Method and related device for surrogate modeling of mechanical response of composite structures

Abstract

This invention discloses a surrogate model analysis method and related equipment for the mechanical response of composite material structures. First, a pre-trained deep material network surrogate model is acquired. Its network structure consists of multi-level building blocks, each corresponding to homogenization and rotation operations. Trainable parameters are determined by sampling multiple sets of material parameters and their corresponding equivalent mechanical parameters from the micromechanical model. Next, a macroscopic finite element model of the composite material structure to be analyzed is established, boundary conditions and load paths are applied, and macroscopic strain data at each integration point are calculated. The data is input into the surrogate model, and the strain is decomposed from top to bottom to the bottom layer. A pre-defined component material constitutive model is called to calculate the mechanical response of each component; then, equivalent convergence is performed from bottom to top to calculate the macroscopic equivalent stress and tangential stiffness at the integration points. Finally, the solution is returned to update the structural response state and output the overall mechanical response result. This method effectively reduces computational costs while ensuring prediction accuracy, meeting the computational efficiency requirements of engineering applications.

Description

Technical Field

[0001] This invention relates to the field of mechanical analysis and computational modeling technology for composite material structures, specifically to a proxy model analysis method and related equipment for the mechanical response of composite material structures. Background Technology

[0002] With the increasing demands for lightweight and high-performance structures in aerospace, transportation, automotive engineering, and marine engineering, composite materials are widely used in engineering structures due to their excellent mechanical properties and good designability. Accurate characterization of the mechanical behavior of composite material structures is crucial for ensuring their safety and reliability during the design, analysis, and service evaluation processes.

[0003] The macroscopic mechanical properties of composite materials are typically influenced by their microstructure morphology and evolutionary behavior during loading, with interactions between different scales through multi-scale coupling mechanisms. To effectively incorporate microscale mechanical information into macroscopic structural analysis, researchers have proposed various multi-scale analysis methods. Existing multi-scale methods can generally be categorized into sequential multi-scale methods and parallel multi-scale methods. Sequential multi-scale methods typically employ a unidirectional information transfer approach, introducing equivalent mechanical parameters obtained at the microscale into macroscopic structural analysis. This simplifies the modeling process and increases computational efficiency. However, these methods have limited ability to characterize microscopic interactions and their nonlinear behavior, resulting in low prediction accuracy. In contrast, parallel multi-scale methods achieve bidirectional coupling between macroscopic and microscale within a single loading increment, more directly reflecting the impact of microstructural evolution on macroscopic mechanical responses. Parallel multi-scale methods are typically implemented by embedding microscopic composite material unit cell models at the integration points of the macroscopic finite element model, offering advantages in prediction accuracy. However, this type of method requires solving a large number of micro-unit cell problems simultaneously during the macro-structural analysis process, which leads to a rapid increase in computational freedom and storage requirements with the scale of the structure. As a result, it faces high computational costs in the analysis of large and complex structures and is difficult to meet the computational efficiency requirements of engineering applications. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides a surrogate model analysis method and related equipment for the mechanical response of composite material structures. Its purpose is to effectively reduce the computational cost while ensuring the accuracy of the prediction of the mechanical response of composite material structures, and to meet the computational efficiency requirements of engineering applications. This overcomes the shortcomings of existing sequential multi-scale methods, which have low prediction accuracy, and parallel multi-scale methods, which have excessively high computational costs in the analysis of large and complex structures, making it difficult to meet the computational efficiency requirements of engineering applications.

[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 surrogate model analysis method for the mechanical response of composite material structures is provided, comprising: A deep material network proxy model is obtained to characterize the equivalent mechanical behavior of the microstructure of composite materials. The deep material network proxy model is a pre-trained network model. The network structure of the deep material network proxy model consists of multi-level building blocks. Each building block corresponds to a homogenization operation based on the constitutive relation of the component materials and a rotation operation characterizing the material orientation. The trainable parameters of the building blocks are determined by training data composed of multiple sets of material parameters obtained by sampling the material parameter space of the composite material components and the equivalent mechanical parameters of the micromechanical model corresponding to the multiple sets of material parameters. A macroscopic finite element model of the composite material structure to be analyzed is established, boundary conditions and load paths are applied to the macroscopic finite element model, and macroscopic strain data at each integration point of the macroscopic finite element model are calculated. The macroscopic strain data is input into the deep material network proxy model, which performs a top-down strain decomposition, assigns the macroscopic strain to the bottom layer of the deep material network proxy model, and calls the preset component material constitutive model to calculate the mechanical response of each component under the current loading step. The deep material network proxy model performs bottom-up equivalent convergence and calculates the macroscopic equivalent stress and macroscopic equivalent tangential stiffness at the integration point based on the mechanical response of each component. The macroscopic equivalent stress and macroscopic equivalent tangential stiffness are returned to the solver of the macroscopic finite element model to update the structural response state, and the overall mechanical response result of the composite material structure is output after all loading steps are completed.

