A method and system for generating a fiber random distribution RVE considering three-dimensional space random pores

Abstract

This invention belongs to the field of multi-scale computational mechanics technology for composite materials, and discloses a method and system for generating random fiber distribution RVEs considering random porosity in three-dimensional space. Existing methods do not incorporate the physical mechanism of porosity formation into the control logic of porosity distribution. The fiber random distribution RVE generation method and system proposed in this invention first plans the RVE model parameters; then, in a two-dimensional sketch, a fiber distribution satisfying periodic boundary conditions is generated through mesh layout and random perturbation algorithm; next, the density labels of the fibers are obtained through an improved density peak clustering algorithm, and the pore size is adaptively adjusted accordingly; subsequently, pores are randomly generated in three-dimensional space by spline curve rotation, ensuring periodic distribution; finally, the final RVE model is obtained through Boolean operations. This invention achieves a pore spatial distribution that conforms to actual physical laws, and can effectively generate fiber random distribution RVEs with controllable porosity, providing a method for parameterized modeling of microstructures in FRC calculations.

Description

Technical Field

[0001] This invention relates to the field of multi-scale computational mechanics technology for composite materials, specifically to a method and system for generating random fiber distribution VE considering random porosity in three-dimensional space. Background Technology

[0002] Fiber-reinforced composites (FRCs) are widely used in aerospace, automotive, and other industries due to their excellent mechanical properties and chemical stability. The finite element method (FEM), as a bridge connecting the mesoscopic and macroscopic structural responses of composite materials, is an important tool for analyzing their mechanical behavior.

[0003] However, porosity, as an unavoidable process defect in composite material preparation, significantly affects the macroscopic properties, service behavior, and failure process of materials. Therefore, establishing a random fiber distribution with pore representative volume element (RFDP-RVE) is crucial for accurately predicting the properties of fiber-reinforced composite materials.

[0004] In existing research, the flow-compaction model is an early theory for constructing the basic model of pore formation mechanism. Subsequent studies have included modeling by pore size classification to avoid the loss of macropores and improve geometric similarity; it has been found that pore morphology is related to porosity, with small pores mostly located in the interface region and large pores concentrated in the resin-rich region; the influence of various factors on pore morphology has also been analyzed, and various RVE generation and modeling strategies have been proposed.

[0005] Clearly, existing research findings have become the theoretical and methodological cornerstone for constructing randomly distributed RVEs containing porous fibers, greatly promoting the iteration and development of micromechanical simulation technology for fiber-reinforced composites. However, none of the existing methods incorporate the physical mechanism of pore formation into the regulation logic of pore distribution, resulting in a lack of rationality and limitations in applicability when characterizing the pore shape and spatial distribution of real materials.

[0006] Specifically, the following are the characteristics: (1) The pore distribution is not related to the local fiber density and cannot reflect the physical law that large pores appear in the resin-rich area and small pores appear in the fiber-dense area; (2) The pore shape is mostly assumed to be a regular geometric shape, which does not match the real irregular morphology; (3) The periodic boundary conditions are not fully realized, which affects the accuracy of multi-scale calculations.

[0007] Therefore, there is an urgent need to develop a method for generating RVE in fiber-reinforced composites that can comprehensively consider physical mechanisms, geometric characteristics, and boundary conditions. Summary of the Invention

[0008] The purpose of this invention is to provide a method and system for generating random fiber distribution RVEs that considers random porosity in three-dimensional space, so as to solve the problems mentioned in the background art.

[0009] The main design concept of this invention is as follows: To address the aforementioned technical problems, this invention proposes a fiber random distribution RVE generation method considering three-dimensional spatial random pores. The core of this method lies in achieving precise control of pore morphology, size, and spatial distribution through a physically driven adaptive algorithm. It mainly includes a fiber and matrix basic generation module, a physically-based adaptive adjustment module for pore parameters, and a pore spatial periodic random distribution module.

[0010] To achieve the above objectives, the present invention provides the following technical solution: On one hand, the present invention provides a method for generating random fiber distribution RVE considering random porosity in three-dimensional space, comprising the following steps: Plan the RVE model parameters for FRC, including matrix parameters, fiber parameters, and pore parameters; In the 2D sketch of RVE, the fiber distribution is generated based on the matrix parameters and fiber parameters, and the fiber and matrix components are obtained by stretching. Density labels for each fiber are obtained based on fiber distribution; Within the three-dimensional space of RVE, porous components are generated based on pore parameters, fiber distribution, and density labels. The porous component is assembled with the fiber and matrix components to obtain a porous RVE model.

[0011] More preferably, the matrix parameters include: the computational domain side length of the two-dimensional sketch of the two matrices; The fiber parameters include: fiber quantity, fiber radius, minimum spacing between fibers, and maximum spacing between fibers; The pore parameters include: pore type, minimum distance between pores, minimum value of pore major axis, maximum value of pore major axis, minimum value of pore minor axis, maximum value of pore minor axis, and target porosity.

