Multi-scale analysis method for woven composite material based on clustering order reduction

Abstract

The invention provides a woven composite material multi-scale analysis method based on clustering order reduction, and belongs to the technical field of composite material multi-scale damage evolution evaluation. The method comprises the following steps: 1, defining a microscopic damage constitutive model; defining a fiber damage constitutive equation and a matrix damage constitutive equation; 2, solving an RVE damage problem by using an SCA method; the method comprises the following steps: for a composite material RVE region, converting a control equation of elastic mechanics into a solving L-S equation by introducing reference stiffness; the SCA method comprises an offline stage and an online stage. Step 3, establishing an FE-SCA2 concurrent three-scale model; and the numerical value is solved. According to the method, the problem of low three-scale calculation efficiency is relieved while nonlinear calculation high precision is achieved, and the method has high application value in the field of composite material structure multi-scale calculation.

Description

TECHNICAL FIELD

[0001] The application relates to a woven composite material multi-scale analysis method based on clustering reduction, and belongs to the technical field of composite material multi-scale damage evolution evaluation. BACKGROUND

[0002] Woven composite materials are widely used in aerospace and other fields due to their high-temperature resistance and excellent out-of-plane mechanical properties. Woven composite materials are essentially a material system with macro-meso-micro multi-scale structural characteristics. At the macro scale, woven composite materials can be prepared into complex woven structures; at the meso scale, woven composite materials are composed of resin matrix and fiber bundles with complex paths; at the micro scale, the fiber bundle is composed of resin matrix and fibers with random distribution characteristics. Therefore, the failure behavior of woven composite materials exhibits the characteristics of multi-scale and multi-mode coupling, and it is difficult to efficiently and parallelly predict the damage evolution behavior of woven composite materials at the macro-meso-micro scale.

[0003] In recent years, concurrent multi-scale calculation methods based on computational homogenization have undergone rapid development. The method couples the micro representative volume element (RVE) to the macro material point. In the calculation process, the macro material point strain is taken as the boundary condition of the micro RVE, and the boundary value problem of the micro RVE is solved to realize the stress update of the macro model. This method only needs to define the material parameters and constitutive model of the lowest scale, and has lower dependence on material parameters compared with traditional models. However, there are also challenges: for the two-scale or three-scale parallel damage evolution calculation of woven composite materials, the calculation dimension often reaches more than 1012, the calculation amount is huge, and there is a dimension disaster problem. In order to improve the efficiency of concurrent multi-scale calculation, it is necessary to introduce a data-driven algorithm to establish a concurrent multi-scale model to overcome the dimension disaster. SUMMARY

[0004] The application aims to solve the problems existing in the prior art and provide a woven composite material multi-scale analysis method based on clustering reduction.

[0005] The application is achieved by the following technical scheme:

[0006] A woven composite material multi-scale analysis method based on clustering reduction comprises the following steps:

[0007] Step 1: defining a micro damage constitutive model

[0008] The fiber damage constitutive equation is defined, and the maximum stress criterion is used to characterize the damage initiation of the fiber. The Von Mises criterion is used to characterize the damage initiation of the resin matrix, and the bilinear damage evolution model is used to characterize the gradual degradation of the matrix properties. Damage variables are defined, and then the matrix damage constitutive equation is defined.

[0009] Step 2: Solve the RVE damage problem using the SCA method.

[0010] Step 21: Targeting the RVE region of the composite material By introducing a reference stiffness The governing equations of elasticity are transformed into solving the LS equations;

[0011] Step 22: Introducing characteristic functions To distinguish different clusters, continuous strain and stress are converted into cluster-based strain and stress;

[0012] Step 23: Substitute the cluster-based strain and stress obtained in Step 22 into the LS equation obtained in Step 21 to obtain the cluster-based LS equation.

