A composite structure multi-scale progressive failure analysis method fusing machine learning models

Abstract

The application relates to the field of composite material damage analysis methods, in particular to a composite material structure multi-scale progressive damage analysis method fusing a machine learning model, which comprises the following steps: based on a homogenization theory, combining a finite element method and the machine learning model to establish a multi-scale interactive calculation framework; based on a continuous medium damage mechanics theory, establishing a composite material multi-scale progressive damage model; based on a finite element model, realizing the composite material structure multi-scale progressive damage analysis through secondary development of a program.The application establishes the composite material structure multi-scale progressive damage analysis method based on the homogenization theory and the continuous medium damage mechanics theory, and fuses the machine learning model of K-means++ clustering, so that the interactive calculation of macro / micro scales can be realized, the calculation amount of macro / micro scale repeated iteration solving can be reduced, and the calculation efficiency is improved while the calculation precision is ensured.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of composite material damage analysis methods, in particular to a composite material structure multi-scale progressive damage analysis method fusing a machine learning model. BACKGROUND

[0002] Compared with traditional metal materials, fiber reinforced resin matrix composites have the advantages of high specific stiffness and specific strength, excellent fatigue resistance and strong corrosion resistance, and have been widely used in the field of aerospace. In recent years, with the increasing application of composites in aircraft load-bearing structures, damage and failure during use has become a key problem, which threatens the safety and reliability of the aircraft, therefore, it is necessary to evaluate the load-carrying capacity and damage process of the composite structure by a reliable method.

[0003] The progressive damage analysis method based on the finite element method can effectively predict the strength and damage evolution process of the composite structure, and has been widely concerned by scholars and the industry at home and abroad. The macroscopic mechanical response of the composite structure depends on the microstructure and the performance of the constituent materials, and also determines the micro stress and strain field and damage distribution. The entire damage process usually covers different scales, including various damage modes at the micro scale (such as matrix cracking, interfacial debonding and fiber breakage) and overall damage of the structure at the macro scale. Therefore, a multi-scale method is needed to study the progressive damage process of the composite structure.

[0004] However, in actual use, the two-scale interactive calculation needs to repeatedly iterate the macro / micro scale stress and strain response and damage, which brings difficulties to practical application due to the huge amount of calculation. SUMMARY

[0005] The present application aims to provide a composite material structure multi-scale progressive damage analysis method fusing a machine learning model, to solve the problem of huge amount of calculation caused by repeated iteration of macro / micro scale stress and strain response and damage, which brings difficulties to practical application.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical scheme: a composite material structure multi-scale progressive damage analysis method fusing a machine learning model, comprising the following steps:

[0007] S1, based on the homogenization theory, combining the finite element method and the machine learning model, establishing a multi-scale interactive calculation framework, specifically:

[0008] S11, at the micro scale, taking a representative volume element therefrom and applying periodic boundary conditions thereto, and based on the homogenization theory, establishing a coupling relationship between the macro / micro scale models;

[0009] S12, by introducing K-means++ clustering model, the strain information of potential damage Gauss point in macro model is clustered and analyzed, and a multi-scale interactive calculation framework is established;

[0010] S2, based on the theory of continuum damage mechanics, a composite multi-scale progressive damage model is established, specifically:

[0011] S21, for the micro representative volume element model, the maximum stress criterion is used as the damage initiation criterion for the fiber region, and the modified Von Mises criterion is used as the damage initiation criterion for the matrix region. After identifying the damage initiation of fiber and matrix material, the damage evolution model is used to calculate the damage coefficient, and the material performance is gradually degraded;

[0012] S22, for the macro model, set the potential damage judgment condition, which is used to judge whether the Gauss point needs to call the micro representative volume element model for calculation, and use the three-dimensional Hashin criterion as the potential damage judgment condition;

[0013] S3, based on the finite element model, realize the multi-scale progressive damage analysis of composite structure by secondary development program, specifically:

[0014] S31, according to the configuration and size of composite structure and microstructure composition, the finite element models of macro structure and micro representative volume element are established respectively;