[0012] More preferably, generating the fiber distribution in the two-dimensional sketch of the RVE, based on the matrix parameters and fiber parameters, includes: The computational domain of the 2D sketch is divided into multiple grids, and the number of grids is greater than the number of fibers; Each fiber is distributed at a different grid center, with the grid center being the base position of the fiber; The base position of the fiber is randomly offset to obtain the offset position of the fiber; Boundary detection and collision detection are performed on the offset position of the fibers to obtain the distribution position of the fibers; The distribution location of fibers is determined by boundary and corner identification, and periodically replenished fibers are added.

[0013] More preferably, the boundary detection and collision detection of the fiber offset position includes: Boundary detection needs to meet the following requirements: and ; During collision detection, periodic positions are obtained based on the offset positions, and each periodic position must satisfy the following: and ; in, and These represent the horizontal and vertical coordinates of the distribution location, respectively. This represents half the side length of the computational domain of the 2D sketch. Indicates fiber radius, This represents the distance between any periodic position and any existing fiber. and These represent the minimum and maximum distances between fibers, respectively.

[0014] More preferably, the density label of each fiber based on fiber distribution is obtained through a density peak clustering algorithm.

[0015] More preferably, the density peak clustering algorithm includes: Calculate the distance matrix between fibers; The local density of the fiber is obtained based on the distance matrix; Calculate the relative distance between fibers; The local density and relative distance of the fiber are normalized to obtain the comprehensive index of the fiber. Based on comprehensive indicators, the fiber density label is marked as either high-density or low-density zone.

[0016] More preferably, the generation of porous components in the three-dimensional space of the RVE, based on pore parameters, fiber distribution, and density labels, includes: A point is randomly selected in the three-dimensional space of the RVE as the center position of the new pore; Position conflict detection is performed based on the center position of the new pore; After the collision detection is passed, the fiber closest to the center is obtained, and the pore size is adjusted according to the density label of the fiber; New pores are generated by rotating spline curves based on the center position, pore type, and pore size. Mirror locations are generated based on the center location, and mirror entities are created at each mirror location; Calculate the current porosity. If the current porosity does not reach the target porosity, continue to generate pores.

[0017] More preferably, adjusting the new pore size based on the fiber's density label includes: right In high-density regions, the new pore size is: ; ; right In the low-density region, the new pore size is: ; ; in, Indicates label density, and These represent the minimum and maximum values ​​of the minor axis of the pore, respectively. and These represent the minimum and maximum values ​​of the pore major axis, respectively. Indicates the major axis of the new pore. This indicates the short axis of the new pore.

[0018] More preferably, the positional conflict detection based on the center position of the new pore includes: Calculate the first minimum distance from the center position to any fiber axis. If the first minimum distance is less than the fiber radius, the new pore position is invalid. Calculate the second minimum distance from the center position to any existing pore. If the second minimum distance is less than the minimum distance between pores, the new pore position is invalid.

[0019] On the other hand, the present invention provides a fiber random distribution RVE generation system considering three-dimensional spatial random porosity, comprising the following modules: The fiber and matrix generation module is used to generate fiber distribution and stretch fiber and matrix components in the two-dimensional sketch of RVE based on preset matrix and fiber parameters. The fiber density tag module is used to obtain the density tag of each fiber based on fiber distribution and through a density peak clustering algorithm; The pore component generation module is used to generate pore components in the three-dimensional space of RVE based on preset pore parameters, fiber distribution and fiber density labels; The RVE model generation module is used to assemble porous components with fiber and matrix components to obtain a porous RVE model of FRC.

[0020] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention introduces a physical information guidance mechanism based on density peak clustering (DPC) to achieve a correlation mapping between pore distribution and fiber density distribution. It can accurately simulate the physical law in real composite materials where "small pores appear in dense fiber areas and large pores appear in resin-rich areas." This results in the generated RVE model having higher geometric similarity and physical consistency with the real material in terms of pore spatial distribution.

[0021] 2. This invention achieves comprehensive periodic boundary condition handling in both fiber and pore distribution aspects, ensuring seamless splicing capability of the RVE model in finite element analysis. The fiber distribution employs a 9-periodic position detection and supplementary fiber generation strategy to effectively handle boundary and corner conditions. The pore distribution uses 27-periodic position generation to ensure the continuity of pores in all spatial directions.

[0022] 3. This invention, through a multi-level parameterized control mechanism, can rapidly generate RVE models adapted to different needs, greatly expanding the applicability of this method. By adjusting the fiber quantity to control the fiber volume fraction, and through closed-loop generation and real-time porosity calculation to precisely control porosity, different regular pore shape models can be generated by adjusting the pore type. Attached Figure Description

