A multi-scale analysis method for three-dimensional braided composite thin-walled structures based on local homogenization

Abstract

The present invention discloses a multi-scale analysis method of a three-dimensional woven composite thin-walled structure based on local homogenization, comprising the following steps: on a microscopic scale, an RVE unit cell model of a three-dimensional woven composite thin-walled structure is established based on a four-step weaving method; the local homogenization region of the RVE unit cell model is determined, and the yarns in each direction of the local homogenization region and the part of the matrix around the yarn are locally homogenized to obtain equivalent cells, and the equivalent cells are expanded into equivalent unit cell models; after discretizing the RVE unit cell model, periodic boundary condition constraints are imposed to obtain mechanical performance parameters of the equivalent cells; the equivalent unit cell model is discretized, and on a macroscopic scale, the equivalent unit cell model is arrayed along the circumferential direction and the weaving direction respectively to obtain a macroscopic equivalent model, and the mechanical performance and damage mode analysis are performed on the model. The mechanical performance prediction of the method of the present invention has high accuracy, and improves the computational efficiency of multi-scale analysis of mechanical performance of three-dimensional woven composite materials.

Description

Technical Field

[0001] The invention belongs to the technical field of multi-scale analysis of composite materials. Background Art

[0002] After nearly half a century of development, three-dimensional braided composite materials have been widely used in aerospace, shipbuilding, transportation, medical equipment and other technical fields. The problems they solve involve reducing structural weight, improving damage tolerance and designability. In recent years, multi-scale finite element methods are often used in the mechanical performance analysis of three-dimensional braided composite structures. Modeling and analysis are performed at the micro, meso and macro scales respectively, and information is transmitted between scales based on homogenization theory. At the macro scale, traditional multi-scale analysis methods usually establish a continuous medium model that does not consider the braided structure, which simplifies the calculation process. However, since the geometric structure of the local braided yarn is not considered, it is difficult to characterize the local mechanical behavior and damage behavior of the three-dimensional composite material, and thus the accuracy of the calculation cannot be guaranteed.

[0003] Existing literature 1 "Xu KL, Chen W, Liu LL, Zhao ZH, Luo GA hierarchical multiscale strategy for analyzing the impact response of 3D braided composites. International Journal of Mechanical Sciences, 2021, 193: 106167." discloses a hierarchical multiscale method for the impact response analysis of three-dimensional braided composites. In order to improve the reliability of this hierarchical multiscale method, at the microscale, nine representative volume element (RVE) models with different carbon fiber distributions were established; at the mesoscale, a unit cell model was established based on the yarn braiding structure, and this unit cell model was introduced into the macroscale model according to the transformation matrix from the local coordinate system to the global coordinate system, and the homogenization method was used to transfer the mechanical properties of each scale. Finally, the effectiveness of the hierarchical multiscale analysis method was verified by a high-speed impact test. However, the multiscale modeling method adopted by this method has limited consistency with the simulation of the impact damage morphology of the composite plate, and the accuracy needs to be improved.

[0004] Existing document 2 "Zhang DT, Sun Y, Wang XM, Chen L. Prediction of macro-mechanical properties of 3D braided composites based on fiber embedded matrix method. Composite Structures, 2015, 134: 393-408." discloses a multi-scale analysis method based on a three-unit cell model, which is used to analyze the mechanical behavior of three-dimensional braided composites under uniaxial tensile load. This multi-scale method, at the microscopic scale, establishes a three-unit cell model based on the yarn structure at different positions; at the macroscopic scale, a fiber embedded matrix theory (Fiber Embedded Matrix Method, FEMM) is proposed, and a macro-mechanical properties analysis method of three-dimensional braided composites based on full-field yarn distribution is established. Finally, the model is verified by a uniaxial tensile test. By comparing the stress-strain curves during the uniaxial tensile test, it is found that the prediction results of this multi-scale method are in good agreement with the experimental results. However, it still has certain limitations in predicting the lateral mechanical behavior and damage evolution process of braided composites.