[0006] In one possible implementation of the first aspect, the step of obtaining the deep material network proxy model includes: Within a preset material parameter space for composite material components, multiple combinations of material parameters are generated through random sampling. These combinations of material parameters include elastic modulus, shear modulus, and Poisson's ratio. When randomly sampling the material parameters, the scaling factor of one phase material is fixed to eliminate the unit cell scale effect. For each combination of material parameters, the equivalent mechanical parameters corresponding to each combination of material parameters are calculated based on the micromechanical model, and a training dataset is constructed consisting of the material parameter combination and the equivalent mechanical parameters corresponding to the material parameter combination. The equivalent mechanical parameters in the training dataset are used as training targets to train the constructed deep materials network. The trainable parameters in each building block are adjusted to minimize the error between the prediction output of the deep materials network and the training target, thus obtaining the deep materials network proxy model.

[0007] In one possible implementation of the first aspect, the trainable parameters of the building block include weight parameters characterizing the volume fraction distribution of the sub-building blocks of the building block, and rotation angle parameters characterizing the overall spatial orientation of the building block.

[0008] In one possible implementation of the first aspect, the step of calling a preset constitutive model of the component materials to calculate the mechanical response of each component under the current loading step includes: Based on the strain increments of each component material at the bottom layer of the deep material network proxy model obtained from the decomposition, and combined with the historical state variables of each component material at the end of the previous loading step, the stress increments and tangential stiffness of each component are calculated.

[0009] In one possible implementation of the first aspect, the solver of the macroscopic finite element model is the solver of the ABAQUS finite element analysis software, and the deep material network proxy model interacts with the solver through a predefined model call interface.

[0010] In one possible implementation of the first aspect, the microstructure of the composite material includes at least one of a fiber-reinforced structure, a laminated structure, a braided structure, or a particle-reinforced structure.

[0011] In one possible implementation of the first aspect, the constitutive model of the component material includes a linear elastic constitutive model or an elastoplastic constitutive model.

[0012] 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 surrogate model analysis method for the mechanical response of a composite material structure.

[0013] 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 surrogate model analysis method for the mechanical response of a composite material structure.

[0014] According to a fourth aspect of the present invention, a computer program product is provided that, when executed by a processor, implements the aforementioned surrogate model analysis method for the mechanical response of a composite material structure.

[0015] Compared with the prior art, the present invention has at least the following beneficial effects: This invention provides a surrogate model analysis method for the mechanical response of composite material structures. It replaces the traditional multi-scale analysis method that simultaneously solves the microscopic unit cell problem at each integration point of the macroscopic finite element model by introducing a pre-trained deep material network surrogate model. The deep material network surrogate model consists of multi-level building blocks, each corresponding to a homogenization operation based on the constitutive relations of the component materials and a rotation operation characterizing the material orientation. This structural design allows the surrogate model to distribute macroscopic strain layer by layer to the bottom component material nodes according to the building block hierarchy when performing top-down strain decomposition; and to synthesize macroscopic equivalent stress and macroscopic equivalent tangential stiffness layer by layer based on the stress increments and tangential stiffness calculated from the bottom component materials when performing bottom-up equivalent convergence. Thus, a two-way information transmission channel is established between the macroscopic structural response and the microscopic component material behavior. The macroscopic calculation can fully reflect the changes in the mechanical state of each component material during loading at the microscopic scale, including nonlinear behaviors such as plastic yielding and hardening of the matrix material, thereby ensuring the prediction accuracy of composite material structures in multi-scale coupled analysis.

[0016] After pre-training, the trainable parameters of each building block in the deep materials network surrogate model are determined. During the online response calculation phase, the surrogate model only needs to perform one forward propagation process to complete the mapping from macroscopic strain to macroscopic equivalent stress and equivalent tangential stiffness, without iteratively solving the equilibrium equations of the mesoscopic unit cell at every integration point and every loading step. This characteristic ensures that the computational freedom and storage requirements of macroscopic finite element analysis do not increase with the complexity of the mesoscopic model, significantly reducing the time cost and memory footprint of nonlinear analysis of large composite material structures.

[0017] The Deep Materials Network proxy model interacts with the solver of the macroscopic finite element model through a predefined model call interface. The solver only needs to pass the macroscopic strain data at the integration points to the proxy model and receive the returned macroscopic equivalent stress and macroscopic equivalent tangent stiffness to update the structural response state. This interaction method allows the proxy model to be directly embedded into the standard solution process of existing finite element analysis platforms. Engineers do not need to change their existing modeling and analysis habits, making it easy to promote and apply in actual engineering projects.

[0018] Since the deep materials network surrogate model's ability to represent microstructures stems from the coverage of the training data, by changing the micromechanical model used in the training phase, a surrogate model applicable to different microstructure forms such as fiber reinforcement, lamination, weaving, or particle reinforcement can be obtained. Simultaneously, the component material constitutive model called at the bottom layer of the surrogate model can flexibly select either a linear elastic constitutive model or an elastoplastic constitutive model based on the actual material behavior, enabling this method to adapt to the structural analysis needs of composite materials in different material systems. Attached Figure Description

[0019] 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.