[0023] Figure 1 This is a flowchart of the fiber random distribution RVE generation method of the present invention; Figure 2 This is a true image of the unidirectional FRC cross-section of the present invention; Figure 3 This is the principle of the random perturbation fiber placement algorithm of the present invention; Figure 4 This is a flowchart of the algorithm of the present invention; Figure 5 This is a schematic diagram illustrating the periodic fiber generation rule of the present invention; Figure 6 This is a flowchart illustrating the generation process of the fiber and matrix components of the present invention; Figure 7 This is a flowchart illustrating the calculation of fiber density labels and adjustment of pore size according to the present invention. Figure 8 A flowchart illustrating the generation of porous components and the final assembly of the RVE model according to the present invention; Figure 9 The following are RVE results for the same porosity fiber volume fraction of 10.91% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 10 The following are RVE results for the same porosity fiber volume fraction of 19.63% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 11The following are RVE results for the same porosity fiber volume fraction of 30.54% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 12 The following are RVE results for the same porosity fiber volume fraction of 39.27% ​​according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 13 The following are RVE results for the same porosity fiber volume fraction of 50.18% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 14 The following are RVE results for the same porosity fiber volume fraction of 61.09% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 15 The following are RVE results for the same fiber volume fraction porosity of 2.09% according to the present invention, where figure a is the RVE figure and figure b is the perspective view; Figure 16 The following are RVE results for the same fiber volume fraction porosity of 3.21% according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 17 The following are RVE results for the same fiber volume fraction porosity of 4.04% according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 18 The following are RVE results for the same fiber volume fraction porosity of 5.00% according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 19 The following are RVE results for the same fiber volume fraction porosity of 6.02% according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 20 The following are RVE results for the same fiber volume fraction porosity of 7.04% according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 21 The above are RVE results for the same fiber volume fraction and porosity with pore type A in this invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 22 The above are RVE results for the same fiber volume fraction and porosity with pore type B in this invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 23 The above are RVE results for the same fiber volume fraction and porosity with pore type C in this invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 24The above are RVE results for the same fiber volume fraction and porosity with pore type D in this invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 25 The above are RVE results for the same fiber volume fraction and porosity with pore type E in this invention, where figure a is the RVE figure and figure b is the RVE perspective view; Figure 26 The above are RVE results for the same fiber volume fraction and porosity with pore type F according to the present invention, where figure a is the RVE figure and figure b is the RVE perspective view. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] In the description of this invention, it should be noted that the terms "upper," "lower," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, the terms "installation" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0026] Example 1 like Figures 1 to 8 As shown, this embodiment provides a method for generating random fiber distribution RVEs considering random porosity in three-dimensional space, including the following steps: Plan the RVE model parameters for FRC, including matrix parameters, fiber parameters, and pore parameters; In the 2D sketch of RVE, the fiber distribution is generated based on the matrix parameters and fiber parameters, and the fiber and matrix components are obtained by stretching. Density labels for each fiber are obtained based on fiber distribution; Within the three-dimensional space of RVE, porous components are generated based on pore parameters, fiber distribution, and density labels. The porous component is assembled with the fiber and matrix components to obtain the porous RVE model of FRC.

[0027] A true image of a unidirectional FRC cross section is attached. Figure 1 As shown, based on the random distribution of fibers, large pores appear in resin-rich areas, while small pores appear in fiber-dense areas. This invention proposes a fiber random distribution RVE generation method that considers three-dimensional spatial random porosity, based on density peak clustering (DPC) spatial optimization considering physical mechanisms and improved random perturbation.

[0028] This method mainly includes three modules: a fiber and matrix foundation generation module, a pore parameter adaptive adjustment module based on physical information, and a pore space periodic random distribution module.

[0029] The fiber and matrix foundation generation module generates a basic RVE model with randomly distributed fibers through a random perturbation algorithm and periodic boundary conditions. This includes steps such as parameter initialization, meshed foundation layout generation, fiber placement and conflict detection, and periodic fiber replenishment. Controllable random perturbation balances the uniformity and randomness of the distribution, and rigorous periodic checks ensure boundary continuity.

[0030] The pore parameter adaptive adjustment module based on physical information analyzes fiber distribution density using an improved density peak clustering (DPC) algorithm and adaptively adjusts pore parameters based on physical observations. The improved DPC algorithm does not perform hard clustering; instead, it outputs a density label (0 or 1) for each fiber to guide pore size generation.

[0031] The pore space periodic random distribution module realizes the random distribution of pores and periodic boundary conditions in three-dimensional space. By generating 27 periodic locations, the continuity of pores at the RVE boundary is ensured. Conflict detection includes pore-fiber conflict (avoiding pores from being completely embedded in fibers) and pore-pore conflict (controlling minimum spacing). Finally, a complete RVE is obtained through Boolean operations and assembly.

[0032] 1. Overall process of the technical solution of this invention The inputs of this invention include RVE geometric parameters, fiber parameters, and pore parameters, and the output is a fiber-reinforced RVE model with three-dimensional random pores. The entire process is parameter-driven, ensuring the repeatability and controllability of the model.

[0033] The Rectangular Velocity (RVE) is the smallest volumetric unit for the macroscopic properties of composite materials. Its core assumption is that macroscopic homogeneity can be statistically characterized through microstructure. Mirroring ensures the continuity of the RVE boundary, supporting simulation of infinitely large materials. The random distribution of fibers and pores must meet homogeneity requirements to avoid local aggregation. The pore distribution is related to the local fiber density, consistent with observations during material preparation processes.