[0005] Existing document 3 "Liu T, Sun Y, Wu XY, Sun BZ, Wei F, Han WL, Yi HL. Investigations of defect effect on dynamic compressive failure of 3D circular braided composite tubes with numerical simulation method. Thin-Walled Structures, 2021, 160: 107381." discloses a numerical simulation method for the impact compression behavior of a three-dimensional braided tubular structure. The model used is a full-scale finite element analysis model based on the real geometric structure of the tubular preform. This method can accurately simulate the dynamic compression damage evolution process and stress-strain distribution of three-dimensional braided composite tubes, but it has the problems of large calculation files, long calculation time, and high calculation difficulty. Summary of the invention

[0006] In order to solve the technical problem that the existing multi-scale analysis methods have low accuracy in predicting mechanical properties at a macroscopic scale, the present invention provides a multi-scale analysis method for thin-walled structures of three-dimensional woven composite materials based on local homogenization.

[0007] Based on the above purpose, the present invention adopts the following technical solutions:

[0008] A multi-scale analysis method for a three-dimensional braided composite thin-wall structure based on local homogenization comprises the following steps:

[0009] 1) At the microscopic scale, the RVE unit cell model of the 3D braided composite thin-walled structure is established based on the four-step braiding method;

[0010] 2) First determine the local homogenization area of ​​the RVE unit cell model (the area where the equivalent cell is located), locally homogenize the yarns in each direction of the local homogenization area and the matrix around the yarn to obtain the equivalent cell, and expand the equivalent cell into an equivalent unit cell model according to the yarn motion law of the four-step weaving method;

[0011] 3) After discretizing the RVE unit cell model in step 1), periodic boundary conditions are imposed, and the mechanical performance parameters of the equivalent cell in the equivalent unit cell model in step 2) are obtained by calculating the equivalent stress-strain relationship;

[0012] 4) The equivalent unit cell model of step 2) is discretized. On a macro scale, the equivalent unit cell model is arrayed along the circumferential direction and the weaving direction to obtain a macro scale equivalent model of the thin-walled structure. The mechanical properties and damage mode of the macro scale equivalent model are analyzed.

[0013] Step 2) Modeling method of equivalent cell: set the rectangular surface as the cross-sectional shape of the equivalent cell, and based on the yarn movement law of the four-step weaving method, sweep the rectangular surface along the yarn path to form an equivalent cell. The circumferential angle occupied by the cross section of the equivalent cell is θ, θ = 2π / n; the cross-sectional height h of the equivalent cell is e =h / 2, where n is the number of columns of the main yarn array and h is the unit cell length of the RVE unit cell model.

[0014] In step 4), the equivalent unit cell model is arrayed at an angle of (m-1)θ along the circumferential direction and at a unit cell length of the RVE unit cell model along the weaving direction, where m is the number of layers of the main yarn array.

[0015] In step 3), the RVE unit cell model of step 1) is discretized using the tetrahedral mesh method in the finite element software Abaqus; in step 4), the equivalent unit cell model of step 2) is discretized using the hexahedral mesh method in the finite element software Abaqus.

[0016] In step 3), the displacement field on the boundary of the discretized RVE unit cell model is:

[0017]

[0018] Where: represents the global equivalent effect variable, i represents the direction, k represents the node number; x k Represents the coordinate value of the corresponding point; u i* represents the periodic part of the displacement component at the boundary;

[0019] The constraint equations for the periodic boundary conditions are as follows:

[0020] U Z (P1)-U Z (P2) = U Z (F′)-U Z (B′)

[0021] U R (P1)-U R (P2) = U R (F′)-U R (B′)

[0022]

[0023] U Z (P3)-U Z (P4) = U Z (A′)-U Z (B′)

[0024] U R (P3)-U R (P4) = U R (A′)-U R (B′)

[0025] U T (P3)-U T (P4) = U T (F′)-U T (B′)

[0026] Among them, U represents the node displacement, R, T, and Z represent the directions, and P1, P2, P3, P4, A′, B′, and F′ represent the nodes of the RVE unit cell model.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] 1) The present invention establishes an RVE unit cell model of a three-dimensional woven composite material at a microscopic scale, but performs local homogenization in the macro-microscopic scale information transmission stage, couples the yarns in different directions in the RVE unit cell model and part of the matrix around them to form an equivalent cell (sub-RVE) corresponding to the yarn direction, and further expands it into an equivalent unit cell model, and arrays the equivalent unit cell model to obtain a macroscopic equivalent model. This modeling method not only has good accuracy in predicting mechanical properties, but also can accurately predict stress-strain distribution and damage morphology through this method; in addition, this method greatly improves the computational efficiency of multi-scale analysis of mechanical properties of three-dimensional woven composite materials;