[0020] Figure 1 This is a flowchart of a surrogate model analysis method for the mechanical response of composite material structures according to the present invention; Figure 2 For the construction block description; Figure 3 The average loss trend between the training and test sets; Figure 4 This represents the number of activated nodes at the bottom layer before and after training. Figure 5 A comparison of the prediction results of the surrogate model and the finite element method at the unit cell level; Figure 6 The training process for deep materials networks; Figure 7 This is a schematic diagram of the structural response calculation process; Figure 8 The diagrams show three calculation examples, including loading methods and fiber orientations. Figure 9 A comparison of the stress-strain distribution across the entire field of the ∑ structure; Figure 10 Comparison of stress and strain distribution across the entire field in an L-shaped perforated plate structure; Figure 11 Comparison of stress and strain distribution across the entire field of a D-shaped plate (1); Figure 12 Comparison of stress and strain distribution across the entire field in a D-shaped plate (2); Figure 13 Comparison of local responses of sigma structures; Figure 14 Comparison of local responses of L-shaped perforated plates; Figure 15 Comparison of local responses of the D-shaped plate. Detailed Implementation

[0021] 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.

[0022] like Figure 1 As shown, this invention provides a surrogate model analysis method for the mechanical response of composite material structures, specifically including the following steps: S1. Obtain a deep material network proxy model that characterizes the equivalent mechanical behavior of the microstructure of composite materials. The deep material network proxy model is a pre-trained network model. The network structure of the deep material network proxy model consists of multi-level building blocks. Each building block corresponds to a homogenization operation based on the constitutive relation of the component materials and a rotation operation that characterizes the material orientation. The trainable parameters of the building blocks are determined by training data consisting of multiple sets of material parameters obtained by sampling the material parameter space of the composite material components and the equivalent mechanical parameters of the micromechanical model corresponding to the multiple sets of material parameters.

[0023] In detail, a building block is the basic building block of a deep material network proxy model. For a structural diagram of a building block, please refer to the appendix. Figure 2 As attached Figure 2 As shown, a building block contains two sub-building blocks as inputs, and the overall output of the building block is an equivalent mechanical property after homogenization and rotation operations. In Mandel notation, stress... and strain It can be written as:

[0024] The subscripts 3, 4, and 5 indicate the shearing direction.

[0025] The overall stress-strain relationship of the building block can be expressed as: For the two sub-construction blocks of the construction block, the stress-strain relationship is expressed as follows: The stiffness tensor of each building block ( , , Adding a horizontal line above indicates that the stiffness tensor is not the original material parameter, but an equivalent result obtained by homogenizing and rotating the stiffness tensor of its sub-construction blocks.

[0026] Each building block corresponds to two operations: one is a homogenization operation based on the constitutive relations of the constituent materials, which is performed by a function. The other is a rotational operation characterizing the spatial orientation of the material, represented by a function. The entire process is shown in the attached document. Figure 2As shown, the building block contains trainable parameters, which are determined through a training process. The training data used in the training process consists of two parts: one part is multiple sets of material parameters obtained by sampling the material parameter space of the composite material components, and the other part is the equivalent mechanical parameters of the micromechanical model corresponding to these material parameters. Through training, the trainable parameters of the building block are determined, enabling the deep material network surrogate model to have the ability to characterize the equivalent mechanical behavior of the composite material microstructure.

[0027] Deep Materials Networks are constructed based on a binary tree structure, as shown in the attached diagram. Figure 6 As shown. The top layer is layer 0, corresponding to macroscopic homogeneous material, i.e., a unit cell; the bottom layer is layer 1. A layer, representing a single microscopic material layer that has not yet undergone homogenization, is used to introduce material parameters for each phase. For a depth of... The network, the Layer contains Nodes ( The entire network contains Each node represents a single microstructure and undergoes only a rotation operation. Except for the bottommost node, which represents only a single microstructure and undergoes only a rotation operation, each node corresponds to a building block, which sequentially completes one homogenization operation and one rotation operation during the calculation. The macroscopic equivalent constitutive relation of a unit cell can be viewed as the material phases being constructed step-by-step through interlayer interactions, undergoing continuous homogenization and rotation.

[0028] S2. Establish a macroscopic finite element model of the composite material structure to be analyzed, apply boundary conditions and load paths to the macroscopic finite element model, and calculate the macroscopic strain data at each integration point of the macroscopic finite element model.

[0029] It should be understood that, based on actual engineering requirements, corresponding boundary conditions and load paths are applied to the macroscopic finite element model, and macroscopic strain data at each integration point of the macroscopic finite element model are obtained through finite element calculation.

[0030] S3. Input the macroscopic strain data into the deep material network proxy model. The deep material network proxy model performs a top-down strain decomposition, allocates the macroscopic strain to the bottom layer of the deep material network proxy model, and calls the preset component material constitutive model to calculate the mechanical response of each component under the current loading step.

[0031] In other words, the macroscopic strain data calculated in step S2 is used as input and fed into the deep materials network proxy model. After receiving the macroscopic strain data, the deep materials network proxy model performs a top-down strain decomposition process. In this process, the macroscopic strain is decomposed layer by layer and distributed to the bottom layer of the deep materials network proxy model. At the bottom layer, the system calls the pre-set component material constitutive model to solve for the stress state of each component material under the current loading step, and obtains the mechanical response of each component.