[0013] Step 24: Offline Stage of the SCA Method: Using the Strain Concentration Tensor Characterizing strain similarity, elements with similar strain responses in the RVE are grouped into a single cluster: using... The algorithm performs clustering reduction of RVE to obtain the interaction tensor;

[0014] Step 25: Online phase of the SCA method: The Newton-Raphson method is used to solve the cluster-based LS equations obtained in Step 23 to obtain cluster strain, stress, and damage;

[0015] Step 3: Establish FE-SCA 2 Concurrent three-scale model

[0016] Equilibrium equations, macroscopic geometric equations, fiber-matrix damage constitutive equations, scale coupling equations, and macroscopic boundary condition equations for woven composite materials are established at macroscopic, mesoscopic, and microscopic scales, respectively, forming FE-SCA. 2 The concurrent three-scale model, using the SCA method in step two, performs FE-SCA. 2 Numerical solutions are obtained for the mesoscopic three-dimensional woven composite material unit cell and the microscopic fiber bundle unit cell in the concurrent three-scale model.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] This invention is based on the FE-SCA concurrent multi-scale model for woven composite materials with clustering-based order reduction. 2The proposed method achieves high accuracy in nonlinear calculations while alleviating the problem of low efficiency in three-scale calculations, and has high application value in the field of multi-scale calculations of composite material structures.

[0019] In this invention, woven composite materials, as materials with macro-fine-micro three-scale structural characteristics, face the curse of dimensionality in multi-scale calculation methods based on the finite element method. This invention proposes FE-SCA... 2 It can significantly reduce the dimensionality of multi-scale calculations and effectively reveal the microscopic damage and failure mechanism and macroscopic strain field of woven composite material structures by combining microscopic constitutive models, thus realizing three-scale parallel damage analysis. Attached Figure Description

[0020] Figure 1 This invention relates to the FE-SCA concurrent multi-scale model for woven composite materials based on clustering-based order reduction. 2 The flowchart of the numerical solution method.

[0021] Figure 2 This is a schematic diagram of the macroscopic modeling method for three-dimensional woven composite perforated plates according to the present invention.

[0022] Figure 3 This is a schematic diagram of the three-dimensional woven composite material fine-micro reconstruction method of the present invention; wherein:

[0023] Figure 3 (a) is a schematic diagram of the microstructure of a three-dimensional woven composite material;

[0024] Figure 3 (b) is Figure 3 (a) Schematic diagram of section A;

[0025] Figure 3 (c) is Figure 3 (a) Schematic diagram of section B;

[0026] Figure 3 (d) is Figure 3 (a) Schematic diagram of section C;

[0027] Figure 3 (e) is Figure 3 (a) Schematic diagram of section D;

[0028] Figure 3 (f) is a schematic diagram of the compression of a voxel three-dimensional woven composite material unit cell into a clustered three-dimensional woven composite material unit cell;

[0029] Figure 3 (g) is a schematic diagram of the microscopic reconstruction method of three-dimensional woven composite materials.

[0030] Figure 4This is a schematic diagram illustrating the convergence verification of the number of microfiber bundle unit cells in this invention; wherein:

[0031] Figure 4 (a) is a schematic diagram of the convergence verification of matrix 16 clusters and fiber 16, 32 and 64 clusters;

[0032] Figure 4 (b) is a schematic diagram of the convergence verification of fiber 16 cluster and matrix 16, 32 and 64 clusters.

[0033] Figure 5 This is a schematic diagram illustrating the convergence verification of the number of unit cells in the microscopic three-dimensional woven composite material of the present invention; wherein:

[0034] Figure 5 (a) is a schematic diagram of the convergence verification of matrix 32 clusters and fiber 96, 192 and 288 clusters;

[0035] Figure 5 (b) is a schematic diagram of the convergence verification of the fiber 96 cluster and the matrix 32, 64 and 96 clusters.

