Methods and apparatus for processing finite element constitutive models

Abstract

This invention discloses a method and apparatus for processing finite element constitutive models. The method includes: acquiring at least one mesh element to be updated and its corresponding configuration data in the current finite element model; obtaining the first Jacobian matrix of the mesh element to be updated at the current time step based on an implicit algorithm; and obtaining the second Jacobian matrix of the mesh element to be fine-tuned at the current time step based on mechanical parameters; and determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step. This solves the problem of high time cost and low analysis efficiency caused by traditional implicit algorithms in finite element model analysis in existing technologies, thereby improving the efficiency of finite element model analysis and reducing the time cost of processing finite element models.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and material constitutive models, and in particular to a method and apparatus for processing finite element constitutive models. Background Technology

[0002] Currently, in the vehicle design phase, the finite element method is usually used to analyze and predict vehicle stress and deformation in order to ensure that the designed vehicle meets the preset safety conditions, thereby ensuring the safety of the vehicle during actual driving.

[0003] Existing finite element analysis methods typically use implicit algorithms to analyze vehicle finite element models constructed based on a large amount of vehicle simulation test data. During the analysis and calculation process, a large number of iterative calculations are involved. If a structural feature or material property in a certain part of the finite element model is adjusted, a large number of iterative calculations still need to be performed again based on the vehicle finite element model, which consumes a lot of time and greatly reduces the efficiency of finite element model analysis. Summary of the Invention

[0004] This invention provides a method and apparatus for processing finite element constitutive models, so as to improve the efficiency of finite element model analysis and reduce the time cost of processing finite element models.

[0005] According to one aspect of the present invention, a method for processing a finite element constitutive model is provided, the method comprising:

[0006] Obtain at least one mesh element to be updated and its corresponding configuration data to be updated in the current finite element model; wherein, the finite element model includes at least one mesh element to be updated and a mesh element to be fine-tuned;

[0007] For each grid cell to be updated, the configuration data to be updated for the current grid cell and the first Jacobian matrix of the previous time step are processed based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell at the current time step; and,

[0008] For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step; wherein, the second Jacobian matrix is ​​determined based on the mechanical property parameters.

[0009] The updated finite element model is determined based on the first and second Jacobian matrices corresponding to the last time step.

[0010] According to another aspect of the present invention, a processing apparatus for a finite element constitutive model is provided, the apparatus comprising:

[0011] The configuration data acquisition module is used to acquire at least one mesh element to be updated and the corresponding configuration data to be updated in the current finite element model; wherein, the finite element model includes at least one mesh element to be updated and a mesh element to be fine-tuned;

[0012] The Jacobian matrix determination module is used to process the configuration data to be updated and the first Jacobian matrix of the previous time step for each grid cell to be updated based on an implicit algorithm, to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step; and,

[0013] For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step; wherein, the second Jacobian matrix is ​​determined based on the mechanical property parameters.

[0014] The finite element model determination module is used to determine the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step.

[0015] The technical solution of this invention involves obtaining at least one mesh element to be updated and its corresponding configuration data in the current finite element model; using an implicit algorithm to fit the constitutive equation of experimental stress-strain to obtain the first Jacobian matrix of the mesh element to be updated at the current time step; and obtaining the second Jacobian matrix of the mesh element to be fine-tuned at the current time step based on a neural network model determined by mechanical parameters; and determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step. This solves the problem of high time cost and low analysis efficiency caused by the analysis of finite element models based on traditional implicit algorithms in the prior art, thereby improving the analysis efficiency of finite element models and reducing the time cost of processing finite element models.

[0016] It should be understood that the description in this section is not intended to identify key or essential features of the invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a finite element constitutive model processing method provided in Embodiment 1 of the present invention;

[0019] Figure 2 This is a flowchart of a finite element constitutive model processing method provided in Embodiment 2 of the present invention;

[0020] Figure 3 This is a schematic diagram of a finite element constitutive model processing method provided in Embodiment 2 of the present invention;

[0021] Figure 4 This is a schematic diagram of determining the second Jacobian matrix based on a mechanical parameter determination model according to Embodiment 2 of the present invention;

[0022] Figure 5 This is a schematic diagram of the structure of a finite element constitutive model processing device provided in Embodiment 3 of the present invention. Detailed Implementation

[0023] 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.

[0024] Before introducing this technical solution, the processing method of the finite element constitutive model in this technical solution can be illustrated by example. The method can include the following steps: Step 1: Construct a finite element mesh model according to the experimental specimen size, select a constitutive equation that can fit the experimental stress-strain for this finite element simulation calculation, and obtain the mechanical state variables (including original mechanical property data and theoretical deformation result data) of the constitutive model at all mesh elements and all time steps, and save them as a neural network model training sample set, wherein the training sample set includes multiple training samples; Step 2: For each training sample, use the original mechanical property data of the current training sample as the input of the BP neural network model, and use the theoretical deformation result data as the output of the BP neural network model to train the BP neural network model based on the mechanical parameters; Step 3: Based on the finite element mesh model constructed in Step 1, fine-tune the structural or material parameters of a certain part of the model to construct the current finite element model, and obtain at least one mesh element to be fine-tuned and the corresponding configuration data to be updated in the current finite element model; wherein, in the finite element model The model includes at least one mesh element to be updated and a mesh element to be fine-tuned. The mesh element to be fine-tuned represents the mesh element in the current finite element model where the structural shape / material parameters have not been adjusted, and the mesh element to be updated represents the mesh element in the current finite element model where the structural shape / material parameters have been adjusted. Step 4: For each mesh element to be updated, based on an implicit algorithm, the strain, deformation gradient data, and Jacobian matrix ① of the current mesh element to be updated are processed using a constitutive equation that can fit the experimental stress-strain, to obtain the Jacobian matrix ① and stress data of the current mesh element to be updated at the current time step. Step 5: For each mesh element to be fine-tuned, the strain, deformation gradient data, and Jacobian matrix ② of the current mesh element to be fine-tuned are processed based on a BP neural network model (i.e., a mechanical parameter determination model), to obtain the Jacobian matrix ② and stress data of the current mesh element to be fine-tuned at the current time step. Step 6: Based on the Jacobian matrix ① and Jacobian matrix ② corresponding to all time steps, it is determined whether the mechanical response of the updated finite element model has converged.