[0032] S4. The deep material network proxy model performs bottom-up equivalent convergence, and the macroscopic equivalent stress and macroscopic equivalent tangential stiffness at the integration point are calculated based on the mechanical response of each component.

[0033] In other words, the deep materials network proxy model performs a bottom-up equivalent convergence process. In this process, the deep materials network proxy model converges and synthesizes the mechanical responses calculated from the components of the bottom layer layer by layer, and finally calculates the macroscopic equivalent stress and macroscopic equivalent tangential stiffness at the integration point level.

[0034] S5. Return the macroscopic equivalent stress and the macroscopic equivalent tangential stiffness to the solver of the macroscopic finite element model, update the structural response state, and output the overall mechanical response result of the composite material structure after all loading steps are completed.

[0035] In other words, after the equivalent convergence is completed in step S4, the calculated macroscopic equivalent stress and macroscopic equivalent tangential stiffness are returned to the solver of the macroscopic finite element model. The solver uses this data to update the response state of the structure. The above process is repeated until all preset loading steps are completed. After all loading steps are completed, the overall mechanical response results of the composite material structure under the load condition are output, including the displacement distribution field, stress distribution field, strain distribution field, and response curves of key parts.

[0036] Appendix Figure 7 A flowchart illustrating the response calculation phase is provided. (See attached image.) Figure 7 As shown, in the online phase, macroscopic strain is first obtained from ABAQUS, and then strain decomposition and underlying constitutive solution are performed from top to bottom through the deep materials network proxy model. Then, the macroscopic equivalent stress and stiffness are obtained through bottom-up equivalent convergence, and finally the structure response is updated by returning to ABAQUS.

[0037] This implementation introduces a pre-trained deep materials network surrogate model, replacing the high-cost computational process of solving microscopic unit cell problems simultaneously at each integration point in traditional multi-scale analysis with the rapid inference process of the surrogate model. The surrogate model is composed of building blocks with clear physical meaning. Each building block performs homogenization and rotation operations, making the model not only a numerical fitting tool but also embedding the mechanical mechanisms of composite materials. The top-down strain decomposition and bottom-up equivalent convergence mechanism establish a bidirectional information transmission channel between the macroscopic structural response and the microscopic component material behavior, enabling macroscopic calculations to fully reflect microscopic material behavior and significantly improving computational efficiency while ensuring analytical accuracy.

[0038] In one possible implementation, the steps for obtaining the deep material network proxy model are as follows: 1) Within the preset material parameter space of composite material components, multiple sets of material parameter combinations are generated by random sampling. The material parameter combinations include elastic modulus, shear modulus and Poisson's ratio. When randomly sampling the material parameters, the scaling factor of one phase material is fixed to eliminate the unit cell scale effect.

[0039] Specifically, when constructing the training dataset for the deep materials network proxy model, random sampling is performed within a predefined material parameter space for composite material components. It is assumed that the materials used during training are orthotropic, and the material parameters include the three elastic moduli in different directions for each component material. , , ), 3 shear moduli ( , , ) and 3 Poisson's ratios ( , , ), superscript The number represents the component material. When there are two component materials, ... .

[0040] To incorporate the anisotropy of materials and enable deep materials networks to learn the structure of individual cells as much as possible, Monte Carlo sampling is used to sample the aforementioned material properties. The modulus of the phase material in the tensile direction is randomly assigned a value. ,in, It represents a uniform distribution.

[0041] During the random sampling of material parameters, a scaling factor for the first phase material is fixed to eliminate unit cell size effects. Scaling factor Sample as follows: The scaling factor of the first phase material remains constant to eliminate the scaling effect of the unit cell. Then, according to... Update the tensile modulus of each material phase, where .

[0042] Shear modulus is sampled as follows: To ensure the positive definiteness of the flexibility matrix, Poisson's ratio is calculated according to... Perform sampling.

[0043] 2) For each combination of material parameters, the equivalent mechanical parameters corresponding to each combination of material parameters are calculated based on the micromechanical model, and a training dataset is constructed consisting of the combination of material parameters and the equivalent mechanical parameters corresponding to the combination of material parameters.

[0044] In other words, for each combination of material parameters obtained through the above sampling method, a micromechanical unit cell model is constructed. The selection of the micromechanical unit cell model is determined according to the actual simulation requirements of composite materials, and can include various micromechanical models such as fiber reinforcement, lamination, weaving, or particle reinforcement. High-fidelity numerical calculations are performed based on the micromechanical model to obtain the equivalent mechanical parameters corresponding to that set of material parameters. The equivalent mechanical parameters include the equivalent stiffness matrix or the equivalent flexibility matrix. Each combination of material parameters and its corresponding equivalent mechanical parameters are paired to construct a training dataset.

[0045] 3) Using the equivalent mechanical parameters in the training dataset as the training objective, train the constructed deep material network, adjust the trainable parameters in each building block to minimize the error between the prediction output of the deep material network and the training objective, and obtain the deep material network surrogate model.