[0034] This invention first generates a fiber distribution in a two-dimensional plane, then stretches it into a three-dimensional basic RVE; next, it uses DPC to analyze fiber density to guide the adaptive generation of pore parameters; finally, it randomly distributes pores in three-dimensional space and controls porosity through Boolean operations. The entire process achieves precise control of porosity through iterative iteration, ultimately assembling the RVE model.

[0035] 2. Fiber and matrix basic generation module The goal of this module is to generate a basic model of the random fiber distribution that satisfies periodic boundary conditions, providing a geometric basis for subsequent pore generation. (See attached image) Figure 3 As shown, the process includes five steps: parameter initialization, mesh layout, fiber placement and collision detection, periodic fiber replenishment, and creation of fiber and matrix components.

[0036] 2.1 Planning Model Parameters Parameter initialization is fundamental; its purpose is to transform the macroscopic parameters input by the user into microscopic parameters (such as the number of fibers N) that the algorithm can manipulate through geometric relationships. This includes: RVE matrix parameters: the computational domain side length 2a and depth b of the RVE 2D sketch; Fiber parameters: fiber radius r, number of fibers N, minimum spacing between fibers Maximum spacing between fibers ; Pore ​​parameters: Pore type Minimum spacing between fibers; maximum spacing between fibers; The pore parameters include: pore type and minimum distance between pores. Minimum value of pore major axis Maximum value of the major axis of the pore Minimum value of pore minor axis Maximum value of pore minor axis Target porosity , long axis of pores Pore ​​short axis Tolerance .

[0037] fiber volume fraction This formula is derived based on the two-dimensional cross-sectional area ratio, assuming that the fibers are uniformly distributed in the depth direction. Parameter settings must meet process constraints, such as the minimum spacing between fibers. It needs to be greater than zero to avoid overlap; typical values ​​are 0.1-0.5 μm.

[0038] In practical implementation, the basic dimensional parameters of the RVE must first be determined. The selection of the RVE size should meet the following conditions: the side length 2a in the X and Y directions should contain at least 10-15 fibers to ensure statistical representativeness; the depth b in the Z direction is usually equal to or proportional to 2a. The fiber radius r is determined according to the actual material system, and the number of fibers N is calculated by back-calculating the target fiber volume fraction.

[0039] 2.2 Grid Layout The purpose of a gridded layout is to provide an initial uniform distribution of fibers and avoid local clustering caused by random placement.

[0040] First, calculate the grid size. Ensure that the number of meshes is greater than the number of fibers; Next, calculate the grid step size. , Then generate within the range [-a, a]. A uniformly distributed grid, with each grid point serving as the base position for the fiber.

[0041] The gridded layout strategy is based on the principle of space filling to ensure maximum uniformity of the initial distribution. Finally, the perturbation range is set to 20% of the grid step size. By setting the perturbation range, randomness and placement success rate are balanced. .

[0042] In practical implementation, boundary handling needs to be considered during the meshing layout process. Since fibers can partially extend beyond the boundaries of the RVE (in preparation for periodic mirroring), the generation of mesh points needs to ensure coverage of the entire area, including the boundary extension.

[0043] After the grid layout is divided, the coordinates of each grid cell are: , Where i and j are the horizontal and vertical indices of the grid, with values ​​ranging from 0 to 1. .

[0044] 2.3 Fiber Placement and Collision Detection Fiber placement is done fiber-by-fiber, introducing randomness through the aforementioned random perturbation, while collision detection ensures distribution compliance. The implementation process includes the following technical details.

[0045] For each fiber's candidate location, in its vicinity ( An adaptive random offset is added to obtain the offset position of the fibers, and the offset amount follows a uniform distribution. The setting of the perturbation range is crucial; too small a range will result in an overly regular fiber distribution, losing randomness; too large a range will increase the probability of collision detection failure. In this invention, extensive experimental verification has shown that a 20% grid step size range achieves a good balance.

[0046] Check that the fiber is completely within the effective area, allowing the fiber center to extend beyond the RVE boundary by a maximum distance of one radius. and .

[0047] Boundary detection provides the conditions for periodic mirroring, achieved by comparing fiber coordinates with the boundary distance. During implementation, the fiber coordinates are checked. Is it in Within the range, and Is it in Within the range.

[0048] Collision detection involves calculating all nine periodic positions of the new fiber (primary position + eight periodic complementary mirror positions) and performing distance constraint checks with all periodic positions of existing fibers. Spatial indexes (such as KD-trees) are used to accelerate collision detection and reduce computational complexity.

[0049] The distance calculation formula is: It needs to meet the following requirements. (Minimum spacing) and (Maximum distance).

[0050] If a new fiber location violates the distance constraint check, the current candidate location is rejected and a new location is generated by re-perturbing. Each fiber can attempt a maximum of [number] times. If it fails, it will revert to the grid position.

[0051] 2.4 Periodic fiber supplementation If the fiber distribution location passes all the above collision detections, the fiber distribution location can be determined. Then, draw it on the RVE sketch. A circle with radius r as the center is drawn, and then periodically supplemented, as shown in the attached diagram. Figure 5 As shown, this ensures fiber continuity during RVE splicing. Periodic replenishment includes both boundary and corner cases.