[0015] S32, firstly, the micro representative volume element model is analyzed by preliminary stress and strain, and the equivalent elastic constant of the composite material under the undamaged state is obtained by homogenization calculation, which is transmitted to the macro model;

[0016] S33, stress and strain analysis is carried out on the macro model, and the potential damage Gauss point is identified by using the potential damage judgment condition, and K-means++ model is used for clustering analysis;

[0017] S34, the strain information after clustering is transmitted to the micro representative volume element model, and the micro progressive damage analysis is carried out, and the global average stress and equivalent elastic constant after damage are obtained by homogenization calculation, which are transmitted to the macro model, and step S33 is entered;

[0018] S35, repeat the process of step S33 and step S34 until the macro structure fails, and obtain the mechanical response results and multi-scale progressive damage process of composite structure.

[0019] Preferably, the coupling relationship expression of macro / micro scale model established in step S11 based on homogenization theory is:

[0020]

[0021] In the formula, ui Displacement component of a point on the boundary of the micro RVE model, subscript j + and j - represent the positive and negative directions along the direction, respectively;

[0022] is the distance between parallel boundary surfaces;

[0023] is the micro global average strain, equal to the macro strain transmitted by the macro model at the corresponding Gauss point; the constitutive relation of the fiber material in the RVE is expressed as:

[0024]

[0025] In the formula, Δε and Δσ are micro strain increment and stress increment, respectively;

[0026] C ε is the micro local tangent stiffness matrix;

[0027] x is the micro coordinate, and V is the calculation domain of the micro RVE model;

[0028] The expression of the global average strain and stress obtained by homogenization is:

[0029]

[0030] In the formula, is the macro coordinate;

[0031] ε and σ are the local strain and stress tensors in the micro RVE model, respectively;

[0032] and are the global average strain and stress tensors of the micro RVE model, and are the macro strain and stress tensors, respectively;

[0033] The constitutive relation expression of the macro scale is:

[0034]

[0035] In the formula, and are the macro strain increment and stress increment, respectively;

[0036] is the macro local tangent stiffness matrix;

[0037] is the calculation domain of the macro model.

[0038] Preferably, the strain information of the potential damage Gauss point in the macro model in the step S12 is subjected to cluster analysis, specifically:

[0039] The K-means++ clustering model is used to cluster the damage Gauss points based on the strain state data, and the cluster centers are determined through repeated probability calculation and roulette selection until all the cluster centers do not change.

[0040] Preferably, the fiber region damage initiation criterion in the step S21 comprises:

[0041] Fiber tensile damage

[0042]

[0043] Fiber compression damage

[0044]

[0045] In the formula, is the fiber longitudinal stress, T f and C f are the tensile strength and compressive strength of the fiber, respectively;

[0046] The matrix region damage initiation criterion in the step S21 comprises:

[0047]

[0048]

[0049] In the formula, I1 and I2 are the first stress invariant and the second stress invariant of the matrix, respectively, σ 11 , σ 22 , and σ 33 are the normal stresses in three directions of the matrix, σ 12 , σ 23 , and σ 13 are the shear stresses of the matrix, T m and C m are the tensile strength and compressive strength of the matrix, respectively.

[0050] Preferably, the damage coefficient is calculated using a damage evolution model in the step S21, and the material properties are gradually degraded, specifically: the equivalent displacement is used as the damage variable, the damage coefficient is determined by calculating the equivalent displacement under the damage initiation state and the complete failure state, and the elastic constant of the material is multiplied by a degradation coefficient to realize the gradual degradation of the material properties.

[0051] Preferably, the three-dimensional Hashin criterion in the step S22 comprises:

[0052] Fiber damage:

[0053]

[0054] Matrix damage:

[0055]

[0056] In the formula, σ 11 , σ 22 and σ 33 are normal stresses;

[0057] σ 12 , σ 13 and σ 23 are shear stresses;

[0058] X T and X C are the longitudinal tensile and compressive strengths of the composite material, respectively;

[0059] Y T and Y C are the transverse tensile and compressive strengths of the composite material, respectively;

[0060] S 12 , S 13 and S 23 are the shear strengths of the composite material.