[0036] Figure 6 For the strain field of the loading stage I of this invention A schematic diagram of the distribution comparison results; where:

[0037] Figure 6 (a) is the strain field during loading stage I of this invention. A schematic diagram of the DIC results;

[0038] Figure 6 (b) is the strain field during the loading stage I of this invention. FE-SCA 2 Result diagram.

[0039] Figure 7 The strain field during loading stage II of this invention A schematic diagram of the distribution comparison results; where:

[0040] Figure 7 (a) is the strain field during loading stage II of this invention. A schematic diagram of the DIC results;

[0041] Figure 7 (b) is the strain field during loading stage II of this invention. FE-SCA 2 Result diagram.

[0042] Figure 8 For the DIC and FE-SCA of the present invention 2 Acquired strain field Numerical comparison diagram; where:

[0043] Figure 8 (a) DIC and FE-SCA in loading stage I of the present invention 2 Acquired strain field Numerical comparison diagram;

[0044] Figure 8 (b) DIC and FE-SCA in loading stage II of the present invention 2 Acquired strain field Numerical comparison diagram.

[0045] Figure 2 In the attached diagram, Y=25mm, D=6mm, W=25mm.

[0046] Figure 3 In the attached diagram, 1 represents the warp yarn, 2 represents the weft yarn, and 3 represents the sewing warp yarn. Detailed Implementation

[0047] The present invention will be further described in detail below with reference to the accompanying drawings: This embodiment is implemented under the premise of the technical solution of the present invention, and detailed implementation methods are given, but the protection scope of the present invention is not limited to the following embodiments.

[0048] The present invention provides a concurrent multi-scale model for woven composite materials based on clustering-based order reduction, FE-SCA. 2 At the microscopic woven unit cell and microscopic fiber bundle unit cell scales, the self-consistent clustering analysis (SCA) method is used to efficiently solve the nonlinear mechanical response of the unit cell; at the macroscopic structural scale, the finite element method (FEM) is used to solve the boundary value problem of the composite material structure. A computational homogenization method is used to achieve macro-microscale coupling.

[0049] To achieve the above objectives, this embodiment presents a multi-scale analysis method for woven composite materials based on clustering-based order reduction, the technical solution of which is as follows:

[0050] Based on FE-SCA 2 The method for a concurrent multi-scale damage evolution model of woven composite materials comprises the following four key parts:

[0051] 1. SCA method for solving RVE damage problem

[0052] For the representative volume element (RVE) region of composite materials By introducing a reference stiffness The governing equations of elasticity are transformed into solving the Lippmann–Schwinger (LS) equations:

[0053] (1)

[0054] In the formula, It is a fourth-order Green's function. For far-field strain, For stress, and These are the strain tensors in two different Cartesian coordinate systems.

[0055] In the SCA method, a feature function is introduced. To distinguish between different clusters, continuous strain and stress can be written as cluster-based strain and stress:

[0056] (2)

[0057] In the formula, and The first The strain and stress tensors of each cluster; It represents the number of clusters. By substituting equation (2) into equation (3), the cluster-based LS equation can be derived as:

[0058] (3)

[0059] In the formula, For clustering and clustering Interaction tensors between them and The first The strain and stress tensors of each cluster;

[0060] (4)

[0061] Generally speaking, the SCA method can be divided into an offline phase and an online phase.

[0062] (1.1) Offline stage

[0063] Elements with similar strain responses in the RVE are grouped into a single cluster. The strain lumped tensor is used. Characterizing strain similarity:

[0064] (5)

[0065] In the formula, For microscopic RVE regions The elastic strain tensor.

[0066] For 3D RVE, It has 36 independent components, which can be obtained through linear elastic finite element calculation under 6th orthogonal macroscopic loading. (Using...) The algorithm implements cluster order reduction for Recurrent Virtual Vessels (RVEs). A micro-RVE with tens of thousands of units is reduced to a micro-RVE with hundreds of clusters, which can be written as:

[0067] (6)

[0068] In the formula, and These are the components of the interaction tensor, which are only related to the microstructure of the microscopic RVE and can be calculated offline. and It is the reference material stiffness Because the reference material is isotropic, its stiffness matrix can be derived from... and Represented by two constants.