[0046] During training, the trainable parameters of each building block in the deep materials network are continuously adjusted to gradually reduce the error between the equivalent mechanical parameters predicted by the deep materials network and the training target, until the error converges to a preset range. After training, the trained model is converted into a deployable proxy model, and a model calling interface for interfacing with structural analysis programs is generated for online integration.

[0047] Appendix Figure 6 The training process for deep materials networks is demonstrated. (See attached image.) Figure 6 As shown, the offline stage includes generating a training dataset based on random sampling, constructing a deep materials network, training with equivalent mechanical parameters as the target, and finally obtaining a trained surrogate model.

[0048] This embodiment effectively eliminates the bias caused by the unit cell scale effect in the training data by adopting a sampling strategy that fixes the scaling factor of the first phase material. This allows the trained surrogate model to more accurately learn the true impact of material phase contrast on equivalent mechanical properties, rather than being interfered with by the overall scaling of the unit cell. This training data generation method improves the generalization ability and prediction robustness of the surrogate model.

[0049] In one implementation, the trainable parameters of the building block include weight parameters characterizing the volume fraction distribution of the sub-building blocks of the building block, and rotation angle parameters characterizing the overall spatial orientation of the building block.

[0050] To elaborate, in the deep materials network proxy model, each building block contains two types of trainable parameters.

[0051] The first type of trainable parameter is the weight parameter, which characterizes the volume fraction distribution between two sub-constructions within a construct. To describe the impact of phase volume fraction on the homogenization process, weight parameters are introduced at the bottom-level nodes. This is used to characterize the volume fraction distribution of micro-components in each building unit. A building block contains a first sub-building block and a second sub-building block, with corresponding weight parameters of [missing parameters]. and The volume fraction of each sub-construction block is determined by the corresponding weight parameters through a normalized mapping. The volume fraction of the first sub-construction block... Volume fraction of the second sub-constructing block .

[0052] The second type of trainable parameter is the rotation angle parameter, used to characterize the overall spatial orientation of the building blocks. To enhance the representational flexibility of deep material networks, rotation operations are introduced, and these are implemented through trainable parameters. Controlling the overall orientation of each building block. In three-dimensional space, any rotation can be achieved through a combination of three basic rotations, the rotation matrix. It can be decomposed into the product of three fundamental rotation matrices. Three-dimensional rotation is decomposed into... The three rotational steps of the representation: The rotation matrix , , The specific form is as follows: The transformation matrix for rotation around the first coordinate axis:

[0053] The transformation matrix for rotation around the second coordinate axis:

[0054] The transformation matrix for rotation around the third coordinate axis:

[0055] During the training phase, weight parameters and rotation angle parameters All parameters are used as trainable variables in backpropagation and parameter updates. After training, these parameters are determined and remain fixed during the online inference phase.

[0056] In this embodiment, by setting volume fraction distribution and spatial orientation as trainable parameters, the deep materials network surrogate model can autonomously learn and optimize these parameters reflecting the internal structural characteristics of materials during training, without relying on manual presets or empirical formulas. This design allows the surrogate model to flexibly adapt to different types of microstructures, enhancing the model's expressive power and applicability.

[0057] In one possible implementation, the step of calling a preset constitutive model of the component materials to calculate the mechanical response of each component under the current loading step includes: calculating the stress increment and tangential stiffness of each component based on the strain increment corresponding to each component material at the bottom layer of the deep material network proxy model obtained by decomposition, combined with the historical state variables of each component material at the end of the previous loading step.

[0058] Specifically, after the deep materials network proxy model performs a top-down strain decomposition, the macroscopic strain is distributed to the component material nodes at the bottom layer of the network. For each component material node at the bottom layer, a pre-set component material constitutive model is invoked to calculate the mechanical response under the current loading step.

[0059] Before performing the homogenization operation, the homogenization stiffness matrix of the building blocks needs to be determined. Homogenization function In mathematics, this can be represented as For a two-layer building block, the homogenization function The analytical form is derived based on the interface equilibrium condition and the kinematic constraint condition.

[0060] Assuming the overall stress of the building blocks before homogenization and rotation ,strain They are respectively denoted as Stress in the two sub-building blocks ,strain They are respectively denoted as .

[0061] The interface equilibrium condition of the building block is expressed as: The kinematic constraints are as follows: In directions where strain is unequal, the building blocks satisfy the average strain relationship. Therefore, we can obtain .

[0062] By utilizing the constitutive relation of the sub-construction block material, the unknown strain components of sub-construction block 1 can be determined. , and Expressed as a function of overall strain:

[0063] in, , ,as well as

[0064] In directions 11, 22, and 12, the sub-construction blocks satisfy kinematic constraints, and the strain condensation tensor of sub-construction block 1 can be obtained. : ,in , , All other components are 0.

[0065] The relationship between stress and strain of the building block before the rotation operation is expressed as: .

[0066] Finally, the homogenized stiffness matrix before the block rotation operation is expressed as: .