[0061] Preferably, in the step S31 of establishing the finite element model of the macrostructure and the micro-representative volume element, an external load is applied to the macrostructure model, and a periodic boundary condition is applied to the micro-representative volume element model.

[0062] Compared with the prior art, the present application has the following beneficial effects:

[0063] 1. The present application is based on the homogenization theory and the damage mechanics theory of continuous medium, and establishes a multi-scale progressive failure analysis method for composite material structure, and integrates a machine learning model of K-means++ clustering, and proposes a new multi-scale progressive failure algorithm, which can realize the interactive calculation of macro / micro scales on the one hand, and can reduce the calculation amount of macro / micro scale iterative solution on the other hand, while ensuring the calculation accuracy and improving the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 is a flowchart of the multi-scale progressive failure analysis method for composite material structure of the present application;

[0065] Figure 2 is a flowchart of the multi-scale progressive failure analysis method for composite material structure of the present application. DETAILED DESCRIPTION

[0066] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and completely. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0067] Please refer to Figures 1-2 The present application provides a technical solution: a composite structure multi-scale progressive failure analysis method based on a fusion machine learning model, comprising the following steps:

[0068] S1, based on the homogenization theory, the finite element method and the machine learning model are combined to establish a multi-scale interactive calculation framework, specifically:

[0069] S11, on the micro scale, considering that the composite material has a periodic repeating structure, a representative volume element (RVE) is taken, which is composed of fibers and matrix. In order to ensure the continuity of displacement and stress, periodic boundary conditions need to be applied to the RVE, which can be expressed as:

[0070]

[0071] In the formula, u i is the displacement component of the point on the boundary of the micro RVE model, and the superscripts j + and j - respectively represent the positive and negative directions along the direction;

[0072] is the distance between the parallel boundary surfaces;

[0073] is the micro global average strain, which is equal to the macro strain transmitted by the macro model at the corresponding Gauss point. The fiber material in the RVE can be regarded as an isotropic material, and the matrix material in the RVE can be regarded as an isotropic material, and the constitutive relationship can be expressed as:

[0074]

[0075] In the formula, Δε and Δσ are micro strain increment and stress increment respectively;

[0076] C ε is the micro local tangent stiffness matrix, x is the micro coordinate, and V is the calculation domain of the micro RVE model.

[0077] Based on the strain and stress field results calculated in the micro RVE model, the global average strain and stress are obtained by homogenization:

[0078]

[0079] where, are macroscopic coordinates;

[0080] ε and σ are local strain and stress tensors within the micro RVE model, respectively;

[0081] and are global average strain and stress tensors of the micro RVE model, and are macroscopic strain and stress tensors, respectively.

[0082] Based on the calculated global average strain and stress, the macroscopic equivalent elastic constants of the composite material can be estimated through the constitutive relation of the elastic body, which are then passed to the corresponding Gauss points in the macro model. At the macro scale, the constitutive relation expression is:

[0083]

[0084] where, and are macroscopic strain and stress increments, respectively;

[0085] is the macroscopic local tangent stiffness matrix;

[0086] is the computational domain of the macro model.

[0087] S12, in the process of multi-scale progressive damage analysis of composite structures, the elastic constants and stress-strain redistribution of the local damage position in the macro model need to be updated through repeated multi-scale interactive calculation based on the homogenization theory. If each Gauss point of the macro model is associated with a micro RVE model, it will bring huge computational cost.

[0088] In fact, for the undamaged Gauss points in the macro model, there is no need to call the micro RVE model to update the calculation of the macroscopic equivalent elastic constants, so the potential damage judgment condition is set in the macro model, and only the Gauss points that meet the condition are called to calculate the micro RVE model. Considering that under the action of incremental external load, the number of Gauss points with potential damage in the macro model will increase significantly with the expansion of damage, and many of these points have similar strain states, in order to reduce the computational cost, the K-means++ clustering model is used to cluster these damage Gauss points based on strain state data.