[0069] (1.2) Online Phase

[0070] For ease of numerical solution, the incremental LS equation based on clustering can be expressed as:

[0071] (7)

[0072] In the formula, the incremental strain tensor The variable to be solved in equation (7) is the incremental stress tensor. and Related to constitutive models. It is the first The incremental strain tensor of each cluster, It is the first The tangent stiffness matrix of each cluster. It is the far-field strain tensor experienced by the unit cell.

[0073] Using the Newton-Raphson method to solve equation (7), the residuals and Jacobian matrix can be derived as follows:

[0074] (8)

[0075] In the formula, Indicates the first Tangent constitutive tensors of each cluster, It is the symbol of Kroneko. , It is the identity matrix;

[0076] Considering the solution of equation (7) and the reference stiffness Relatedly, the reference stiffness is updated self-consistently using a projection method. In this method, it is necessary to first calculate the macroscopic tangent constitutive tensor of the RVE. :

[0077] (9)

[0078] In the formula, Indicates the first The average strain condensation tensor of each cluster. For the composite material RVE, its macroscopic tangent constitutive tensor is anisotropic; its projection is used to calculate the isotropic reference stiffness of the RVE. :

[0079] (10)

[0080] and It is written in the form of an indicator, as follows:

[0081] (11)

[0082] In the formula, and It is in the form of an indicator.

[0083] 2. FE-SCA 2 Concurrent three-scale model

[0084] FE-SCA 2 The mathematical expression of the concurrent multi-scale model can be written as:

[0085] (12)

[0086] In the formula, , and These represent spatial coordinates at macroscopic, mesoscopic, and microscopic scales, respectively. and These are macroscopic stress and strain, respectively. It is the first microscale The strain increment of each cluster, It is a macroscopic scale displacement. The first three equations represent the equilibrium equations of the woven composite material at the macroscopic, mesoscopic, and microscopic levels, respectively. The fourth equation represents the macroscopic geometric equation. The fifth equation represents the equation of fiber-matrix damage constitutive equation and scale coupling relationship. The sixth equation represents the boundary condition equation at the macroscopic scale.

[0087] FE-SCA 2 Numerical solution methods for concurrent multi-scale models, such as Figure 1As shown. In the offline phase of this method, strain-based clustering is used to reduce the order of the RVE of the woven composite material and the RVE of the fiber bundle. In the online phase, the strain response of each macroscopic material point is calculated in parallel.

[0088] For the macro incremental step N+1, load the macro strain increment. ,

[0089]

[0090] in, and These are the far-field strain increments at step N+1 and step N, respectively.

[0091] Macroscopic strain increment Apply to macroscopic integral point Solve the boundary value problem on the corresponding microstructure RVE.

[0092] For each micro-incremental step First, the interaction tensor of the microstructure RVE needs to be calculated. The mesoscopic strain increments for each cluster are updated based on the mesoscopic SCA solver. For mesoscopic matrix clustering, matrix damage constitutive equations are used to calculate matrix damage variables. and tangent stiffness tensor If it is fiber bundle clustering, first calculate the microscopic strain increment. and The model is transformed from the meso-global coordinate system (Meso GCS) to the meso-local coordinate system (Meso LCS). Then, the meso-strain increments are... As far-field strain is applied to the micro-clustered unit cell, the micro-clustered LS equation is solved using a micro-SCA solver based on the damage constitutive equations of the fiber and matrix. When the first norm of the strain increment... Less than Newton's iteration tolerance The Newton iteration ends; the obtained micro-stress increments are then calculated. Homogenization yields the microscopic fiber bundle stress increment in the local coordinate system. The micro-stress increment of the fiber bundle and tangent stiffness tensor The system is transformed from a local mesoscopic coordinate system to a global coordinate system. Finally, the mesoscopic stress increment is calculated. Volume homogenization to update the stress increment at each macroscopic integration point Complete FE-SCA 2 Multi-scale computation. FE-SCA 2 The multi-scale method will be implemented based on the VUMAT subroutine of Abaqus.