[0025] Example 1

[0026] Figure 1 This is a flowchart illustrating a method for processing a finite element constitutive model according to Embodiment 1 of the present invention. This embodiment is applicable to the processing of finite element constitutive models. The method can be executed by a finite element constitutive model processing device, which can be implemented in hardware and / or software and can be configured in a computing device. Figure 1 As shown, the method includes:

[0027] S110. Obtain at least one mesh element to be updated and its corresponding configuration data in the current finite element model.

[0028] The finite element model includes at least one mesh element to be updated and mesh elements to be fine-tuned. The mesh element to be fine-tuned represents the mesh element in the finite element model where the structural shape / material parameters have not been adjusted, while the mesh element to be updated represents the mesh element in the finite element model where the structural shape / material parameters have been adjusted. It should be noted that the finite element model can be built based on any subject. For example, the subject can be a vehicle, a transmission, or a generator. When building the finite element model, it can be meshed into a finite element model containing multiple mesh elements, where the material or structural mechanical parameters corresponding to different mesh elements may differ.

[0029] In practical applications, a finite element mesh model can be constructed based on the size of the experimental specimen. The structural or material parameters of a certain part of the mesh model can be fine-tuned to construct the current finite element model. At this time, the mesh elements in the model where the structural shape / material parameters have not been adjusted can be used as mesh elements to be fine-tuned, and the mesh elements where the structural shape / material parameters have been adjusted can be used as mesh elements to be updated. Furthermore, the mechanical parameter information (such as structure and material) corresponding to each mesh element to be updated can be obtained as the configuration data to be updated.

[0030] It should be noted that when obtaining at least one mesh element to be updated and its corresponding configuration data in the current finite element model, it is also considered that the mesh element to be updated has been obtained when it is detected that the configuration data corresponding to a certain mesh element in the current finite element model has changed.

[0031] Optionally, at least one mesh element to be updated and its corresponding configuration data to be updated in the current finite element model can be obtained, including: identifying at least one mesh element to be updated in the current finite element model whose configuration data has changed; and obtaining the configuration data to be updated for each mesh element to be updated.

[0032] The configuration data to be updated includes material configuration data and structural configuration data. For example, it may include, but is not limited to, deformation gradient, initial yield stress, strain hardening modulus, strain-stress relationship, hardening index, and material thermal softening index.

[0033] In this embodiment, when a change in the configuration data corresponding to a certain mesh cell is detected, it is considered that a mesh cell to be updated has been obtained. The mesh cell whose configuration data has changed can be regarded as the mesh cell to be updated. Then, the configuration data to be updated for each mesh cell can be obtained, so as to determine the finite element model after the change in mechanical parameters based on the configuration data to be updated.

[0034] S120. For each grid cell to be updated, the configuration data to be updated and the first Jacobian matrix of the previous time step of the current grid cell to be updated are processed based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step.

[0035] The first Jacobian matrix can be understood as the element stiffness matrix, which characterizes the stress and deformation relationship of the mesh element. The element stiffness matrix can include the relationship between the strain tensor and the stress tensor. It should be noted that the first and second Jacobian matrices are relative. The Jacobian matrix of the mesh element to be updated, determined based on an implicit algorithm, is used as the first Jacobian matrix, and the Jacobian matrix of the mesh element to be fine-tuned, determined based on a mechanical parameter determination model, is used as the second Jacobian matrix. The implicit algorithm can be the Johnson-Cook constitutive algorithm.

[0036] In practical applications, when the model parameters or structure of the current finite element model change, the structure of each mesh element in the finite element model may deform over time. The time step corresponding to the deformation can be preset; the time step can be 0.1s or 0.05s. Assuming a time step of 0.1s, the finite element model may undergo a certain amount of deformation every 0.1s. To improve the accuracy of the final finite element model construction, the Jacobian matrix of the mesh elements can be determined every 0.1s. Then, based on the Jacobian matrices of all mesh elements at the current time step, the finite element model for the current time step can be assembled and constructed.

[0037] Specifically, the implicit finite element algorithm can be used to process the configuration data to be updated for the current mesh element and the first Jacobian matrix of the previous time step, and solve for the Jacobian matrix of the current mesh element at the current time step, which is then used as the first Jacobian matrix.

[0038] It should be noted that in the implicit algorithm-based calculation process, the mechanical parameter data (such as load, deformation gradient, etc.) required for the solution calculation can be determined based on the configuration data to be updated of the current mesh cell to be updated. Then, the first Jacobian matrix of the current mesh cell to be updated at the current time step can be calculated based on the mechanical parameter data corresponding to the current mesh cell to be updated at the current time step and the mechanical parameter data corresponding to the previous time step.

[0039] Optionally, the configuration data to be updated for the current grid cell to be updated and the first Jacobian matrix of the previous time step are processed based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step, including: determining the mechanical property data to be used for the current grid cell to be updated at the current time step based on the configuration data to be updated for the current grid cell to be updated; and processing the mechanical property data to be used and the first Jacobian matrix of the previous time step based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step.