[0089] where, the first cluster center c1 is randomly selected from the data set (x1, x2,..., x n ). Then, the data points x iThe Euclidean distance to the cluster center c1, then the shortest distance between the data point and the current cluster center is calculated, and then the probability of each data point being selected as the next cluster center can be calculated by formula (5):

[0090]

[0091] According to the calculated selection probability of each data point, the commonly used roulette method is used to select the next cluster center. By repeating the above probability calculation and roulette selection, k initial cluster centers can be selected from the data set. Then, the distance between the data point and each initial cluster center can be calculated by formula (5), and the data point is assigned to the cluster where the nearest cluster center is located according to the shortest distance principle.

[0092] Then, the cluster centers are updated by averaging the data points in each cluster, which can be represented as:

[0093]

[0094] Finally, the above data clustering process and cluster center updating are repeated until all cluster centers do not change.

[0095] S2, based on the theory of continuum damage mechanics, a multi-scale progressive damage model of composite materials is established, specifically:

[0096] S21, on the microscale, for the fiber region in the RVE model, the maximum stress criterion is used as the fiber damage initiation criterion:

[0097] Fiber tensile damage

[0098]

[0099] Fiber compression damage

[0100]

[0101] where, is the fiber longitudinal stress, T f and C f are the tensile strength and compressive strength of the fiber, respectively;

[0102] For the matrix region in the RVE model, the modified Von Mises criterion is used as the matrix damage initiation criterion:

[0103]

[0104]

[0105] where I1 and I2 are the first and second stress invariants of the matrix, σ 11 22 33 are the normal stresses in three directions of the matrix, σ 12 23 13 are the shear stresses of the matrix, T m m are the tensile and compressive strengths of the matrix, respectively.

[0106] After the fiber and matrix material damage initiation is identified by the above criteria, the damage coefficient is calculated by using the damage evolution model:

[0107]

[0108] where δ is the equivalent displacement;

[0109] δ0 and δ f are the equivalent displacements in the damage initiation state and the complete failure state, respectively.

[0110] The damage coefficient d is in the range of [0, 1], and the material performance gradually degrades as the damage coefficient increases. The degradation is realized by multiplying the elastic constants of the material by a degradation coefficient γ, and the relationship between d and γ is:

[0111] γ = 1 - d (12)

[0112] According to the degraded material elastic constants, the damage stiffness matrix of the material is updated, and the damage constitutive model is:

[0113]

[0114] S22. In the multi-scale interactive calculation process of the progressive damage of the composite structure, the damage state of the Gauss point in the macroscopic model depends on the damage analysis results of the RVE model, and there is no need for a macroscopic damage initiation criterion and a damage evolution model.

[0115] However, in order to reduce the calculation cost, a potential damage judgment condition needs to be set in the macroscopic model, which is only used to preliminarily judge whether the Gauss point needs to call the micro RVE model for calculation. The commonly used three-dimensional Hashin criterion is adopted:

[0116] Fiber damage:

[0117]

[0118] Matrix damage:

[0119]

[0120] where σ 11 ​​​​​, σ 22 and σ 33 is the normal stress;

[0121] σ 12 , σ 13 and σ 23 are shear stresses;

[0122] X T and X C are the longitudinal tensile and compressive strengths of the composite material, respectively;

[0123] Y T and Y C are the transverse tensile and compressive strengths of the composite material, respectively;

[0124] S 12 , S 13 and S 23 are the shear strengths of the composite material.