[0029] 2) On a macroscopic scale, the finite element model is discretized using a hexahedral grid with high computational accuracy and strong anti-distortion ability, which can reduce the number of grids, improve computational efficiency, and improve the accuracy of predicting the mechanical properties of three-dimensional woven composite materials. The present invention does not need to establish a model based on the complex topological structure of the woven yarn, and does not need to consider the difficulty of grid division of the complex structure. The predicted values ​​of stiffness and strength are within 5% of the experimental values, and the morphology of the damaged area is also consistent with the experimental results. Moreover, the mechanical properties of three-dimensional woven composite components with more complex configurations can be predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings used in the embodiments. The drawings are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 It is a schematic diagram of the yarn motion trajectory of the four-step weaving method;

[0032] Figure 2 Schematic diagram of the three-dimensional braided composite thin-wall structure preform and the mesoscale RVE unit cell model;

[0033] Figure 3 It is a schematic diagram of the regional division and yarn classification of the meso-scale RVE unit cell model of the present invention;

[0034] Figure 4 Schematic diagram of the geometric dimensions of the equivalent unit cell model;

[0035] Figure 5 A schematic diagram of the local homogenization step of the present invention;

[0036] Figure 6 A comparison diagram of the mesoscale RVE unit cell model and its equivalent unit cell model;

[0037] Figure 7 Schematic diagram of the method for applying periodic boundary conditions;

[0038] Figure 8 , a is a schematic diagram of the meso-scale RVE unit cell model; b is a schematic diagram of the meso-scale equivalent unit cell model;

[0039] Fig. 9 , a is a schematic diagram of the compression simulation stress distribution of a three-dimensional braided composite material thin-wall structure in the prior art literature 3; b is a schematic diagram of the compression simulation stress distribution of a three-dimensional braided composite material thin-wall structure of the present invention;

[0040] Fig.10, a is a schematic diagram of the damage morphology of the compression simulation of the meso-scale RVE unit cell model; b is a schematic diagram of the damage morphology of the compression simulation of the meso-scale equivalent unit cell model;

[0041] Fig.11 Schematic diagram of the calculation time of the meso-scale RVE unit cell model, the equivalent unit cell model of the present invention and the macro-scale equivalent model. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention is described in detail below, but the following embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by those skilled in the art without making creative work belong to the scope of protection of the present invention.

[0043] Example 1

[0044] like Figure 1-4 As shown in the figure, the braiding angle α of the three-dimensional four-way braided preform is 45°, the knot length h is 5 mm, the number of main yarn layers m is 3, and the number of columns n is 32; the reinforcing fiber in the thin-walled structure specimen is T700-12K carbon fiber, the matrix is ​​TDE-86 epoxy resin, the specimen wall thickness is 2.34 mm, the outer diameter is 51 mm, the length is 50 mm, the carbon fiber volume content is 43.62%, and the material parameters of the thin-walled structure specimen components are shown in Table 1. The ellipse is used as the braided yarn cross-section, and it is assumed that all braided yarns have the same geometric properties, and the braided structure is modeled as a uniform periodic structure.

[0045] A multi-scale analysis method for a three-dimensional braided composite thin-wall structure based on local homogenization comprises the following steps:

[0046] 1) On a microscopic scale, based on the four-step weaving method, the movement law of the yarn 1 during the weaving process, the main yarn array is composed of yarn carriers 2 arranged in radial and circumferential directions, wherein the number of layers (m) is determined by the number of yarn carriers in the radial direction, and the number of columns (n) is determined by the number of yarn carriers in the circumferential direction, n is an even number, and each yarn carrier 2 carries a weaving yarn. The weaving process is realized by the radially and circumferentially arranged yarn carriers 2 through four-step intermittent motion. A machine cycle is completed after the four-step motion is completed. Repeat the above weaving steps, and the yarns 1 will be interwoven to form a preform 3 with a certain length and thickness. The length of the preform 3 obtained in a machine cycle of the four-step weaving is defined as the flower node length, represented by h. The structure of the preform 3 can be defined by the number of layers (m) and the number of columns (n) of the main yarn array (the number of layers and the number of columns of the preform are equal to the number of layers m and the number of columns n of the main yarn array, respectively), as shown in Figure 1As shown, then, according to the real structure of the preform 3, on the basis of the three-unit cell model (Three-RVEs Model), the RVE unit cell model of the three-dimensional braided composite material thin-wall structure is established, as shown in FIG. Figure 8 As shown in a, the RVE unit cell model includes three regions: the internal region, the inner surface region and the outer surface region. The internal region, the inner surface region and the outer surface region all include yarns in all directions and the matrix around the yarns.