[0040] In this embodiment, the mechanical parameter data required for the implicit algorithm to calculate the Jacobian matrix, such as strain tensor and deformation gradient, can be obtained based on the configuration data to be updated of the current mesh element. Furthermore, based on the implicit algorithm, constitutive equations that can fit the experimental stress-strain can be used to process the strain, deformation gradient, and other mechanical parameter data of the current mesh element to be updated, along with the first Jacobian matrix of the previous time step, to obtain the first Jacobian matrix and stress data (such as stress tensor) of the current mesh element to be updated at the current time step. It is understood that calculating the Jacobian matrix based on the implicit algorithm has high accuracy, but requires a large number of iterations, resulting in a long computation time. To reduce computational time costs, for mesh elements whose mechanical parameter information has not been adjusted, the Jacobian matrix can be calculated based on a pre-trained mechanical parameter determination model.

[0041] It should be noted that, in order to ensure that the implicit algorithm can converge effectively, the second Jacobian matrix of the mesh cell to be fine-tuned connected to the mesh cell to be updated can also be calculated based on the implicit algorithm.

[0042] S130. For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step.

[0043] The mechanical parameter determination model can be a pre-trained model used to determine the mechanical property parameters, such as a BP (Back Propagation) neural network model. The second Jacobian matrix, determined based on the mechanical property parameters, can be used to characterize the force and deformation relationship of the mesh element. The mechanical property parameters can be strain tensors and stress tensors.

[0044] In practical applications, the original configuration data of the mesh element to be fine-tuned can be processed to obtain the input data for the mechanical parameter determination model. The mechanical parameter determination model can then process the input data and the second Jacobian matrix from the previous time step, outputting the second Jacobian matrix of the mesh element to be fine-tuned at the current time step. Optionally, processing the original configuration data of the mesh element to be fine-tuned and the second Jacobian matrix from the previous time step based on the mechanical parameter determination model to obtain the second Jacobian matrix of the mesh element to be fine-tuned at the current time step includes: determining the deformation gradient at the current time step based on the original configuration data of the mesh element to be fine-tuned; determining the strain tensor of the mesh element to be fine-tuned at the current time step based on the deformation gradient and the second Jacobian matrix of the mesh element to be fine-tuned at the previous time step; and inputting the deformation gradient and strain tensor at the current time step into the mechanical parameter determination model to obtain the second Jacobian matrix of the mesh element to be fine-tuned at the current time step.

[0045] In practical applications, the original configuration data of the mesh element to be fine-tuned can be processed to obtain the deformation gradient of the mesh element at the current time step. The strain increment at the current time step can also be determined based on the deformation gradient. The strain tensor at the previous time step can be determined based on the second Jacobian matrix of the mesh element to be fine-tuned at the previous time step. Alternatively, the strain tensor at the current time step can be determined based on the strain tensor at the previous time step and the strain increment at the current time step. For example, the sum of the strain tensor at the previous time step and the strain increment at the current time step can be used as the strain tensor at the current time step. Based on mechanical parameters, the model can process the strain, deformation gradient, and other data of the mesh element to be fine-tuned at the current time step, as well as the second Jacobian matrix from the previous time step, to obtain the second Jacobian matrix and stress data (such as the stress tensor) of the mesh element to be fine-tuned at the current time step.

[0046] It should be noted that S120 to S130 can be executed sequentially or in parallel. The specific execution order is not limited. The above order is only the order in which the technical solutions in each step are explained, not the execution order of each step.

[0047] S140. Based on the first and second Jacobian matrices corresponding to the last time step, determine the updated finite element model.

[0048] In this embodiment, the first Jacobian matrix of each mesh element to be updated and the second Jacobian matrix of each mesh element to be fine-tuned corresponding to the last time step can be assembled into a total stiffness matrix to obtain the final finite element model.

[0049] It should be noted that, in order to further improve the accuracy of finite element model construction, before determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step, the finite element model corresponding to the current time step can be constructed based on the first and second Jacobian matrices corresponding to the current time step. It is then determined whether the finite element model satisfies the overall stiffness matrix assembly principle, that is, whether the mechanical response of the finite element model converges. If so, the next time step can be taken as the current time step to further determine the first and second Jacobian matrices corresponding to the current time step.

[0050] Optionally, before determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step, the method further includes: constructing a finite element model at the current time step based on each of the first and second Jacobian matrices at the current time step; if the finite element model at the current time step satisfies the preset deformation balance rule, then the next time step of the current time step is used as the current time step again.

[0051] Among them, the preset deformation equilibrium rule can be understood as a preset overall stiffness matrix assembly principle. For example, the overall stiffness matrix assembly principle can be that after the discrete structure in the overall model is deformed, it should be ensured that each mesh element is connected to each other in a coordinated manner at the node, that is, all elements have the same displacement at the node; it can also be that each node of the discrete structure in the overall model should satisfy the equilibrium condition, that is, the sum of the nodal forces acting on the node by all mesh elements surrounding each node should be equal to the nodal load acting on the node.

[0052] In practical applications, the first Jacobian matrix and the second Jacobian matrix at the current time step can be assembled based on the total stiffness matrix to construct the finite element model at the current time step. When constructing the finite element model at the current time step, it can be determined whether the constructed finite element model satisfies the preset deformation equilibrium rule. If so, it means that the mechanical response of the finite element model has converged, and the next time step can be used as the current time step again for the calculation of the next time step.

[0053] It should be noted that if the constructed finite element model does not satisfy the preset deformation equilibrium rule, it indicates that the mechanical response of the finite element model has not converged. Since the deformation intensity of each mesh element connected to each mesh element to be updated may be relatively close to the deformation intensity of each mesh element to be updated, implicit algorithms (such as the Johnson-Cook constitutive model) can be used to solve the Jacobian matrix of each mesh element connected to each mesh element to be updated. The finite element model can then be reconstructed based on the solved high-precision Jacobian matrix, thereby improving the convergence speed of the mechanical response of the finite element model.