[0052] The boundary judgment rule is that if the distance from the fiber center to the boundary is less than the fiber radius, periodically supplemented fibers in the corresponding direction are required. For example: Right boundary: →Left-side periodic fiber supplementation ; Left boundary: →Right-periodic fiber supplementation ; Upper boundary: →Replenish fiber in the next cycle ; Lower boundary: → Periodically supplement fiber .

[0053] The corner determination rule is that if the distance from the fiber center to the corner is... It requires periodic fiber replenishment in multiple directions. (Distance from corner) At this time, it is necessary to replenish fibers in three directions periodically. For example, the upper right corner needs to replenish fibers in the left, lower, and lower left directions periodically.

[0054] In practice, it is necessary to generate corresponding periodic mirror fibers for each fiber near the boundary. The coordinates of these mirror fibers are obtained by adding or subtracting 2a from the original coordinates, thereby ensuring that the fiber pattern can be continuous when multiple RVEs are spliced ​​together.

[0055] 2.5 Creating fiber and matrix components After completing the 2D sketch, extrude it along the Z-axis to a depth of b to generate a 3D solid. The extrusion operation is based on the software's basic functionality; it's essential to ensure the sketch plane is perpendicular to the extrusion direction. Boolean operations remove the fiber components from the base component, generating an RVE component with fiber holes. Key parameters include: During the creation of fiber and matrix components, the XY plane is typically defined as the transverse section, and the Z-axis is defined as the material thickness direction. The stretching operation should ensure that all fibers are continuous in the Z-direction and perpendicular to the XY plane. During Boolean operations, it is necessary to ensure that the fiber entity completely penetrates the matrix material to generate correct fiber pores.

[0056] 3. Pore parameter adaptive adjustment module based on physical information This module uses the DPC algorithm to analyze and transform fiber density information into a basis for pore parameter control. (See attached...) Figure 4 As shown, it specifically includes two parts: calculating the fiber density label and adaptive adjustment of pore size.

[0057] 3.1 Calculate the fiber density label An improved DPC algorithm is used to cluster density peaks of successfully placed fibers. Unlike the standard DPC algorithm, which explicitly divides fibers into different clusters, this algorithm outputs a density label for each fiber based on its location information. .

[0058] First, the distance matrix between fibers is calculated, and then the local density of fiber i is calculated based on the Gaussian kernel. ,in, This represents the distance between fibers i and j. The cutoff distance is typically taken as the 2nd quantile of the distance distribution. Then, the relative distance to fiber i is calculated. (Minimum distance from fiber i to a higher density point).

[0059] Next, after normalizing the local density and relative distance of fiber i to the [0,1] interval, the comprehensive index is calculated. Finally, according to The median will be the density label of the fiber. The density is labeled as 0 (low density) or 1 (high density). This method avoids the instability of hard clustering and directly outputs density labels.

[0060] The improved DPC algorithm needs to solve several key problems: the first is the cutoff distance. The determination, A value that is too small will cause the local density calculation to be overly sensitive. A value that is too large will make the density difference insignificant. Experiments have shown that taking the 2% quantile of the upper triangular elements (excluding the diagonal) of the distance matrix as the optimal value is... This approach yields good results. Secondly, in calculating local density, using a Gaussian kernel function instead of a truncated kernel function makes the density calculation smoother. The sensitivity to values ​​is reduced. Finally, normalization is performed to normalize ρ and δ to the [0,1] interval.

[0061] 3.2 Adaptive adjustment of pore size First, randomly select the pore center position inside the RVE, calculate the distance from the new pore position to the center of all fibers, find the nearest fiber and its density label, and then perform adaptive adjustment of pore size.

[0062] For density labels In the high-density fiber zone, smaller pores are generated using the lower 30% of the parameter range, i.e. , .

[0063] For density labels In the low-density fiber region, the upper 70% of the parameter range generates larger pores, i.e. , .

[0064] in, and These represent the minimum and maximum values ​​of the minor axis of the pore, respectively. and These represent the minimum and maximum values ​​of the pore long axis, respectively. This physical mechanism simulates the physical law that the pore growth space is large in the resin-rich region (low density) and the space is limited in the fiber-dense region (high density).

[0065] 4. Pore space periodic random distribution module The pore space periodic random distribution module realizes the random distribution of pores and periodic boundary conditions in three-dimensional space. It includes pore generation, collision detection, Boolean operations, and assembly steps.

[0066] 4.1 Three-dimensional modeling of pores Pore ​​modeling is based on the principle of spline curve rotation, with the core being the use of cubic spline interpolation to generate irregular pore cross-sectional profiles. Firstly, according to... (AF) Select control points, such as type B control points which include the start point, vertex, and interpolation point.

[0067] Then, using the Y-axis as the rotation axis, rotate the 2D sketch 360° to generate a 3D solid of revolution. The spline curve parameters are determined by the pore size ( , The size is adjusted by scaling the control point coordinates. The rotation operation ensures that the aperture is a closed solid and is suitable for Boolean operations.