[0093] 3. Constitutive Model of Microscopic Damage

[0094] In formula (12), it is necessary to define the damage constitutive models for the fiber and the matrix. The fiber is modeled as a transversely isotropic brittle material, and the fiber constitutive equation can be expressed as:

[0095] (13)

[0096] In the formula, It is the fiber elastic stiffness matrix. It is a variable related to fiber damage.

[0097] Considering that fiber fracture is the main failure mode of fibers, the maximum stress criterion is used to characterize the damage initiation of fibers:

[0098] (14)

[0099] In the formula, and These are the fiber's compressive and tensile strengths, respectively.

[0100] The Von Mises criterion was used to characterize the damage initiation of the resin matrix:

[0101] (15)

[0102] In the formula, and These are the tensile and compressive failure criterion equations for the matrix, respectively. and These are the tensile strength and compressive strength of the matrix, respectively. It is the first stress invariant. It is the matrix von Mies stress. It is the matrix stress tensor;

[0103] A bilinear damage evolution model is used to characterize the progressive degradation of matrix properties, and the damage variables are defined as follows:

[0104] (16)

[0105] In the formula, and The equivalent displacements for complete failure and initial failure, respectively, can be expressed as:

[0106] (17)

[0107] In the formula, For fracture toughness of matrix failure mode n; This is equivalent stress.

[0108] The matrix damage constitutive equation can be expressed as:

[0109] (18)

[0110] in, It is the matrix stiffness matrix;

[0111] Then, the Duvaut-Lions method is used to improve the convergence of numerical calculations, and strain increments are determined at the microscale based on the Newton-Raphson method. The corresponding stress increment Calculated based on the damage constitutive model.

[0112] 4. Results and Discussion

[0113] (1) A multi-scale modeling method for three-dimensional woven composite materials, encompassing macro-fine-micro scales.

[0114] like Figure 2 As shown, the central 25mm region of the three-dimensional woven composite perforated plate is taken as the region of interest for modeling and finite element discretization is performed using a 1mm mesh size. The macroscopic three-dimensional woven composite perforated plate is discretized into 604 reduced integral C3D8R elements.

[0115] like Figure 3 As shown, at the microscale, the warp and weft yarns of the three-dimensional woven composite material extend vertically to form a multi-layered interwoven structure. The sewn warp yarns interweave with the weft yarns of adjacent layers in the thickness direction, thereby enhancing the out-of-plane mechanical properties of the three-dimensional woven composite material. Unlike the extension path of the warp yarns, the yarn path of the weft yarns exhibits slight undulation, while the sewn warp yarns exhibit obvious periodic undulation. Based on the TexGen software, a Python script was developed to reconstruct the microstructure of the three-dimensional woven composite material and extract the unit cells. Voxel meshes were divided in the Hypermesh software, and periodic boundary conditions were applied to the unit cells in the Abaqus software. Based on the offline clustering scheme proposed in (1.1), the voxel three-dimensional woven composite material unit cells were compressed into clustered three-dimensional woven composite material unit cells. At the microscale, a fiber bundle unit cell was established using a regular hexagonal fiber distribution configuration, with a length, width, and height ratio of 1:0.04:1.732, and a corresponding mesh density of 100:4:174 in the length, width, and height directions. By compressing voxel fiber bundle units into clustered fiber bundle units, a multi-scale modeling method for the macro-fine-micro scale of three-dimensional woven composite material structures was established.