[0054] Optionally, before determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step, the method further includes: constructing a finite element model at the current time step based on each first and second Jacobian matrix at the current time step; if the finite element model at the current time step does not meet the preset deformation balance rule, then determining the associated mesh elements related to each mesh element to be updated; processing the original configuration data of the associated mesh elements and the second Jacobian matrix of the previous time step based on an implicit algorithm to obtain the third Jacobian matrix of the associated mesh elements at the current time step, and updating the second Jacobian matrix of the associated mesh elements at the current time step based on the third Jacobian matrix.

[0055] In practical applications, if the finite element model at the current time step does not meet the preset deformation balance rule, the mesh elements connected to each mesh element to be updated can be regarded as associated mesh elements. An implicit algorithm can be used to process the original configuration data of each associated mesh element and the second Jacobian matrix of the previous time step to obtain the element stiffness matrix of each associated mesh element at the current time step, which serves as the third Jacobian matrix. This third Jacobian matrix can then be used as the second Jacobian matrix of the associated mesh element at the current time step. Based on the first and second Jacobian matrices at the current time step, the finite element model at the current time step can be constructed, and it can be re-determined whether the finite element model meets the preset deformation balance rule, thus improving the construction accuracy of the finite element model. Optionally, mesh elements in the finite element model at the current time step that do not satisfy the preset deformation balance rule (i.e., the model has not achieved the convergence target) can be used as associated mesh elements. Then, the third Jacobian matrix of these associated mesh elements at the current time step can be recalculated using the implicit algorithm, and used as the second Jacobian matrix of the associated mesh elements at the current time step. The second Jacobian matrix of the deformation gradient and strain tensor at the next time step is determined based on the second Jacobian matrix of the associated mesh elements at the current time step and the deformation gradient and strain tensor at the next time step.

[0056] It should be noted that if the finite element model at the current time step does not satisfy the preset deformation balance rule, an implicit algorithm can be used to process the configuration data to be updated for each mesh element to be updated and the first Jacobian matrix of the previous time step to obtain the Jacobian matrix of each mesh element to be updated at the current time step, which serves as the first Jacobian matrix. Similarly, an implicit algorithm can be used to process the original configuration data of each mesh element to be fine-tuned and the second Jacobian matrix of the previous time step to obtain the Jacobian matrix of each mesh element to be fine-tuned at the current time step, which is the second Jacobian matrix. Based on the first and second Jacobian matrices at the current time step, a finite element model at the current time step is constructed, and it is then re-determined whether the finite element model satisfies the preset deformation balance rule at the current time step.

[0057] This embodiment's technical solution obtains at least one mesh element to be updated and its corresponding configuration data in the current finite element model. It then determines the first Jacobian matrix of the mesh element to be updated at the current time step based on an implicit algorithm. Furthermore, it determines the second Jacobian matrix of the mesh element to be fine-tuned at the current time step based on a mechanical parameter-based model. Finally, based on the first and second Jacobian matrices corresponding to the last time step, it determines the updated finite element model. This solves the problem of high time cost and low analysis efficiency caused by traditional implicit algorithms in existing finite element model analysis. It achieves processing of each mesh element to be updated whose configuration data has changed in the current finite element model based on a mechanical parameter-based model, obtaining the second Jacobian matrix of each mesh element to be updated. This eliminates the need to repeatedly use traditional implicit algorithms to analyze and calculate the mesh elements to be updated. The final finite element model is determined based on the first and second Jacobian matrices corresponding to the last time step, greatly improving the efficiency of finite element model analysis and achieving the technical effect of reducing the time cost of processing finite element models.

[0058] Example 2

[0059] Figure 2 This is a flowchart of a finite element constitutive model processing method according to Embodiment 2 of the present invention. Based on the foregoing embodiments, the mechanical parameter determination model can also be pre-trained. Specific implementation methods can be found in the technical solution of this embodiment. Technical terms that are the same as or corresponding to those in the above embodiments will not be repeated here.

[0060] like Figure 2 As shown, the method specifically includes the following steps:

[0061] S210. Obtain the training sample set.

[0062] It should be noted that before training to obtain the mechanical parameters and determine the model, training sample data needs to be acquired first for training. To improve the accuracy of the model, as many and varied training samples as possible should be obtained.

[0063] The training sample set includes multiple training samples, which contain raw mechanical property data and theoretical deformation result data. The raw mechanical property data includes deformation gradient and strain tensor, while the theoretical deformation result data includes Jacobian matrix.

[0064] In this embodiment, the Johnson-Cook (JC) constitutive model can be selected to calculate the model that needs to be simulated by finite element method (FEM), i.e., the current FEM model. During the model simulation calculation, the mechanical state variables of the constitutive model at each time step are obtained. The mechanical state variables may include strain tensor, stress tensor, deformation gradient, Jacobian matrix, etc. For example, the objective function of the JC constitutive model can be as shown in formula (1):

[0065]

[0066] Where ε can represent the strain tensor, σ can represent the stress tensor, A can represent the initial yield stress, B can represent the strain hardening modulus, n can represent the hardening exponent, m can represent the material's thermal softening exponent, and T can represent the test temperature. room It can be expressed as room temperature, T melt It can be expressed as the softening temperature of the material. For example, a square model with a length, width and height of 10mm*10mm*10mm can be built in ABAQUS software. The mesh element in the finite element model is of type C3D8R. The mesh element can be spherical, and the corresponding diameter is randomly selected from 0.5-4mm. Finally, finite element model A can be constructed. Based on the establishment of finite element model A, the material parameters of each mesh element in finite element model A can be assigned (e.g., material 7039 aluminum alloy, initial yield stress of 337MPa, strain hardening modulus of 343MPa, hardening index of 0.41, material thermal softening index of 1.00). Then, after using the 7039 aluminum alloy parameters, the objective function of the JC constitutive model can be as shown in formula (2):

[0067]