[0047] 2) First determine the local homogenization area of ​​the RVE unit cell model (the area where the equivalent cell is located, determined according to the position of the yarns in each direction), locally homogenize the yarns in each direction of the local homogenization area and the matrix around the yarn to obtain the equivalent cell, and expand the equivalent cell into an equivalent unit cell model according to the yarn movement law of the four-step weaving method, as follows: Figure 8 As shown in Fig. 2, the specific modeling method of the equivalent cell (modeling software Solidworks) is as follows: Since the microstructure of the three-dimensional woven composite material is uniform, the woven yarns in different directions have the same volume content. For the equivalent unit cell model, taking the unit cell in the inner region as an example (the modeling method of the unit cell in the inner surface region and the unit cell in the outer surface region is the same), the front surface of the unit cell in the inner region should be equally divided by each equivalent cell ( Figure 4 ), set the rectangular surface as the cross-sectional shape of the equivalent cell, and based on the yarn movement law of the four-step weaving method, sweep the rectangular surface along the yarn path to form an equivalent cell. Considering the mesh quality and model accuracy during finite element analysis, its edge is processed into a step shape, such as Figure 5 As shown, the angle of the circle occupied by the cross section of the equivalent cell is θ, θ = 2π / n; the cross section height h of the equivalent cell e =h / 2, where n is the number of columns of the main yarn array, and h is the unit cell length of the RVE unit cell model (equal to the length of the flower node), such as Figure 4 As shown; Based on the yarn movement law of the four-step weaving method, the weaving yarns in all directions are locally homogenized with the surrounding part of the matrix to form equivalent cells based on this method, thereby expanding to an equivalent unit cell model, such as Figure 6 shown.

[0048] 3) After discretizing the RVE unit cell model in step 1) using the tetrahedral mesh (C3D4) in the finite element software Abaqus, periodic boundary conditions are imposed.

[0049] For materials composed of periodic unit cells, when subjected to external loads, a continuous and periodic stress-strain field will be generated, and the displacement field on its boundary can be expressed as:

[0050]

[0051] Where: represents the global equivalent effect variable, i represents the direction, k represents the node number; x k Represents the coordinate value of the corresponding point; u i * represents the periodic part of the displacement component at the boundary. Figure 7 For example, for the thin-walled structure unit cell model, its inner and outer surfaces are free surfaces and are not periodic. Therefore, the periodic boundary condition constraint equation used in this paper is as follows:

[0052]

[0053] Among them, U represents the node displacement, R, T, and Z represent the directions, and P1, P2, P3, P4, A′, B′, and F′ represent the nodes of the RVE unit cell model.

[0054] Then, 9 sets of independent displacement loads are applied to the RVE unit cell model, such as Figure 7 As shown in the figure, they are the tensile and compressive loads in the R, T, and Z directions, and the shear loads in the RT, RZ, and TZ planes. The python language is used to write a script to calculate the equivalent stress and equivalent strain of the equivalent cell under each load condition, and 9 equations are obtained. By solving these 9 sets of independent equations, the equivalent flexibility matrix [S] of the equivalent cell can be obtained, and then the equivalent mechanical parameters of each cell in the equivalent unit cell model are determined by the equivalent elastic constants.

[0055] The formula for the equivalent stress-strain relationship is as follows:

[0056]

[0057] Where [S] is the equivalent flexibility matrix, which is defined as follows:

[0058]

[0059] The equivalent elastic constant can be calculated from the equivalent flexibility constant:

[0060]

[0061] They are the equivalent strain and equivalent stress matrices, respectively, and are defined as follows:

[0062]

[0063] In the formula, i and j represent directions, V represents volume, and n e represents the number of units, e represents the unit, and k represents the corresponding unit number.