[0067] Taking a node representing a specific component material as an example, the input data received by this node includes the strain increment of the current loading step. Simultaneously, this node also stores the historical state variables at the end of the previous loading step. When calling the constitutive model, the current strain increment and the historical state variables are used as input. The constitutive model calculates the stress increment and tangential stiffness of this component material node in the current loading step based on the preset material constitutive relation.

[0068] This embodiment preserves an independent constitutive model invocation mechanism for each component material at the underlying layer of the proxy model, enabling the accurate capture and calculation of the nonlinear mechanical behavior of different component materials at the lowest level. The homogenization function is derived based on interface equilibrium conditions and kinematic constraints. The analytical form provides a forward propagation path with clear physical meaning for deep material networks. These mesoscale nonlinear responses are then reflected to the macroscale through bottom-up equivalent convergence, thus achieving a true coupling between mesoscale nonlinear behavior and macroscopic structural responses.

[0069] In one possible implementation, the solver of the macroscopic finite element model is the solver of the ABAQUS finite element analysis software, and the deep material network proxy model interacts with the solver through a predefined model call interface.

[0070] Specifically, the workflow of the model call interface is as follows: In each loading step at each integration point of the macroscopic finite element model, the ABAQUS solver calculates the macroscopic strain increment at that integration point and then passes the macroscopic strain increment to the deep materials network proxy model via the call interface. Upon receiving the data, the proxy model internally performs a top-down strain decomposition, decomposing the macroscopic strain increment and distributing it to each bottom-level node. Each bottom-level node calls the constitutive model and, in conjunction with its own historical state variables, calculates the stress increment, residual stress increment, and tangential stiffness of that node in the current loading step. Subsequently, the proxy model performs bottom-up homogenization calculations on the physical quantities calculated by each node, generating macroscopic equivalent stress and macroscopic equivalent tangential stiffness. These two results are returned to the ABAQUS solver through the same call interface. The solver uses the returned data to update the stress state and stiffness contribution at that integration point for equilibrium solution and response update of the macroscopic structure.

[0071] The model call interface can be implemented as a user-defined materials subroutine in ABAQUS. Within the subroutine framework, the Deep Materials Network proxy model is loaded and called in the form of a pre-trained parameter file.

[0072] By encapsulating the deep materials network proxy model into a standardized model calling interface, seamless integration between the proxy model and the commercial finite element software ABAQUS is achieved. Engineers can directly call the proxy model for calculations without changing their conventional workflow for composite material structure analysis using ABAQUS, significantly lowering the application threshold of the new method and improving engineering deployability.

[0073] In one possible implementation, the microstructure of the composite material includes at least one of a fiber-reinforced structure, a laminated structure, a braided structure, or a particle-reinforced structure.

[0074] For fiber-reinforced structures, the micromechanical model consists of continuous or chopped fibers embedded in the matrix material. The fiber orientation, volume fraction, and distribution determine the degree of anisotropy of the material. For laminated structures, the micromechanical model consists of single-layer plates with different layup angles stacked in a specific order, with each layer connected by interfaces. For woven structures, the micromechanical model consists of warp and weft yarns interwoven according to a specific weaving pattern. For particle-reinforced structures, the micromechanical model consists of reinforcing particles randomly or regularly distributed within the matrix material.

[0075] For different types of microstructures, during the surrogate model training phase, a corresponding micromechanical model for that structure type is constructed as a high-fidelity numerical solution object, generating a matching training dataset. This allows for the training of a deep materials network surrogate model suitable for that structure type. The network structure and training process of the deep materials network surrogate model remain consistent and are unaffected by changes in microstructure type. During the training phase, surrogate models with different parameters can be trained to proxy different micromechanical models. In the online phase, different types of constitutive models can be replaced at the bottom-level nodes of the surrogate model to achieve nonlinear analysis for different material behaviors.

[0076] This method does not rely on any specific microstructural form, but rather provides a general framework for building and applying surrogate models. By changing the micromechanical model used in the training phase, surrogate models applicable to different structural forms such as fiber reinforcement, lamination, braiding, and particle reinforcement can be quickly obtained. This design expands the applicability of the method, giving it good versatility and scalability, enabling efficient and accurate modeling of most composite material structures.

[0077] In one possible implementation, the constitutive model of the component material includes a linear elastic constitutive model or an elastoplastic constitutive model.

[0078] For example, a linear elastic constitutive model is used for brittle reinforced materials such as boron fibers and carbon fibers. The linear elastic constitutive model only requires two material parameters, the elastic modulus and Poisson's ratio, and maintains a linear relationship between stress and strain, without involving plastic deformation and damage accumulation.

[0079] For example, an elastoplastic constitutive model is used for tough matrix materials such as aluminum and polymer matrices. In addition to elastic constants, the elastoplastic constitutive model also requires the definition of yield criteria, hardening laws, and plastic flow rules.

[0080] At the bottom-level nodes of the proxy model, the corresponding constitutive model type is invoked according to the actual mechanical properties of each component material. The calculation results of different constitutive models are output in the form of stress increments and tangential stiffness for use in equivalent convergence.