[0068] In the actual simulation calculation, the JC constitutive model can be compressed in the X direction using a strain rate-independent method. The test temperature T can be selected as 25℃, and the model is compressed to a maximum engineering strain of 0.2. Each time step is set to a constant value, such as 0.1s. After constructing the finite element model, you can refer to... Figure 3The finite element model calculation process begins by decoupling the calculation of the JC constitutive model parameters and conducting simulation experiments. During the model simulation calculation, the mechanical state variables of the constitutive model for all mesh elements at all time steps are obtained. These mechanical state variables may include strain tensor, stress tensor, deformation gradient, Jacobian matrix, etc. The current finite element model calculation ends here. For example, the mesh element number and the corresponding time step, strain increment, deformation gradient, stress tensor, and Jacobian matrix for each time step can be stored according to the time step order and element number. The strain tensor ε can be calculated based on the strain increment for each time step. Since the strain tensor ε and stress tensor σ satisfy the symmetry relationship and the incompressible nature of metallic materials, the strain tensor data is stored as follows: Stress tensor data is stored as follows: The input data B can be the time step, deformation gradient, and strain tensor corresponding to the current grid cell number in the current time step order. The output data C can be the Jacobian matrix and stress tensor corresponding to the current grid cell number in the current time step order. Input data B and output data C can be used as a training sample, resulting in multiple training samples. All training samples can then be normalized to obtain a training sample set. It should be noted that to ensure that the data stored in each grid cell does not interfere with each other during the calculation, the computer's computation threads and processes can be set to 1 during processing.

[0069] S220. For each training sample, the original mechanical property data of the current training sample is used as the input of the parameter determination model to be trained, and the theoretical deformation result data is used as the output of the parameter determination model to be trained, thereby training the parameter determination model to be trained.

[0070] Among them, the model to be trained can be a BP neural network model. In the neural network, two adjacent layers can be connected by neurons. The relationship between the input and output of neurons is expressed by the following formula (3):

[0071]

[0072] G i It is the output of each neuron, G i-1 It is the input of each neuron. The weights calculated for the neuron, b i The threshold calculated for the neuron is used, and the tansig function is used as the parameter to be trained to determine the activation function of the model. The activation function can be... The number of hidden layers is set to 2. The number of neurons in the hidden layers can be determined by automatically calculating the number of neurons in hidden layers from 1 to 20, and selecting the number with the smallest mean square variance of the overall loss. When it is necessary to determine the Jacobian matrix corresponding to each training sample, the Jacobian matrix of any training sample can be used as the Jacobian matrix of the current training sample for explanation.

[0073] In practical applications, the model for determining the parameters to be trained can be trained using each training sample in the training sample set to obtain the mechanical parameter determination model. For example, see [link to example]. Figure 3 The BP neural network model to be trained can be used as the parameter determination model. The BP neural network model is trained based on each training sample in the training sample set. The BP neural network model is trained and self-validated by data. Each original mechanical property data in the training sample can be input into the parameter determination model to be trained. The model can process the training sample and output the Jacobian matrix corresponding to the training sample. Then, the algorithm can be used to perform loss processing on the output Jacobian matrix and the theoretical deformation result data to obtain the loss value. Based on the loss value, the model parameters in the parameter determination model to be trained are corrected, and the parameter determination model to be trained is trained to obtain a trained BP neural network model based on mechanical parameters.

[0074] S230. The convergence of the loss function of the parameter determination model to be trained is taken as the training objective to obtain the mechanical parameter determination model.

[0075] Among them, the convergence of the preset loss function can be used as the training objective. When it is determined that the preset loss function of the model to be trained converges, it indicates that the adjustment result meets the requirements of the scheme and the trained model has been obtained, thus obtaining the mechanical parameter determination model.

[0076] In this embodiment, neural network technology can be used to process the original mechanical property data corresponding to the current training sample. The model to be trained can output the Jacobian matrix corresponding to the current training sample. Since the model parameters in the model to be trained are uncorrected, the obtained Jacobian matrix will also differ from the theoretical deformation result data corresponding to the current training sample. Based on the Jacobian matrix corresponding to the current training sample and the theoretical deformation result data, the error value can be determined, and then the model parameters in the model to be trained can be corrected based on the error value.

[0077] In this embodiment, the loss function in the model can be determined using the parameters to be trained. This loss function is then compared with the Jacobian matrix corresponding to the current training sample and the theoretical deformation result data to calculate the loss value. For example, the loss value for the training dataset can be calculated using the mean-squared error cost function between the Jacobian matrix output by the neural network training and the expected true output Jacobian matrix. The formula for calculating the mean-squared error is as follows: The model parameters of the model to be trained are then corrected based on the obtained loss results. Furthermore, the training error of the loss function, i.e., the loss parameters, can be used as a condition to detect whether the loss function has reached convergence. For example, whether the training error is less than a preset error or whether the error trend is stable. For instance, convergence can be considered until the final training satisfies that the overall mean square variance of the loss is less than 0.001, or whether the current number of iterations equals a preset number. If the convergence condition is met, such as the training error of the loss function being less than the preset error or the error trend being stable, it indicates that the model to be trained is complete, and iterative training can be stopped. If the convergence condition is not met, further training samples can be obtained to continue training the model to be trained until the training error of the loss function is within a preset range. When the training error of the loss function converges, the model to be trained is considered to be well trained, i.e., a mechanical parameter determination model is obtained. This allows the model to accurately output the Jacobian matrix and stress tensor corresponding to the deformation gradient and strain tensor when the deformation gradient and strain tensor are input into the mechanical parameter determination model.