[0064] 4) The equivalent unit cell model of step 2) is discretized using the hexahedral grid method in the finite element software Abaqus. On a macro scale, based on the size of the experimental specimen, the equivalent unit cell model is arrayed at an angle of (m-1)θ along the circumferential direction and at the unit cell length of the RVE unit cell model along the weaving direction to obtain a macro-scale equivalent model of the thin-walled structure. The macro-scale equivalent model is imported into the Abaqus software for simulation calculation, and mechanical properties are analyzed based on the calculation result data (such as force, displacement, stress, strain, etc.), and damage mode analysis is performed based on the result cloud map, where m is the number of rows of the main yarn array.

[0065] In step 1), taking a three-dimensional four-directional three-layer 45° braiding angle preform as an example, in the cylindrical coordinate system, the braided yarns are divided into group I along the clockwise direction and group II along the counterclockwise direction; each group of yarns is divided into two parts, and the direction in which the R coordinate of the yarn increases with the increase of the Z coordinate is defined as direction 1, and the direction in which the R coordinate decreases with the increase of the Z coordinate is defined as direction 2. According to the real structure of the preform, on the basis of the three-unit cell model (Three-RVEs model), a Figure 2 The mesoscopic geometric model shown in Figure 1 includes three regions: the inner region, the inner surface, and the outer surface region (e.g. Figure 3 ), the circumferential angles occupied by the unit cells in the three regions are all 2θ (θ=2π / n), n is the number of main yarn arrays, and the length of the unit cell of the RVE unit cell model is equal to the length of the flower node. For the internal region, the yarns in the unit cell can be divided into four categories: A, B, C, and D, which are: group I yarns in directions 1 and 2 and group II yarns in directions 1 and 2; the yarns in the unit cells in the surface region can be divided into four categories: E, F, G, and H by the same method.

[0066] The finite element mesh information of the full-scale model (model established based on the real structure and size of the material) of the three-dimensional woven composite thin-wall structure at the mesoscale and macroscale and its equivalent unit cell model are shown in Tables 2 and 3, respectively.

[0067] Table 1 Material parameters of thin-walled structure specimens of the present invention

[0068]

[0069] Table 2 Finite element mesh information of the full-scale model and its equivalent unit cell model at the mesoscopic scale of thin-walled structures

[0070]

[0071] Table 3 Finite element mesh information of the full-scale model and its equivalent unit cell model at the macroscopic scale of thin-walled structures

[0072]

[0073] Example 2 Performance Comparison Test

[0074] 2.1 Computation time test

[0075] Tables 2 and 3 show the finite element mesh information of the full-size model and its equivalent unit cell model at the microscopic and macroscopic scales of the three-dimensional woven composite thin-wall structure, respectively. The finite element mesh information is shown in Table 2 and Table 3. The finite element mesh information is shown in Table 3. The finite element mesh information is shown in Table 3. Fig.11 shown.

[0076] Depend on Fig.11 It is known that at the microscopic scale, the calculation time of the RVE unit cell model compression simulation is about 10 hours, and the calculation time of its equivalent unit cell model is about 0.1 hours; the calculation time of the macroscopic equivalent model is about 0.5 hours. This shows that under the same geometric parameters, the number of meshes of the finite element model established by the multi-scale analysis method of the present invention is reduced, the mesh quality is improved, and the calculation cost is reduced by more than 95%.

[0077] 2.2 Compression simulation stress analysis

[0078] Comparing the multi-scale analysis method of the present invention with the method of background technology document 3, the compression simulation stress distributions are shown as follows: Fig. 9 b, as shown in 9a.

[0079] Depend on Fig. 9 b, the calculation results of the multi-scale analysis method of the present invention accurately reflect the unevenness of the stress distribution of the braided yarn and the resin matrix, as well as the stress concentration at the contact point between the two, and the multi-scale model is consistent with Fig. 9 The stress level and distribution of a (full-scale model of the background technology existing document 3) are consistent with each other.

[0080] 2.3 Compression simulation damage morphology analysis

[0081] The mesoscale equivalent unit cell model of the multi-scale analysis method of the present invention is compared with the mesoscale RVE unit cell model method of the prior art document 1. The compression simulation damage morphologies are shown as follows: Fig.10 b, as shown in 10a.