[0081] By supporting different types of constitutive models at the bottom-level nodes, the surrogate model can accurately reflect the inherent mechanical behavior characteristics of different components in composite materials. Whether it is the linear elastic response of the brittle reinforcing phase or the elastoplastic response of the tough matrix phase, it can be accurately characterized, making the surrogate model applicable to the structural analysis of composite materials in a variety of material systems.

[0082] The technical effects of the present invention will be verified and explained through specific calculation examples below.

[0083] To evaluate the number of network layers The impact on deep material networks, selected The networks with epochs 3, 4, 5, and 6 were compared. The evolution history of the average error between the training and validation sets, assuming each network was trained for 500 epochs, is shown in the appendix. Figure 3 As shown in (a) and (b) in the figure, the number of layers has little impact on the deep material network surrogate model, based on the average error.

[0084] Appendix Figure 4 The number of activated nodes in the bottom layer of the deep materials network was compared before and after training. In the initial training phase, all nodes in the bottom layer were active, with 8, 16, 32, and 64 activated nodes for the different network depths considered. After training convergence, the number of activated nodes decreased to 5, 9, 20, and 38, respectively. Each activated node represents an integration point in subsequent multi-scale calculations. The current unit cell contains 576 finite element elements, each containing 8 integration points, for a total of 4608 integration points. The significant reduction in the number of activated nodes after training demonstrates that the surrogate model indeed achieves significant model compression.

[0085] The results were validated on a single unit cell by comparing the predictions of the deep material network surrogate model with the calculations of the finite element method under uniaxial loading-unloading conditions and complex combined loading paths, as shown in the attached figure. Figure 5 As shown. The results indicate that under three uniaxial loading conditions—transverse tension, transverse shear, and axial shear—as well as complex loading conditions with multi-directional coupling, the network depth is [value missing]. The surrogate models =3, 4, and 5 can all reproduce the homogenized stress-strain response curves of the composite material well. They maintain high consistency with FEM results in both the loading and unloading stages, and can accurately characterize the nonlinear mechanical response characteristics of the material under different loading paths. A comprehensive comparison shows that... =4 has the best overall performance. =3 and =5 also exhibits good predictive ability and stability; in contrast, the network depth of When the value is 6, the prediction bias is relatively large. This indicates that the surrogate model proposed in this invention has good prediction performance for homogenized responses under three uniaxial loading conditions and complex loading conditions within a reasonable network depth range, demonstrating good stability, robustness and applicability, and can be used for efficient response prediction of composite materials under various loading paths.

[0086] To comprehensively evaluate the applicability of the FE×DMN proposed in this invention in structural simulation, three structural models were selected for verification: a ∑ structure, an L-shaped perforated plate, and a D-shaped plate. The geometric dimensions, fiber orientation, boundary conditions, and loading methods of these structures are shown in the attached figures. Figure 8As shown, these structures exhibit significant spatially non-uniform stress and strain distributions, making them well-suited for evaluating the prediction accuracy of the proposed FE×DMN. In the analysis, the prediction results of FE×DMN are compared with the accuracy and efficiency of the traditional FE×FVDAM method.

[0087] All examples used uniaxial boron / aluminum (B / Al) composite materials with a fiber volume fraction of 20%. The boron fibers were modeled using a linear elastic constitutive model, while the aluminum matrix was modeled using an elastoplastic constitutive model. Material parameters are shown in Table 1 below: Table 1 Elastic-plastic parameters of boron / aluminum composites

[0088] In numerical verification, the traditional FE×FVDAM parallel multi-scale method is used as a high-fidelity reference solution, and the prediction results of FE×DMN are compared and evaluated from two aspects: the overall distribution and the local response.

[0089] At the structural level, for typical stress and strain distributions in each example, the spatial distribution contour maps and absolute differences predicted by FE×DMN and FE×FVDAM under representative loading steps are compared. For monotonic loading examples, the final loading step is selected for comparison, and the comparison results for the ∑ structure are attached. Figure 9 As shown in the attached figure, the comparison results of the L-shaped perforated plate are as follows. Figure 10 As shown. For examples involving loading-unloading processes, comparative analyses are performed at the final loading and unloading steps respectively. The results for the D-shaped board are attached. Figure 11 and attached Figure 12 As shown in the figure. The results show that in the four types of structural examples, both methods exhibit highly consistent distribution characteristics in the stress concentration region and the strong gradient region, and the maximum absolute error is less than 5% of the corresponding physical quantity peak value, indicating that FE×DMN can stably track the high-fidelity reference solution.

[0090] At the local response level, force-displacement and stress-strain response curves were further extracted and compared at the maximum displacement point, the high-efficiency stress region, and some random locations. (See attached image) Figure 13 , 13 As shown in Figure 14, the prediction curves of FE×DMN and FE×FVDAM highly overlap at all critical locations and load stages.