[0078] Based on the above scheme, when the structural / material parameters change at a certain point in the current finite element model, for example, the initial yield stress parameters of the constitutive model on some mesh elements in the current finite element model can be changed, or the hardening index can be changed. The finite element model calculation for the change in structural / material parameters at a certain point in the current finite element model can begin. Using any time step as the current time step, the implicit JC constitutive model can be used to calculate the second Jacobian matrix and Cauchy stress tensor of all mesh elements (mesh elements to be updated) in the adjusted model parameters. The validated BP neural network model (i.e., the mechanical parameter determination model) can be used to calculate the second Jacobian matrix and Cauchy stress tensor of all mesh elements (mesh elements to be fine-tuned) in the unadjusted model parameters. The implementation method for calculating the second Jacobian matrix and Cauchy stress tensor of the mesh elements to be fine-tuned based on the mechanical parameter determination model can be found in [reference needed]. Figure 4This allows us to obtain the strain tensor of the current mesh element to be adjusted at the previous time step, as well as the strain increment and deformation gradient at the current time step. Based on the strain tensor at the previous time step and the strain increment at the current time step, we can calculate the strain tensor at the current time step. The strain tensor and deformation gradient at the current time step can be input into the mechanical parameters to determine the model, outputting the second Jacobian matrix and Cauchy stress tensor of the current mesh element to be adjusted. Correspondingly, the second Jacobian matrix and Cauchy stress tensor of each mesh element to be adjusted can be obtained. An implicit algorithm can be used to solve for the first Jacobian matrix of each mesh element to be updated. Further, a finite element model is constructed based on each second and first Jacobian matrix. According to the overall stiffness matrix assembly principle, i.e., the preset deformation equilibrium rule, we determine whether the constructed finite element model converges. If it satisfies the preset deformation equilibrium rule, i.e., the convergence condition is met, the calculation for the next time step can proceed. Otherwise, the associated mesh elements connected to each mesh element to be updated can be identified, and the Jacobian matrix of each associated mesh element can be calculated using traditional implicit finite element algorithms, effectively ensuring model convergence. In this technical solution, the structure of a large proportion of mesh elements in the model that have not changed structural features / material parameters is determined using mechanical parameters to determine the model output results, which can significantly improve the model's computational efficiency while ensuring computational convergence.

[0079] For example, after selecting the JC constitutive model to calculate the model that needs to be simulated by finite element, i.e., the current finite element model A, another model with the same structural division as finite element model A (as finite element model B) can be selected. The same loading conditions as finite element model A are adopted, but the initial yield stress parameter B of the constitutive model on the labeled mesh element 1 is changed (e.g., the Johnson-Cook constitutive model parameters of this mesh element are A=337MPa, B=403MPa, n=0.41, m=1.0). For the labeled mesh element 1 (the mesh element to be updated) and all mesh elements connected to it (associated mesh elements), the traditional implicit finite element solution method is still used to calculate the mechanical constitutive response of the overall model (due to the nonlinear calculation caused by changing the material properties of the labeled mesh element 1, the representative volume element connected to it is also set to use the finite element constitutive response method to ensure effective convergence calculation). The solution method for the other mesh elements in finite element model B, excluding the mesh elements to be updated and the associated mesh elements (the Johnson-Cook constitutive model parameters of the other mesh elements are the same as those calculated in the initial finite element model, namely A = 337 MPa, B = 403 MPa, n = 0.41, m = 1.0), is illustrated by example. The method may include the following steps:

[0080] Step 1, continue to refer to Figure 3Start the current time step (also called the increment step) t n+1 Read the previous time step t from the state variables of the finite element model. n The second-order Cauchy stress tensor σ and strain tensor ε on each mesh element are related to the current time step and the time step from t. n to t n+1 The information includes the strain increment Δε, the total deformation gradient tensor F, and the time step Δn.

[0081] Step 2: Decompose the finite element model into multiple mesh elements. The mechanical response of a single mesh element is calculated from the material constitutive relation at the integration point of that mesh element. The integration point can be selected by uniformly and randomly selecting integration points on mesh elements within the finite element model, with only one integration point per mesh element. Based on the trained mechanical parameter determination model (BP neural network model), use the deformation gradient F corresponding to the current time step order and mesh element number, the time step Δn, and the sum of the strain tensor ε from the previous time step and the strain increment Δε from the current time step as inputs to calculate the stress tensor σ for the current time step and the Jacobian matrix of a single element. Simultaneously, solve for the required stress increment Δσ in the finite element model.

[0082] Step 3: Based on the overall stiffness matrix assembly process, using the stress and strain information at the element integration points obtained in Step 2, determine whether the complete finite element model has converged. If converged, save the stress tensor, strain tensor, and element Jacobian matrix at each mesh element in the current time step into the state variables for use in the next time step. If the overall model is difficult to converge, based on the stress, strain tensor, and deformation gradient information from the previous time step, use a simplified JC constitutive model for finite element calculation and store the corresponding state variables. Then, proceed to the next time step for calculation. It should be noted that after the overall model calculation is completed, in order to enhance the calculation accuracy of the BP neural network model and solve the similarity non-convergence problem, the information of mesh elements that have not achieved convergence using the BP neural network method can be extracted, and the stress and strain response results calculated using the finite element method for these mesh elements can be added to the neural network training sample set to train the BP neural network model.

[0083] It should also be noted that the finite element pseudo-constitutive model used in this technical solution requires training a BP neural network, which incurs significant time costs in the early stages. However, once the constitutive model solution calculation begins, the time costs are significantly reduced. Furthermore, in large-scale, multi-calculation models, since the BP neural network training and self-verification process only needs to be performed once, the advantage of embedding the BP neural network algorithm into the finite element pseudo-constitutive model at the element integration points, as used in this invention, is significantly amplified, greatly improving the efficiency and accuracy of the finite element model solution.

[0084] S240. Obtain at least one mesh element to be updated and its corresponding configuration data in the current finite element model.

[0085] S250. For each grid cell to be updated, the configuration data to be updated and the first Jacobian matrix of the previous time step of the current grid cell to be updated are processed based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step.

[0086] S260. For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step.

[0087] S270. Based on the first and second Jacobian matrices corresponding to the last time step, determine the updated finite element model.