[0082] Depend on Fig.10 b、10a shows that for Fig.10 a) The mesoscopic unit cell model shows that the damage of the resin matrix is ​​mainly distributed at the contact point between the braided yarn and the resin matrix, and the damage extends along the direction of the braided yarn. Fig.10 b The damage position and extension direction of the equivalent unit cell model are the same as Fig.10a The micro-scale unit cell model is relatively consistent, indicating that the present invention has a higher accuracy in predicting the damage morphology of the specimen due to the use of a more sophisticated local homogenization method.

[0083] It can be seen that compared with the method of background technology document 2, the micro-scale equivalent unit cell model and the macro-scale equivalent model of the multi-scale analysis method of the present invention are able to distinguish the weaving yarns with different motion trajectories in terms of geometric structure. Therefore, the prediction of the damage morphology and damage evolution of the specimen when it is damaged has higher accuracy.

Claims

1. A multi-scale analysis method for three-dimensional woven composite thin-walled structures based on local homogenization, characterized in that: The following steps are involved: 1) At the microscopic scale, the RVE unit cell model of the 3D braided composite thin-walled structure is established based on the four-step braiding method; 2) First, determine the local homogenization area of ​​the RVE unit cell model, locally homogenize the yarns in each direction of the local homogenization area and the matrix around the yarn to obtain equivalent cells, and expand the equivalent cells into an equivalent unit cell model according to the yarn motion law of the four-step weaving method; 3) After discretizing the RVE unit cell model in step 1), the constraints of periodic boundary conditions are imposed, and the mechanical performance parameters of the equivalent cell in the equivalent unit cell model in step 2) are obtained by calculating the equivalent stress-strain relationship; wherein, the displacement field on the boundary of the discretized RVE unit cell model is: Where: represents the global equivalent effect variable, i represents the direction, k represents the node number; x k Represents the coordinate value of the corresponding point; u i * represents the periodic part of the displacement component at the boundary; The constraint equations for the periodic boundary conditions are as follows: IN Z (P1)-U Z (P2)=U Z (F′)-U Z (B′) IN R (P1)-U R (P2)=U R (F′)-U R (B′) U Z (P3)-U Z (P4)=U Z (A′)-U Z (B') U R (P3)-U R (P4)=U R (A′)-U R (B') U T (P3)-U T (P4)=U T (F′)-U T (B′) Among them, U represents the node displacement, R, T, and Z represent the directions, and P1, P2, P3, P4, A′, B′, and F′ represent the nodes of the RVE unit cell model; 4) The equivalent unit cell model of step 2) is discretized. On a macro scale, the equivalent unit cell model is arrayed along the circumferential direction and the weaving direction to obtain a macro scale equivalent model of the thin-walled structure. The mechanical properties and damage mode of the macro scale equivalent model are analyzed.

2. The multi-scale analysis method for three-dimensional woven composite thin-walled structure based on local homogenization according to claim 1, characterized in that: Step 2) Modeling method of equivalent cell: set the rectangular surface as the cross-sectional shape of the equivalent cell, and based on the yarn movement law of the four-step weaving method, sweep the rectangular surface along the yarn path to form an equivalent cell. The circumferential angle occupied by the cross section of the equivalent cell is θ, θ = 2π / n; the cross-sectional height h of the equivalent cell is e =h / 2, where n is the number of columns of the main yarn array and h is the unit cell length of the RVE unit cell model.

3. The multi-scale analysis method for three-dimensional woven composite thin-walled structure based on local homogenization according to claim 2, characterized in that: In step 4), the equivalent unit cell model is arrayed at an angle of (m-1)θ along the circumferential direction and at a unit cell length of the RVE unit cell model along the weaving direction, where m is the number of layers of the main yarn array.

4. The multi-scale analysis method for three-dimensional woven composite thin-walled structure based on local homogenization according to claim 3, characterized in that: In step 3), the RVE unit cell model of step 1) is discretized using the tetrahedral mesh method in the finite element software Abaqus; in step 4), the equivalent unit cell model of step 2) is discretized using the hexahedral mesh method in the finite element software Abaqus.

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