[0091] Furthermore, a comparative analysis of computational efficiency and resource consumption was conducted. All multi-scale structural simulations were performed on a high-performance workstation equipped with an AMD EPYC 9654 processor, using ABAQUS 2024 and parallel computation with 24 CPU cores. Table 2 below compares the computation time and memory consumption of FE×DMN and FE×FVDAM at the structural model level: Table 2 compares the FE×DMN and FE×FVDAM methods in terms of memory usage and computation time.

[0092] The results show that, compared with the traditional FE×FVDAM parallel multi-scale method, FE×DMN reduces the online computation time by more than two orders of magnitude, while significantly reducing memory usage, demonstrating a clear advantage in engineering efficiency.

[0093] Based on the above four types of structural examples, it can be concluded that the proposed FE×DMN method can significantly improve computational efficiency while maintaining high prediction accuracy under different geometric configurations, fiber orientations, and load conditions, verifying its reliability and engineering applicability in large-scale composite material structure simulation. This invention is applicable to the prediction of mechanical properties of composite material structures under complex loading conditions and can be widely used in engineering fields such as aerospace, energy equipment, and high-performance material structure design and analysis.

[0094] 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 in 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 a surrogate model analysis method for the mechanical response of composite material structures.

[0095] 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 terminal's operating system. 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 surrogate model analysis method for the mechanical response of a composite material structure in the above embodiments.

[0096] 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.

[0097] 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.

[0098] 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 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0099] 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.

[0100] This invention also provides a computer program product for executing any of the above-described methods for analyzing the mechanical response of composite material structures using a surrogate model. Since the computer program product provided by this invention belongs to the same inventive concept as the above-described method for analyzing the mechanical response of composite material structures using a surrogate model, 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.

[0101] 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.

[0102] 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 surrogate model analysis method for the mechanical response of composite material structures, characterized in that, include: A deep material network proxy model is obtained to characterize the equivalent mechanical behavior of the microstructure of composite materials. The deep material network proxy model is a pre-trained network model. The network structure of the deep material network proxy model consists of multi-level building blocks. Each building block corresponds to a homogenization operation based on the constitutive relation of the component materials and a rotation operation characterizing the material orientation. The trainable parameters of the building blocks are determined by training data composed of multiple sets of material parameters obtained by sampling the material parameter space of the composite material components and the equivalent mechanical parameters of the micromechanical model corresponding to the multiple sets of material parameters. A macroscopic finite element model of the composite material structure to be analyzed is established, boundary conditions and load paths are applied to the macroscopic finite element model, and macroscopic strain data at each integration point of the macroscopic finite element model are calculated. The macroscopic strain data is input into the deep material network proxy model, which performs a top-down strain decomposition, assigns the macroscopic strain to the bottom layer of the deep material network proxy model, and calls the preset component material constitutive model to calculate the mechanical response of each component under the current loading step. The deep material network proxy model performs bottom-up equivalent convergence and calculates the macroscopic equivalent stress and macroscopic equivalent tangential stiffness at the integration point based on the mechanical response of each component. The macroscopic equivalent stress and macroscopic equivalent tangential stiffness are returned to the solver of the macroscopic finite element model to update the structural response state, and the overall mechanical response result of the composite material structure is output after all loading steps are completed.

2. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The steps for obtaining the deep materials network proxy model include: Within a preset material parameter space for composite material components, multiple combinations of material parameters are generated through random sampling. These combinations of material parameters include elastic modulus, shear modulus, and Poisson's ratio. When randomly sampling the material parameters, the scaling factor of one phase material is fixed to eliminate the unit cell scale effect. For each combination of material parameters, the equivalent mechanical parameters corresponding to each combination of material parameters are calculated based on the micromechanical model, and a training dataset is constructed consisting of the material parameter combination and the equivalent mechanical parameters corresponding to the material parameter combination. The equivalent mechanical parameters in the training dataset are used as training targets to train the constructed deep materials network. The trainable parameters in each building block are adjusted to minimize the error between the prediction output of the deep materials network and the training target, thus obtaining the deep materials network proxy model.

3. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The trainable parameters of the construct include weight parameters that characterize the volume fraction distribution of the sub-construction blocks of the construct and rotation angle parameters that characterize the overall spatial orientation of the construct.

4. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The calculation of the mechanical response of each component under the current loading step by calling the preset component material constitutive model includes: Based on the strain increments of each component material at the bottom layer of the deep material network proxy model obtained from the decomposition, and combined with the historical state variables of each component material at the end of the previous loading step, the stress increments and tangential stiffness of each component are calculated.

5. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The solver of the macroscopic finite element model is the solver of the ABAQUS finite element analysis software, and the deep material network proxy model interacts with the solver through a predefined model call interface.

6. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The microstructure of the composite material includes at least one of fiber-reinforced structure, laminated structure, woven structure, or particle-reinforced structure.

7. The surrogate model analysis method for the mechanical response of composite material structures according to claim 1, characterized in that, The constitutive model of the constituent materials includes a linear elastic constitutive model or an elastoplastic constitutive model.

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 surrogate model analysis method for the mechanical response of a composite material structure 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 proxy model analysis method for the mechanical response of a composite material structure 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 proxy model analysis method for the mechanical response of a composite material structure as described in any one of claims 1 to 7.

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