[0088] The technical solution of this embodiment processes the current finite element model based on an implicit algorithm to obtain high-precision original mechanical property data and theoretical deformation result data as training samples. Based on the training samples, a mechanical parameter determination model is trained. This enables the mechanical parameter determination model to process the mesh elements to be fine-tuned without changing the structural features / material parameters when the configuration data in the current finite element model changes, and outputs the second Jacobian matrix of each mesh element to be fine-tuned. This greatly improves the efficiency of finite element model analysis and reduces the time cost of processing the finite element model.

[0089] Example 3

[0090] Figure 5 This is a schematic diagram of a finite element constitutive model processing device according to Embodiment 3 of the present invention. Figure 5 As shown, the device includes: a configuration data acquisition module 510 to be updated, a Jacobian matrix determination module 520, and a finite element model determination module 530.

[0091] The module 510 for acquiring configuration data to be updated is used to acquire at least one mesh element to be updated and its corresponding configuration data in the current finite element model; wherein the finite element model includes at least one mesh element to be updated and a mesh element to be fine-tuned; the Jacobian matrix determination module 520 is used to process the configuration data to be updated and the first Jacobian matrix of the previous time step for each mesh element to be updated based on an implicit algorithm to obtain the first Jacobian matrix of the current mesh element to be updated at the current time step; and, for each mesh element to be fine-tuned, to process the original configuration data and the second Jacobian matrix of the previous time step based on a mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step; wherein the second Jacobian matrix is ​​determined based on mechanical property parameters; the finite element model determination module 530 is used to determine the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step.

[0092] The technical solution of this embodiment obtains at least one mesh element to be updated and its corresponding configuration data in the current finite element model. It then determines the first Jacobian matrix of the mesh element to be updated at the current time step based on an implicit algorithm. Furthermore, it determines the second Jacobian matrix of the mesh element to be fine-tuned at the current time step based on a mechanical parameter determination model. Finally, it determines the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step. This solves the problem of high time cost and low analysis efficiency caused by traditional implicit algorithm analysis of finite element models in existing technologies. It achieves processing of each mesh element to be updated whose configuration data has changed in the current finite element model based on a mechanical parameter determination model, obtaining the second Jacobian matrix of each mesh element to be updated. This eliminates the need to repeatedly use traditional implicit algorithm analysis to calculate the mesh elements to be updated. The final finite element model is determined based on the first and second Jacobian matrices corresponding to the last time step, greatly improving the efficiency of finite element model analysis and achieving the technical effect of reducing the time cost of processing finite element models.

[0093] Optionally, based on the above-mentioned device, the configuration data acquisition module 510 to be updated includes a grid cell determination unit to be updated and a configuration data determination unit to be updated.

[0094] The grid cell to be updated determination unit is used to determine at least one grid cell to be updated in the current finite element model whose configuration data has changed.

[0095] The configuration data to be updated determination unit is used to obtain the configuration data to be updated for each grid cell to be updated, wherein the configuration data to be updated includes material configuration data and structural configuration data.

[0096] Optionally, based on the above-mentioned device, the Jacobian matrix determination module 520 includes a mechanical property data determination unit and a first Jacobian matrix determination unit.

[0097] The mechanical property data determination unit is used to determine the mechanical property data to be used by the current mesh cell at the current time step based on the configuration data to be updated of the current mesh cell;

[0098] The first Jacobian matrix determination unit is used to process the mechanical property data to be used and the first Jacobian matrix of the previous time step based on the implicit algorithm to obtain the first Jacobian matrix of the current mesh cell to be updated at the current time step.

[0099] Based on the above-mentioned device, optionally, the Jacobian matrix determination module 520 includes a deformation gradient determination unit, a strain tensor determination unit, and a second Jacobian matrix determination unit.

[0100] The deformation gradient determination unit is used to determine the deformation gradient at the current time step based on the original configuration data of the current mesh cell to be fine-tuned.

[0101] The strain tensor determination unit is used to determine the strain tensor of the current mesh element to be fine-tuned at the current time step based on the deformation gradient and the second Jacobian matrix of the current mesh element to be fine-tuned at the previous time step.

[0102] The second Jacobian matrix determination unit is used to input the deformation gradient and strain tensor at the current time step into the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step.

[0103] Optionally, based on the above-mentioned device, the device may further include a balance rule judgment module, which includes a finite element model construction unit and a current time step determination unit.

[0104] A finite element model building unit is used to build a finite element model at the current time step based on each of the first Jacobian matrices and each of the second Jacobian matrices at the current time step.

[0105] The current time step determination unit is used to determine the next time step as the current time step if the finite element model at the current time step satisfies the preset deformation balance rule.

[0106] Optionally, based on the above-mentioned device, the device may further include a balance rule determination module, which includes an associated grid cell determination unit and a third Jacobian matrix determination unit.

[0107] The associated mesh element determination unit is used to determine the associated mesh elements associated with each mesh element to be updated if the finite element model at the current time step does not meet the preset deformation balance rule.

[0108] The third Jacobian matrix determination unit is used to process the original configuration data of the associated grid cell and the second Jacobian matrix of the previous time step based on the implicit algorithm to obtain the third Jacobian matrix of the associated grid cell at the current time step, and update the second Jacobian matrix of the associated grid cell at the current time step based on the third Jacobian matrix.

[0109] Optionally, based on the above-mentioned device, the device may further include a mechanical parameter determination model acquisition module, which includes a training sample set determination unit, a parameter determination model training unit, and a mechanical parameter determination model determination unit.

[0110] A training sample set determination unit is used to obtain a training sample set; wherein, the training sample set includes multiple training samples, the training samples include original mechanical property data and theoretical deformation result data, the original mechanical property data includes deformation gradient and strain tensor, and the theoretical deformation result data includes Jacobian matrix;

[0111] The training unit for determining the parameters to be trained is used to train the model by taking the original mechanical property data of the current training sample as the input of the model and the theoretical deformation result data as the output of the model.