[0116] (2) Convergence verification of clustering quantity

[0117] Before performing multi-scale calculations, it is necessary to conduct convergence verification on the number of clusters for fiber bundle unit cells and three-dimensional woven composite unit cells to determine the most suitable clustering scheme, thereby balancing computational efficiency and accuracy. Figure 4 andFigure 5 Stress-strain curves for fiber bundle unit cells and three-dimensional woven composite unit cells are presented respectively. Finite element results are compared as accurate results, and a 5% error band is used to assess the strength calculation error. Figure 4 The stress-strain results of fiber bundle unit cells under longitudinal tension were studied using the following clustering schemes: (fiber 16 cluster, matrix 16 cluster), (fiber 32 cluster, matrix 16 cluster), (fiber 64 cluster, matrix 16 cluster), (fiber 16 cluster, matrix 32 cluster), and (fiber 16 cluster, matrix 64 cluster). It can be seen that the linear segment of SCA (Structured Computational Analysis) agrees well with the finite element results, and the strength predicted by SCA is within the 5% strength error band. For three-dimensional woven composites, radial tension was investigated using the following clustering schemes: (fiber bundle 96 cluster, matrix 32 cluster), (fiber bundle 192 cluster, matrix 32 cluster), (fiber bundle 288 cluster, matrix 32 cluster), (fiber bundle 96 cluster, matrix 64 cluster), and (fiber bundle 96 cluster, matrix 96 cluster). Figure 5 The slope of the stress-strain curves from the SCA results was slightly lower than that from the finite element results. Meanwhile, the strength values ​​predicted by the SCA results were all within the 5% error band. Therefore, fiber bundle unit cells with 16 fiber clusters and 16 matrix clusters, as well as three-dimensional woven composite unit cells with 96 fiber bundle clusters and 32 matrix clusters, were used for multi-scale analysis.

[0118] (3) Strain field verification of three-dimensional woven composite perforated plate

[0119] A uniformly distributed radial tensile displacement load is applied to both sides of the perforated plate, based on FE-SCA. 2 Radial tensile simulation calculations were performed using a concurrent multi-scale model. Two stages during the loading process, I and II, were selected for DIC experimental measurements and FE-SCA. 2 Strain field predicted by the method Compare the distributions, such as Figure 6 and 7 As shown in the figure. It can be seen that the results obtained from the DIC measurement are similar to those obtained from the FE-SCA measurement. 2 The strain fields predicted by the method agree well. An evaluation line is drawn on both sides of the hole to quantitatively compare the strain fields of the two methods. Result. For example. Figure 8 As shown, the DIC measurement yielded... Numerical values ​​and FE-SCA 2 Method prediction The numerical trends are consistent, and the strain at the hole edge is... The value is higher than that far from the edge of the hole. Numerical value. For example... Figure 8 As shown in (a), the DIC measurement results and FE-SCA 2 Method predicts strain on the evaluation line The values ​​exhibit a fairly high degree of consistency. Further loading to Phase II, as follows... Figure 8 (b) shows the strain measured by DIC. The value is slightly higher than FE-SCA 2 The strain values ​​predicted by the method. Studies have shown that FE-SCA 2 The method achieves high accuracy in nonlinear calculations while alleviating the problem of low efficiency in three-scale calculations, and has high application value in the field of multi-scale calculations of composite material structures.

[0120] The FE-SCA developed in this invention 2 Concurrent multi-scale models are expected to be applied to the assessment of multi-scale damage evolution behavior of composite material structures in the future, replacing high-cost experimental methods and reducing the cost of assessing the damage performance of composite materials.