[0068] 4.2 Periodic random placement of pores The periodic placement of pores is achieved by generating 27 mirror positions: including the main position, 8 mirror positions in the XY plane (left, right, top, bottom, and four corners), 2 mirror positions in the Z direction (top and bottom), and 16 combined mirror positions (combinations of XY and Z mirror positions). The specific process is as follows: For the center location of the selected pore, all offset combinations are generated, resulting in 27 mirror locations. A mirror entity is created for each mirror location, the pore entity is copied and translated to ensure geometric consistency; pores near the boundary are automatically mirrored. This process ensures seamless continuity of the pore distribution during RVE stitching and supports periodic boundary finite element analysis.

[0069] 4.3 Conflict Detection Conflict detection includes pore-fiber detection and pore-pore detection.

[0070] Pore-fiber conflict detection checks whether pores are completely embedded within the fiber. The criterion is whether the minimum distance from the pore surface to the fiber axis is less than the fiber radius. If the condition is met, meaning the pore is completely inside the fiber, the pore coordinates are invalid, and new pore coordinates are selected. If the condition is not met, it means the pore is not completely inside the fiber, and the current pore coordinates are valid, proceeding to the next pore for conflict detection.

[0071] Pore-pore conflict detection checks whether the minimum distance between a new pore and an existing pore is less than the minimum distance between pores. If there is a conflict, the current pore coordinates are invalid and need to be reselected. If the conditions are met, proceed to the next step. The calculation takes periodic boundaries into account and is obtained using the minimum mirror distance formula.

[0072] Spatial hashing or KD-trees are used to accelerate nearest neighbor search during collision detection, thereby reducing computational complexity.

[0073] 4.4 Boolean Operations and Porosity Control After collision detection, the base component and all pores are instantiated, and each pore is translated to the correct coordinates. Then, a Boolean cut operation is performed to obtain a new component, and the volume of the new component is calculated and the porosity is updated: Current porosity = (Base volume - New component volume) / Total RVE volume. Specifically, this includes: This is achieved through the software's entity volume query function, ensuring unit consistency; pores are generated iteratively until the porosity meets the target range. ± Each loop attempts a maximum of 1000 times to avoid infinite loops. Tolerance. It is usually set to 0.005 (0.5%), but for high precision requirements it can be set to 0.001.

[0074] Finally, based on the existing RVE components, the final fiber-randomized RVE considering three-dimensional spatial random porosity is assembled. Specifically, intermediate components are cleaned, and fiber and matrix components are assembled with the RVE containing three-dimensional porosity to obtain a fiber-randomized RVE considering three-dimensional spatial random porosity that can be used for composite material micromechanics calculations.

[0075] Example 2 like Figures 1 to 8 As shown, this embodiment provides a fiber random distribution RVE generation system considering three-dimensional spatial random porosity, including the following steps: The fiber and matrix generation module is used to generate fiber distribution and stretch fiber and matrix components in the two-dimensional sketch of RVE based on preset matrix and fiber parameters. The fiber density tag module is used to obtain the density tag of each fiber based on fiber distribution and through a density peak clustering algorithm; The pore component generation module is used to generate pore components in the three-dimensional space of RVE based on preset pore parameters, fiber distribution and fiber density labels; The RVE model generation module is used to assemble porous components with fiber and matrix components to obtain a porous RVE model.

[0076] Example 3 like Figures 1 to 26 As shown, this embodiment, based on the method of embodiment 1, creates RVEs with the same porosity but different fiber volume fractions, RVEs with the same fiber volume fraction but different porosities, and RVEs with the same fiber volume fraction and porosity but different pore shapes by adjusting the initial parameters.

[0077] 1. RVE generation results with the same porosity but different fiber volume fractions The input parameters are: the side length 'a' of the sketch computational domain is 30. The fiber radius r is 5 The required fiber quantities N are 5, 9, 14, 18, 23, and 28, respectively, corresponding to the fiber volume fractions. The percentages were 10.91%, 19.63%, 30.54%, 39.27%, 50.18%, and 61.09%, respectively.

[0078] Secondly, set the minimum spacing between each fiber. =0, pore type B is the minor axis of the pores. pore long axis Target porosity The tolerance is 0.04. Set to 0.

[0079] As attached Figure 9 The image shows the RVE generation results with a porosity of 4.42%, a fiber count of 5, and a fiber volume fraction of 10.91%. (See attached image.) Figure 10 The image shows the RVE generation results with a porosity of 4.41%, a fiber count of 9, and a fiber volume fraction of 19.63%.

[0080] As attached Figure 11 The image shows the RVE generation results with a porosity of 4.07%, a fiber count of 14, and a fiber volume fraction of 30.54%. (See attached image.) Figure 12 The image shows the RVE generation results with a porosity of 4.21%, a fiber count of 18, and a fiber volume fraction of 39.27%.

[0081] As attached Figure 13 The image shows the RVE generation results with a porosity of 4.01%, a fiber count of 23, and a fiber volume fraction of 50.18%. (See attached image.) Figure 14 The image shows the RVE generation results with a porosity of 4.04%, a fiber count of 28, and a fiber volume fraction of 61.09%.

[0082] Depend on Figures 9 to 14 It can be seen that the porosity is close to 4%, controlled between 4.01% and 4.42%, the fiber distribution is uniform, and the pore size varies with... The pore size increases and decreases (the proportion of high-density areas increases), and the pore size adapts to the fiber density.