[0112] The mechanical parameter determination model determination unit is used to converge the loss function of the parameter determination model to be trained as the training objective to obtain the mechanical parameter determination model.

[0113] The finite element constitutive model processing device provided in the embodiments of the present invention can execute the finite element constitutive model processing method provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects of the execution method.

Claims

1. A method for processing finite element constitutive models, characterized in that, include: Obtain at least one mesh element to be updated and its corresponding configuration data to be updated in the current finite element model; wherein, the finite element model includes at least one mesh element to be updated and a mesh element to be fine-tuned; the mesh element to be fine-tuned represents the mesh element in the finite element model where the structural shape or material parameters have not been adjusted, and the mesh element to be updated represents the mesh element in the finite element model where the structural shape or material parameters have been adjusted; For each grid cell to be updated, the configuration data to be updated for the current grid cell and the first Jacobian matrix of the previous time step are processed based on an implicit algorithm to obtain the first Jacobian matrix of the current grid cell at the current time step; and, For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step; wherein, the second Jacobian matrix is ​​determined based on the mechanical property parameters. The updated finite element model is determined based on the first and second Jacobian matrices corresponding to the last time step. The method further includes: training the mechanical parameter determination model, including: Obtain a training sample set; wherein the training sample set includes multiple training samples, and the training samples include original mechanical property data and theoretical deformation result data; For each training sample, the original mechanical property data of the current training sample is used as the input of the parameter determination model to be trained, and the theoretical deformation result data is used as the output of the parameter determination model to be trained, thereby training the parameter determination model to be trained. The convergence of the loss function of the model to be trained is used as the training objective to obtain the mechanical parameter determination model.

2. The method according to claim 1, characterized in that, The step of obtaining at least one mesh element to be updated and the corresponding configuration data to be updated in the current finite element model includes: Identify at least one mesh element in the current finite element model whose configuration data has changed and needs to be updated; Obtain the configuration data to be updated for each grid cell to be updated, wherein the configuration data to be updated includes material configuration data and structural configuration data.

3. The method according to claim 1, characterized in that, The implicit algorithm is used to process the configuration data to be updated for the current grid cell and the first Jacobian matrix of the previous time step to obtain the first Jacobian matrix of the current grid cell at the current time step, including: Based on the configuration data to be updated of the current grid cell to be updated, determine the mechanical property data to be used of the current grid cell at the current time step; The implicit algorithm is used to process the mechanical property data to be used and the first Jacobian matrix of the previous time step to obtain the first Jacobian matrix of the current mesh cell to be updated at the current time step.

4. The method according to claim 1, characterized in that, The mechanical parameter-based model processes the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step, including: Based on the original configuration data of the current mesh element to be fine-tuned, determine the deformation gradient at the current time step; Based on the deformation gradient and the second Jacobian matrix of the current mesh element to be fine-tuned at the previous time step, determine the strain tensor of the current mesh element to be fine-tuned at the current time step. By inputting the deformation gradient and strain tensor at the current time step into the mechanical parameters to determine the model, the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step is obtained.

5. The method according to claim 1, characterized in that, Before determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step, the method further includes: Based on the first Jacobian matrix and the second Jacobian matrix at the current time step, a finite element model is constructed at the current time step. If the finite element model at the current time step satisfies the preset deformation balance rule, then the next time step at the current time step will be used as the current time step again.

6. The method according to claim 1, characterized in that, Before determining the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step, the method further includes: If the finite element model at the current time step does not meet the preset deformation balance rule, then the associated mesh elements related to each mesh element to be updated are determined. The original configuration data of the associated grid cell and the second Jacobian matrix of the previous time step are processed based on the implicit algorithm to obtain the third Jacobian matrix of the associated grid cell at the current time step, and the second Jacobian matrix of the associated grid cell at the current time step is updated based on the third Jacobian matrix.

7. The method according to claim 1, characterized in that, The original mechanical property data includes deformation gradient and strain tensor, and the theoretical deformation result data includes Jacobian matrix.

8. A processing device for a finite element constitutive model, characterized in that, include: The configuration data acquisition module is used to acquire at least one mesh element to be updated and the corresponding configuration data to be updated in the current finite element model; wherein, the finite element model includes at least one mesh element to be updated and a mesh element to be fine-tuned; the mesh element to be fine-tuned represents the mesh element in the finite element model where the structural shape or material parameters have not been adjusted, and the mesh element to be updated represents the mesh element in the finite element model where the structural shape or material parameters have been adjusted; The Jacobian matrix determination module is used to process the configuration data to be updated and the first Jacobian matrix of the previous time step for each grid cell to be updated based on an implicit algorithm, to obtain the first Jacobian matrix of the current grid cell to be updated at the current time step; and, For each mesh element to be fine-tuned, the original configuration data of the current mesh element to be fine-tuned and the second Jacobian matrix of the previous time step are processed based on the mechanical parameter determination model to obtain the second Jacobian matrix of the current mesh element to be fine-tuned at the current time step; wherein, the second Jacobian matrix is ​​determined based on the mechanical property parameters. The finite element model determination module is used to determine the updated finite element model based on the first and second Jacobian matrices corresponding to the last time step. The device further includes a mechanical parameter determination model acquisition module, which includes: A training sample set determination unit is used to acquire a training sample set; wherein, the training sample set includes multiple training samples, and the training samples include original mechanical property data and theoretical deformation result data; The training unit for determining the parameters to be trained is used to train the model by taking the original mechanical property data of the current training sample as the input of the model and the theoretical deformation result data as the output of the model. The mechanical parameter determination model determination unit is used to converge the loss function of the parameter determination model to be trained as the training objective to obtain the mechanical parameter determination model.

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