[0125] S3, realize multi-scale progressive damage analysis of the composite material structure through secondary development program, and the algorithm flow chart is shown in Figure 2 , and specifically:

[0126] S31, establish finite element models of the macroscopic structure and the microscopic RVE according to the configuration and size of the composite material structure and the composition of the microscopic structure, wherein the external load is applied on the macroscopic structure model, and the periodic boundary condition is applied on the microscopic RVE model;

[0127] S32, in the multi-scale progressive damage analysis process of the composite material structure, firstly, perform preliminary stress and strain analysis on the microscopic RVE model, and perform homogenization processing on the calculation results to obtain the equivalent elastic constant of the composite material in the undamaged state, and transfer the equivalent elastic constant to the macroscopic model;

[0128] S33, after the macroscopic model receives the information transferred by the microscopic RVE model, perform stress and strain analysis, and identify the possible damage Gauss points using the latent damage judgment condition, and based on the strain state of these Gauss points, perform clustering analysis using the K-means++ clustering model;

[0129] S34, transfer the strain information after the clustering analysis to the microscopic RVE model to perform microscopic progressive damage analysis, calculate the global average stress and the equivalent elastic constant of the composite material after damage based on the homogenization theory, and transfer the information to the macroscopic model to enter step S33;

[0130] S35, repeat the process of step S33 and step S34 until the macroscopic structure fails, and obtain the mechanical response results of the composite material structure and the multi-scale progressive damage process.

[0131] The application is based on the homogenization theory, combines the finite element method and the machine learning model, and establishes a multi-scale interactive calculation framework, on the micro scale, the periodic repeating structure of the composite material is considered, a representative volume element (RVE) is taken for modeling and analysis, periodic boundary conditions are applied to the RVE, the coupling relationship between the macro / micro scale models is established based on the homogenization theory, and meanwhile, the K-means++ clustering model is introduced to perform clustering analysis on the strain information of the potential damage Gauss points in the macro model, so that the calculation amount is reduced.

[0132] Secondly, based on the continuous medium damage mechanics theory, a multi-scale progressive damage model of the composite material is established, on the micro scale, different damage initiation criteria and damage evolution models are adopted for the fiber and matrix regions to simulate the micro damage process of the composite material, and on the macro scale, potential damage judgment conditions are set to preliminarily judge whether the Gauss points need to call the micro RVE model for calculation.

[0133] Finally, the multi-scale progressive damage analysis of the composite material structure is realized through secondary development program, according to the configuration and size of the composite material structure and the micro structure composition, the finite element models of the macro structure and the micro RVE are established respectively, through multi-scale interactive calculation and clustering analysis, the elastic constants and stress-strain distribution of the local damage position in the macro model are constantly updated until the macro structure fails.

[0134] The application improves the calculation efficiency while ensuring the calculation accuracy, provides effective technical support for multi-scale damage evaluation of the composite material structure, and has important engineering application value and academic significance.

[0135] It should be noted that in this paper, relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the term "include", "contain" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment.

[0136] Although the embodiments of the application have been shown and described, it can be understood by those skilled in the art that various changes, modifications, replacements and variations can be made to the embodiments without departing from the principles and spirits of the application, and the scope of the application is defined by the appended claims and their equivalents.

Claims

1. A multi-scale progressive failure analysis method for composite structures integrated with a machine learning model, characterized by: The following steps are involved: S1. Based on homogenization theory, the finite element method and machine learning model are combined to establish a multi-scale interactive calculation framework. Specifically: S11. At the microscale, take a representative volume unit and impose periodic boundary conditions on it, and establish the coupling relationship between the macro-scale and micro-scale models based on the homogenization theory; S12. By introducing the K-means++ clustering model, the strain information of potential damage Gaussian points in the macro model is clustered and analyzed, and a multi-scale interactive calculation framework is established; S2. Based on the theory of continuum damage mechanics, a multi-scale progressive damage model for composite materials is established. Specifically: S21. For the microscopic representative volume element model, the maximum stress criterion is used as the damage initiation criterion for the fiber region, and the modified Von Mises criterion is used as the damage initiation criterion for the matrix region. After identifying the damage initiation of the fiber and matrix materials, the damage evolution model is used to calculate the damage coefficient and gradually degrade the material properties. S22. For the macro model, set potential damage judgment conditions to determine whether the Gaussian point needs to call the micro representative volume unit model for calculation, and use the three-dimensional Hashin criterion as the potential damage judgment condition; S3. Based on the finite element model, a secondary development program is used to implement multi-scale progressive failure analysis of composite structures. Specifically: S31. Establish finite element models of macrostructure and microrepresentative volume units according to the structural configuration, size and microstructure of the composite material; S32. First, perform a preliminary stress and strain analysis on the microscopic representative volume unit model, obtain the equivalent elastic constants of the composite material in the undamaged state through homogenization calculation, and transfer them to the macroscopic model; S33. Perform stress and strain analysis on the macro model, use potential damage judgment conditions to identify Gaussian points that may be damaged, and perform cluster analysis using the K-means++ model; S34, transferring the clustered strain information to the microscopic representative volume unit model, performing microscopic progressive failure analysis, calculating the global average stress and equivalent elastic constant after damage by homogenization, transferring them to the macroscopic model, and proceeding to step S33; S35. Repeat the process of step S33 and step S34 until the macrostructure fails, and obtain the mechanical response results of the composite material structure and the multi-scale progressive failure process.

2. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: The coupling relationship expression of the macro / micro scale model established based on the homogenization theory in step S11 is: Where u i is the displacement component of the point on the boundary of the microscopic RVE model, and the superscript j + and j - Represent the positive and negative directions along the direction respectively; is the distance between parallel boundary surfaces; is the microscopic global average strain, which is equal to the macroscopic strain transmitted at the corresponding Gaussian point of the macroscopic model; the constitutive relationship of the fiber material in RVE is expressed as: Where Δε and Δσ are the microscopic strain increment and stress increment respectively; C ε is the microscopic local tangent stiffness matrix; x is the microscopic coordinate, V is the computational domain of the microscopic RVE model; The expressions for global average strain and stress obtained by homogenization are: Where, is the macro coordinate; ε and σ are the local strain and stress tensors in the microscopic RVE model, respectively; and are the global average strain and stress tensors of the microscopic RVE model, and are also the macroscopic strain and stress tensors, respectively; The constitutive relation expression at the macroscopic scale is: Where, and are the macroscopic strain increment and stress increment, respectively; is the macroscopic local tangent stiffness matrix; is the computational domain of the macro model.

3. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: In step S12, cluster analysis is performed on the strain information of the potential damage Gaussian points in the macro model, specifically: The K-means++ clustering model is used to cluster these damage Gaussian points based on the strain state data, and the cluster centers are determined by repeated probability calculation and roulette wheel selection until all cluster centers remain unchanged.

4. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: The fiber area damage initiation criteria in step S21 include: Fiber stretch damage Fiber compression damage Where, is the longitudinal stress of the fiber, T f and C f are the tensile strength and compressive strength of the fiber, respectively; The matrix region damage initiation criteria in step S21 include: Where I1 and I2 are the first and second stress invariants of the matrix, respectively, σ 11 , σ 22 and σ 33 is the normal stress in three directions of the matrix, σ 12 , σ 23 and σ 13 is the shear stress of the matrix, T m and C m are the tensile strength and compressive strength of the matrix, respectively.

5. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: In step S21, a damage evolution model is used to calculate the damage coefficient, and the material properties are gradually degraded. Specifically, equivalent displacement is used as the damage variable, the damage coefficient is determined by calculating the equivalent displacement in the damage initial state and the complete failure state, and the elastic constant of the material is multiplied by a degradation coefficient to achieve gradual degradation of the material properties.

6. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: The three-dimensional hashing criterion in step S22 includes: Fiber damage: Matrix damage: Where, σ 11 , σ 22 and σ 33 is the normal stress; σ 12 , σ 13 and σ 23 is the shear stress; X T and X C are the longitudinal tensile and compressive strengths of the composite material, respectively; Y T and Y C are the transverse tensile and compressive strengths of the composite material, respectively; S 12 、S 13 and S 23 is the shear strength of the composite material.

7. The multi-scale progressive failure analysis method for composite materials structure integrated with a machine learning model according to claim 1, characterized in that: When establishing the finite element models of the macrostructure and the microscopic representative volume unit in step S31, an external load is applied to the macrostructure model, and a periodic boundary condition is applied to the microscopic representative volume unit model.

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