[0083] This experiment simulates the physical property of resin-rich regions having larger pores and fiber-dense regions having smaller pores in real materials. It demonstrates the adaptive change of pore morphology with fiber density, verifying that this method can flexibly adapt to different fiber volume fractions while maintaining constant porosity. These models can be directly used to study the influence of fiber volume fraction on the mechanical properties of composite materials (such as elastic modulus).

[0084] 2. RVE generation results with the same fiber fraction but different porosities The input parameters are: the side length 'a' of the sketch computational domain is 30. The fiber radius r is 5 The required number of fibers, N, is 26, and the corresponding fiber volume fraction is... They were 56.72% respectively.

[0085] Set the minimum spacing between each fiber. =0, pore type B is the minor axis of the pores. pore long axis Target porosity The tolerances are 2%, 3%, 4%, 5%, 6%, and 7%. Setting it to 0.005 yields RVE generation results for different porosities, as shown in Figures 15 to 20.

[0086] like Figure 15 As shown, this is a graph illustrating the RVE generation results for a porosity of 2.09%. Figure 16 As shown, this is a graph illustrating the RVE generation results for a porosity of 3.21%. Figure 17 The image shows the RVE generation results with a porosity of 4.04%.

[0087] like Figure 18 The image shows the RVE generation results with a porosity of 5.00%. Figure 19 As shown, this is a graph illustrating the RVE generation results for a porosity of 6.02%. Figure 20 The image shows the RVE generation results with a porosity of 7.04%.

[0088] Depend on Figures 15 to 20 It can be seen that, with only changes in porosity, the porosity is precisely controlled between 2.09% and 7.04%, and the pore morphology changes from circular to elongated as the porosity increases. As the porosity gradually increases, the number and size of pores increase accordingly, but the fiber distribution remains unchanged, highlighting the precision and adaptability of porosity control.

[0089] This experimental process achieves precise porosity control through the periodic random distribution of pore space. As pores are generated cyclically, Boolean operations are used to calculate the current porosity in real time and compare it with the target value until it falls within the tolerance range.

[0090] The adaptive adjustment module for pore parameters ensures that the pore morphology changes with the porosity: at low porosity (e.g., 2%), the pores are mostly small and round, concentrated in the fiber interface region; at high porosity (e.g., 7%), the pores become larger and longer, and are enriched in the resin region.

[0091] Conflict detection avoids pore overlap, ensuring the physical rationality of the distribution. The results verify that this method can generate a continuously varying porosity model under a single fiber volume fraction, making it suitable for studying the influence of porosity on material failure behavior.

[0092] 3. RVE generation results for different pore shapes with the same fiber volume fraction and porosity. The input parameters are: the side length 'a' of the sketch computational domain is 30. The fiber radius r is 5 The required number of fibers, N, is 26, and the corresponding fiber volume fraction is... They were 56.72% respectively.

[0093] Set the minimum spacing between each fiber. =0, pore type The minor axes are A, B, C, D, E, and F, respectively. pore long axis Target porosity The tolerance is 0.04%. Setting it to 0.01 yields RVE generation results for different porosities, as shown in Figures 21 to 26.

[0094] like Figure 21 As shown, this is the RVE generation result for a fiber with a volume fraction porosity of 4.01% and pore type A. Figure 22 As shown, this is the RVE generation result diagram for the same fiber volume fraction porosity of 4.04% and pore type B.

[0095] like Figure 23 As shown, this is the RVE generation result for a fiber with a volume fraction porosity of 4.33% and pore type C. Figure 24 As shown, this is the RVE generation result diagram for the same fiber volume fraction porosity of 4.08% and pore type D.

[0096] like Figure 25 As shown, this is the RVE generation result for a fiber with a volume fraction porosity of 4.11% and pore type E. Figure 26 As shown, this is the RVE generation result diagram for the same fiber volume fraction porosity of 4.32% and pore type F.

[0097] Figures 21 to 26As shown, shape diversity is achieved through the Spline Curve Rotation Control (SCF) method. It can be seen that the porosity is close to 4%, but the pore morphology varies significantly, ranging from nearly circular (A) to highly irregular (F), demonstrating the influence of different pore shapes on the model.

[0098] Control points for the spline curves were defined to generate different geometries: type A might be a regular circle, type B an ellipse, and types C through F gradually increase in irregularity, simulating porosity variations in real materials. A physically-informed adaptive adjustment module ensures that the pore size of all shapes is adjusted according to the fiber density distribution, maintaining physical consistency.

[0099] The periodic distribution module for pore space handles mirror images and collisions of different shapes, ensuring periodic boundary conditions. Results demonstrate that the method can rapidly generate various pore morphologies, enhancing the geometric realism and applicability of the model, and is suitable for studying the influence of pore shape on the transverse elastic properties of composite materials.

[0100] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention, and no reference numerals in the claims should be construed as limiting the scope of the claims.

