the inversion method for multiple constitutive parameters of a material in the above embodiments.
[0061] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, optical storage, etc.) containing computer-usable program code.
[0062] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0063] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0064] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0065] This invention also provides a computer program product for executing any of the above-described methods for inverting multiple constitutive parameters of a material. Since the computer program product provided by this invention belongs to the same inventive concept as the above-described method for inverting multiple constitutive parameters of a material, it possesses all the advantages of the above-described method. Therefore, the beneficial effects of the computer program product provided by this invention will not be elaborated upon here.
[0066] In this invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.
[0067] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit them. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the scope of the technology disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention.
Claims
1. A method for inverting multiple constitutive parameters of a material, characterized in that, include: S1. Input the candidate constitutive parameter combination into the pre-trained surrogate model to obtain the dimensionality reduction representation of the mechanical response corresponding to the candidate constitutive parameter combination; S2. Based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and the pre-determined set of basis functions, the predicted mechanical response curve corresponding to the candidate constitutive parameter combination is reconstructed. S3. Calculate the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve. S4. Determine whether the convergence condition is met based on the matching degree: if it is met, output the current candidate constitutive parameter combination as the inversion result; if it is not met, update the candidate constitutive parameter combination and return to step S1.
2. The method for inverting multiple constitutive parameters of a material according to claim 1, characterized in that, The proxy model is a physical information neural network model, the mechanical response dimensionality reduction characterization is the intrinsic orthogonal decomposition mode coefficients, and the basis function set is the intrinsic orthogonal decomposition mode basis function set; The training method for the physical information neural network model is as follows: Obtain a training dataset, which includes multiple sets of constitutive parameters and the corresponding mechanical response curves obtained by finite element simulation for each set of constitutive parameters; The corresponding mechanical response curves obtained by finite element simulation for all constitutive parameters are subjected to intrinsic orthogonal decomposition to obtain the set of intrinsic orthogonal decomposition mode basis functions, the cumulative energy contribution rate of intrinsic orthogonal decomposition modes, and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters. The number of intrinsic orthogonal decomposition modes is determined based on the cumulative energy contribution rate of the intrinsic orthogonal decomposition modes; Based on the number of intrinsic orthogonal decomposition modes, a physical information neural network model is constructed. The number of fully connected layers in the physical information neural network model is equal to the number of intrinsic orthogonal decomposition modes. Each set of constitutive parameters is used as input, and the intrinsic orthogonal decomposition mode coefficients corresponding to each set of constitutive parameters are used as output. The physical information neural network model is trained using the training dataset, wherein the loss function used for training includes constraint terms based on the physical laws of mechanical response.
3. The method for inverting multiple constitutive parameters of a material according to claim 2, characterized in that, The loss function is specifically as follows: In the formula, The loss function; The mean square error of the intrinsic orthogonal decomposition mode coefficients; The mean square error of the mechanical response curve; The energy contribution error to the intrinsic orthogonal decomposition; To predict the intrinsic orthogonal decomposition mode coefficients; The target intrinsic orthogonal decomposition modal coefficients; The mechanical response curve is reconstructed based on the predicted intrinsic orthogonal decomposition mode coefficients and the intrinsic orthogonal decomposition mode basis function set; The mechanical response curve is reconstructed based on the target intrinsic orthogonal decomposition modal coefficients and the intrinsic orthogonal decomposition modal basis function set.
4. The method for inverting multiple constitutive parameters of a material according to claim 1, characterized in that, The inversion method is implemented through a visual user interface, including: Import the target experimental mechanical response curve into the visual user interface; The candidate constitutive parameter combination is input through the parameter adjustment control provided by the visual user interface, and the mechanical response prediction curve corresponding to the reconstructed candidate constitutive parameter combination is displayed in real time in the visual user interface based on the output of the surrogate model. When the matching degree between the mechanical response prediction curve corresponding to the candidate constitutive parameter combination and the target experimental mechanical response curve meets the convergence condition, the current candidate constitutive parameter combination is output as the inversion result through the visual user interface.
5. The method for inverting multiple constitutive parameters of a material according to claim 4, characterized in that, The parameter adjustment control is a slider; The updated candidate constitutive parameter combination specifically refers to changing the candidate constitutive parameter combination in real time in response to the user's drag operation command on the slider.
6. The method for inverting multiple constitutive parameters of a material according to claim 1, characterized in that, The mechanical response prediction curve corresponding to the candidate constitutive parameter combination is reconstructed based on the dimensionality reduction characterization of the mechanical response corresponding to the candidate constitutive parameter combination and a pre-determined set of basis functions, specifically as follows: The mechanical response prediction curve corresponding to the candidate constitutive parameter combination is obtained by multiplying the dimensionality reduction representation of the mechanical response corresponding to the basis function in the basis function set and summing the results.
7. The method for inverting multiple constitutive parameters of a material according to claim 1, characterized in that, The matching degree is obtained by calculating the error norm between the predicted mechanical response curve and the target experimental mechanical response curve. The convergence condition is that the error norm is less than a preset threshold.
8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements a method for inverting multiple constitutive parameters of a material as described in any one of claims 1 to 7.
9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements a method for inverting multiple constitutive parameters of a material as described in any one of claims 1 to 7.
10. A computer program product, characterized in that, When the computer program product is executed by a processor, it implements a method for inverting multiple constitutive parameters of a material as described in any one of claims 1 to 7.