[0121] The above description is merely a preferred embodiment of the present invention. These specific embodiments are different implementations based on the overall concept of the present invention, and the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-scale analysis method for woven composite materials based on clustering-based order reduction, characterized in that, Includes the following steps: Step 1: Define the constitutive model of microscopic damage The fiber damage constitutive equation is defined, and the maximum stress criterion is used to characterize the damage initiation of the fiber. The Von Mises criterion is used to characterize the damage initiation of the resin matrix, and the bilinear damage evolution model is used to characterize the gradual degradation of the matrix properties. Damage variables are defined, and then the matrix damage constitutive equation is defined. Step 2: Solve the RVE damage problem using the SCA method. Step 21: Targeting the RVE region of the composite material By introducing a reference stiffness The governing equations of elasticity are transformed into solving the LS equations; Step 22: Introducing characteristic functions To distinguish different clusters, continuous strain and stress are converted into cluster-based strain and stress; Step 23: Substitute the cluster-based strain and stress obtained in Step 22 into the LS equation obtained in Step 21 to obtain the cluster-based LS equation. Step 24: Offline Stage of the SCA Method: Using the Strain Concentration Tensor Characterizing strain similarity, elements with similar strain responses in the RVE are grouped into a single cluster: using... The algorithm performs clustering reduction of RVE to obtain the interaction tensor; Step 25: Online phase of the SCA method: The Newton-Raphson method is used to solve the cluster-based LS equations obtained in Step 23 to obtain cluster strain, stress, and damage; Step 3: Establish FE-SCA 2 Concurrent three-scale model Equilibrium equations, macroscopic geometric equations, fiber-matrix damage constitutive equations, scale coupling equations, and macroscopic boundary condition equations for woven composite materials are established at macroscopic, mesoscopic, and microscopic scales, respectively, forming FE-SCA. 2 The concurrent three-scale model, using the SCA method in step two, performs FE-SCA. 2 Numerical solutions are obtained for the mesoscopic three-dimensional woven composite material unit cell and the microscopic fiber bundle unit cell in the concurrent three-scale model.

2. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The fiber damage constitutive equation defined in step one is as follows: (1) In the formula, It is the fiber elastic stiffness matrix. It is a variable related to fiber damage; The maximum stress criterion is used to characterize the damage initiation of the fiber, and the formula is as follows: (2) In the formula, and These are the fiber's compressive and tensile strengths, respectively.

3. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The Von Mises criterion used in step one to characterize the damage initiation of the resin matrix is ​​as follows: The Von Mises criterion was used to characterize the damage initiation of the resin matrix: (3) In the formula, and These are the tensile and compressive failure criterion equations for the matrix, respectively. and These are the tensile strength and compressive strength of the matrix, respectively. It is the first stress invariant. It is the matrix von Mies stress. It is the matrix stress tensor; The bilinear damage evolution model is used to characterize the gradual degradation of matrix properties, and its damage variables are defined as follows: (4) In the formula, and The equivalent displacements for complete failure and initial failure, respectively, are expressed as: (5) In the formula, For matrix failure modes fracture toughness; Equivalent stress; The matrix damage constitutive equation is expressed as follows: (6) in, It is the matrix stiffness matrix; Then, the Duvaut-Lions method is used to improve the convergence of numerical calculations, and strain increments are determined at the microscale based on the Newton-Raphson method. The corresponding stress increment Calculated based on the damage constitutive model.

4. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, Step 2.1 involves transforming the governing equations of elasticity into solving the LS equations, as shown in the following formula: (7) In the formula, It is a fourth-order Green's function. For far-field strain, For stress, and These are the strain tensors in two different Cartesian coordinate systems.

5. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, In step two, the formulas for converting continuous strain and stress into cluster-based strain and stress are as follows: (8) In the formula, and The first The strain and stress tensors of each cluster; It represents the number of clusters.

6. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The cluster-based LS equation described in steps two and three is as follows: (9) In the formula, For clustering and clustering kind Interaction tensors between them and The first The strain and stress tensors of each cluster; (10)。 7. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The use of strain lumped tensors in step two and four The formula for characterizing strain similarity is as follows: (11) In the formula, For microscopic RVE regions The elastic strain tensor; The use The algorithm implements clustering order reduction for RVE, and the interaction tensor formula is as follows: (12) In the formula, and These are the components of the interaction tensor, which are only related to the microstructure of the microscopic RVE and can be calculated offline. and It is the reference material stiffness A constant, because the reference material is isotropic, and its stiffness matrix can be obtained from... and Represented by two constants.

8. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, In step two, for the convenience of numerical solution, the incremental LS equation based on clustering can be expressed as: (13) In the formula, the incremental strain tensor The incremental stress tensor is the solution variable for formula (13). and Related to constitutive models, It is the first The incremental strain tensor of each cluster, It is the first The tangent stiffness matrix of each cluster. It is the far-field strain tensor experienced by the unit cell; The residuals and Jacobian matrices are derived by solving formula (13) using the Newton-Raphson method: (14) In the formula, Indicates the first Tangent constitutive tensors of each cluster, It is the symbol of Kroneko. , It is the identity matrix; Considering the solution of formula (13) and the reference stiffness Relatedly, the reference stiffness is updated self-consistently using a projection method. In this method, it is necessary to first calculate the macroscopic tangent constitutive tensor of the RVE. : (15) In the formula, Indicates the first The average strain lumped tensor of each cluster, for the composite material RVE, has anisotropic macroscopic tangent constitutive tensor. Projecting this tensor is used to calculate the isotropic reference stiffness of the RVE. : (16) and It is written in the form of an indicator, as follows: (17) In the formula, and It is in the form of an indicator.

9. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The FE-SCA mentioned in step three 2 The expression for the concurrent three-scale model is as follows: (18) In the formula, , and These represent spatial coordinates at macroscopic, mesoscopic, and microscopic scales, respectively. and These are macroscopic stress and strain, respectively. It is the first microscale The strain increment of each cluster, It is a macroscopic scale displacement. The first three equations represent the equilibrium equations of the woven composite material at the macroscopic, mesoscopic, and microscopic levels, respectively. The fourth equation represents the macroscopic geometric equation. The fifth equation represents the equation of fiber-matrix damage constitutive equation and scale coupling relationship. The sixth equation represents the boundary condition equation at the macroscopic scale.

10. The multi-scale analysis method for woven composite materials based on clustering-based order reduction according to claim 1, characterized in that, The FE-SCA mentioned in step three 2 The numerical solution method for concurrent multi-scale models is as follows: In the offline stage, strain-based clustering is used to reduce the order of woven composite material RVE and fiber bundle RVE. In the online stage, the strain response of each macroscopic material point is calculated in parallel. For the macro incremental step N+1, load the macro strain increment. , in, and These are the far-field strain increments at step N+1 and step N, respectively. Macroscopic strain increment Apply to macroscopic integral point Solving the boundary value problem on the corresponding microstructure RVE; For each micro-incremental step First, the interaction tensor of the microstructure RVE needs to be calculated. ; The mesoscopic strain increments for each cluster are updated based on the mesoscopic SCA solver. For mesoscopic matrix clustering, matrix damage constitutive equations are used to calculate matrix damage variables. and tangent stiffness tensor If it is fiber bundle clustering, first calculate the microscopic strain increment. and Transform from the meso-global coordinate system (Meso GCS) to the meso-local coordinate system (MesoLCS); then, measure the meso-strain increments. As far-field strain is applied to the micro-clustered unit cell, the micro-clustered LS equation is solved using a micro-SCA solver based on the damage constitutive equations of the fiber and matrix. When the first norm of the strain increment... Less than Newton's iteration tolerance The Newton iteration ends; the obtained micro-stress increments are then calculated. Homogenization yields the microscopic fiber bundle stress increment in the local coordinate system. ; Incremental micro-stress of fiber bundles and tangent stiffness tensor Transform from the local coordinate system to the global coordinate system; finally, calculate the microstress increments. Volume homogenization to update the stress increment at each macroscopic integration point Complete FE-SCA 2 Multiscale computation; FE-SCA 2 The multi-scale method will be implemented based on the VUMAT subroutine of Abaqus.

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