[0101] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for generating random fiber distribution RVE considering random porosity in three-dimensional space, characterized in that, Includes the following steps: Preset the RVE model parameters for FRC, including matrix parameters, fiber parameters, and pore parameters; In the 2D sketch of RVE, the fiber distribution is generated based on the matrix parameters and fiber parameters, and the fiber and matrix components are obtained by stretching. Density labels for each fiber are obtained based on fiber distribution; Within the three-dimensional space of RVE, porous components are generated based on pore parameters, fiber distribution, and density labels. The porous component is assembled with the fiber and matrix components to obtain the porous RVE model of FRC.

2. The method for generating random fiber distribution RVE considering three-dimensional spatial random porosity according to claim 1, characterized in that, The matrix parameters include: the side length of the computational domain of the two-dimensional sketch of the matrix; The fiber parameters include: fiber quantity, fiber radius, minimum spacing between fibers, and maximum spacing between fibers; The pore parameters include: pore type, minimum distance between pores, minimum value of pore major axis, maximum value of pore major axis, minimum value of pore minor axis, maximum value of pore minor axis, and target porosity.

3. The fiber random distribution RVE generation method considering three-dimensional spatial random porosity according to claim 2, characterized in that, In the two-dimensional sketch of RVE, generating the fiber distribution based on matrix parameters and fiber parameters includes: The computational domain of the 2D sketch is divided into multiple grids, and the number of grids is greater than the number of fibers; Each fiber is distributed at a different grid center, with the grid center being the base position of the fiber; The base position of the fiber is randomly offset to obtain the offset position of the fiber; Boundary detection and collision detection are performed on the offset position of the fibers to obtain the distribution position of the fibers; The distribution location of fibers is determined by boundary and corner identification, and periodically replenished fibers are added.

4. The fiber random distribution RVE generation method considering three-dimensional spatial random porosity according to claim 3, characterized in that, The boundary detection and collision detection of the fiber offset position includes: Boundary detection needs to meet the following requirements: and ; During collision detection, periodic positions are obtained based on the offset positions, and each periodic position must satisfy the following: and ; in, and These represent the horizontal and vertical coordinates of the distribution location, respectively. This represents half the side length of the computational domain of the 2D sketch. Indicates fiber radius, This represents the distance between any periodic position and any existing fiber. and These represent the minimum and maximum distances between fibers, respectively.

5. The method for generating random fiber distribution RVE considering three-dimensional spatial random porosity according to claim 1, characterized in that, The density label of each fiber based on fiber distribution is obtained through a density peak clustering algorithm.

6. The method for generating random fiber distribution RVE considering three-dimensional spatial random porosity according to claim 5, characterized in that, The density peak clustering algorithm includes: Calculate the distance matrix between fibers; The local density of the fiber is obtained based on the distance matrix; Calculate the relative distance between fibers; The local density and relative distance of the fiber are normalized to obtain the comprehensive index of the fiber. Based on comprehensive indicators, the fiber density label is marked as either high-density or low-density zone.

7. The method for generating random fiber distribution RVE considering three-dimensional spatial random porosity according to claim 2, characterized in that, The process of generating porous components within the three-dimensional space of the RVE, based on pore parameters, fiber distribution, and density labels, includes: A point is randomly selected in the three-dimensional space of the RVE as the center position of the new pore; Position conflict detection is performed based on the center position of the new pore; After the collision detection is passed, the fiber closest to the center is obtained, and the pore size is adjusted according to the density label of the fiber; New pores are generated by rotating spline curves based on the center position, pore type, and pore size. Mirror locations are generated based on the center location, and mirror entities are created at each mirror location; Calculate the current porosity. If the current porosity does not reach the target porosity, continue to generate pores.

8. The fiber random distribution RVE generation method considering three-dimensional spatial random porosity according to claim 7, characterized in that, The adjustment of the new pore size based on the fiber's density label includes: for In high-density regions, the new pore size is: ； ； for In the low-density region, the new pore size is: ； ； in, Indicates label density, and These represent the minimum and maximum values ​​of the minor axis of the pore, respectively. and These represent the minimum and maximum values ​​of the pore major axis, respectively. Indicates the major axis of the new pore. This indicates the short axis of the new pore.

9. The method for generating random fiber distribution RVE considering three-dimensional spatial random porosity according to claim 7, characterized in that, The positional conflict detection based on the center position of the new pore includes: Calculate the first minimum distance from the center position to any fiber axis. If the first minimum distance is less than the fiber radius, the new pore position is invalid. Calculate the second minimum distance from the center position to any existing pore. If the second minimum distance is less than the minimum distance between pores, the new pore position is invalid.

10. A fiber-randomized RVE generation system considering three-dimensional spatial random porosity, characterized in that, Includes the following modules: The fiber and matrix generation module is used to generate fiber distribution and stretch fiber and matrix components in the two-dimensional sketch of RVE based on preset matrix and fiber parameters. The fiber density tag module is used to obtain the density tag of each fiber based on fiber distribution and through a density peak clustering algorithm; The pore component generation module is used to generate pore components in the three-dimensional space of RVE based on preset pore parameters, fiber distribution and fiber density labels; The RVE model generation module is used to assemble porous components with fiber and matrix components to obtain a porous RVE model of FRC.

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