Method for establishing RVE model of aerogel composite considering randomness of fiber characteristics

Abstract

The application discloses an aerogel composite RVE model establishing method considering fiber characteristic randomness, and comprises the following steps: S1: establishing a matrix model; S2: establishing a fiber network model, wherein the spatial characteristic parameters comprise fiber starting point coordinates in the matrix, fiber inclination and rotation angle, and fiber minimum spacing; the shape characteristic parameters comprise fiber length, fiber local curvature, fiber cross-section diameter, and further comprise fiber quantity or fiber volume fraction; and S3: assembling an overall model. The method can fully consider the spatial characteristic randomness and shape characteristic randomness of the fiber reinforcement, the spatial characteristic randomness comprises stratified arrangement in the matrix, fiber direction in the layer, normal inclination angle, fiber minimum spacing, etc., the shape characteristic randomness comprises fiber curvature characteristic and cross-section size characteristic, etc., a plane circular arc method is adopted to simulate real fiber morphology at a mesoscale, and a fiber model with local change curvature characteristic can be obtained.

Description

Technical Field

[0001] This invention relates to the field of composite materials technology, and in particular to a method for establishing RVE models of aerogel composite materials that considers the randomness of fiber characteristics. Background Technology

[0002] In the aerospace field, aerogel composites have attracted much attention as a novel thermal insulation material, possessing a certain load-bearing capacity, which also provides new possibilities for structural design. How to prepare aerogel composites with superior thermal insulation and mechanical properties is not only a crucial problem that materials researchers are striving to solve, but also key to meeting the urgent needs of industry. At the microscale, utilizing computer-aided design and finite element simulation calculations for mechanical modeling and simulation analysis is an important way to reduce R&D costs and improve engineering efficiency.

[0003] According to the search, Chinese patent application number CN111639451A discloses a refined modeling and simulation method for two-dimensional plain weave fiber-reinforced composite materials. It proposes that fiber-reinforced composite materials present a mixed state composed of fibers, matrix and interface phases at the microscopic level, which has a complex microstructure and is very difficult to model. The method establishes a three-dimensional geometric model by determining the performance parameters of the fiber bundle. Chinese patent application number CN114091298A discloses a multi-scale simulation method for complex structures of short fiber reinforced thermoplastic composites, which constructs an accurate material constitutive model by considering the material anisotropy caused by the injection molding process. However, while some methods exist for establishing mesoscale structural models of short fiber reinforced composites for finite element analysis, they still cannot fully meet the needs of aerogel composite research and development. Firstly, existing modeling methods do not adequately consider the spatial and shape randomness of the fiber reinforcement. Spatial randomness includes the layered arrangement within the matrix, fiber orientation within layers, normal tilt angle, and minimum fiber spacing, while shape randomness includes fiber curvature, length, and cross-sectional dimensions. Secondly, while the three-dimensional solid fiber models used in conventional structural composites can account for the influence of local stress distribution at fiber ends in aerogel composite mechanical calculations, the excessive number of meshes and elements leads to low computational efficiency and difficulty in convergence, hindering rapid engineering research and development.

[0004] Therefore, there is an urgent need to develop a method for establishing a representative volume element (RVE) model that fully considers the spatial and shape randomness of fiber characteristics, in order to generate a composite material finite element calculation model that satisfies a certain fiber volume fraction, for efficient simulation calculation and engineering design. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a method for establishing an RVE model for aerogel composite materials that considers the randomness of fiber characteristics.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for establishing a Reactive Energy (RVE) model for aerogel composites that considers the randomness of fiber characteristics includes the following steps: S1: Establish the base model, where the parameters of the base model include: the length a, width b, and height h of the RVE model; S2: Establish a fiber network model, wherein the parameters of the fiber network model include: spatial feature parameters and shape feature parameters; Spatial characteristic parameters include fiber origin coordinates, fiber tilt angle, fiber rotation angle, and minimum fiber spacing within the matrix, as well as fiber number or fiber volume fraction. Shape characteristic parameters include fiber length, local curvature of the fiber, and diameter of the fiber cross section; A fiber network model contains a certain number of individual fibers or a certain fiber volume fraction. A single fiber can be a straight fiber with no curvature change or a curved fiber with continuously changing curvature. S3: Assemble the overall model: Merge the generated fiber network model with the matrix model, embedding the fiber network into the matrix to form a composite material RVE model. Constraints and loads are then added for mesoscale mechanical and thermodynamic calculations.

[0007] Furthermore, in step S1, the specific steps for establishing the matrix model are as follows: The length, width, and height of the base model are determined to be a, b, and h, respectively. A base model with a cuboid spatial shape is generated. The entire base is the area where fibers are deployed. The base model can be meshed using three-dimensional solid elements.

[0008] Furthermore, in step S2, the specific steps for establishing the fiber network portion are as follows: (1) Determine the fiber delivery target, including the fiber quantity n or fiber volume fraction V. f； (2) Complete the establishment of a single fiber model, including straight fibers with no curvature change or curved fibers with constantly changing curvature; (3) Randomly place fibers in a spatial region that is the same size as the matrix model.

[0009] Furthermore, in step S2, the specific steps for generating a single fiber are as follows: (1) Determine the range of variation for fiber length, fiber curvature, and fiber diameter; (2) Straight fiber generation: The length l0 and diameter d of the fiber are generated using the Weibull distribution function. The starting point of the fiber is (0, 0) and the ending point is (0, l0). The fiber is modeled as a two-dimensional solid straight line. The diameter is defined by the cross-sectional properties of the model, thus obtaining a single fiber model. The probability density function of the Weibull distribution is:

[0010] Where x is a random variable, λ>0 is a scaling parameter, and k>0 is a shape parameter; (3) Generation of curved fibers: First, the total length l0 and diameter d of the fiber are generated using the Weibull distribution function. Then, the single curved fiber model is obtained using the planar circular arc method. A single curved fiber is composed of n circular arcs connected together. The number of circular arcs can be set manually. (4) For straight or curved fiber models, two-dimensional rod elements or beam elements can be used for mesh generation.

[0011] Furthermore, the planar circular arc method used in the generation of bent fibers is as follows: The range of length variation for each arc segment can be determined by the upper limit l0 / (n-1) and the lower limit l0 / n. The lengths of the first to n-1 arc segments can be determined using the Weibull distribution function. The length of the nth arc segment is determined by subtracting the sum of the lengths of the previous n-1 arc segments from the total length l0, thereby randomly distributing the total length to each arc segment. The curvature of each arc segment is randomly generated using the Weibull function.

[0012] Furthermore, in step S3, the specific steps for assembling the overall model are as follows: The generated fiber network model is merged with the matrix model. The matrix model is meshed using three-dimensional solid elements, while the fiber network model is meshed using two-dimensional rod or beam elements. The fiber network is embedded into the matrix to form a composite material RVE model. Constraints and loads are then added for calculation.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: This method can fully consider the spatial and shape randomness of fiber reinforcement. Spatial randomness includes the layered arrangement within the matrix, fiber orientation within layers, normal tilt angle, and minimum fiber spacing, while shape randomness includes fiber curvature, length, and cross-sectional dimensions. Second, compared to three-dimensional solid fiber models used in conventional structural composites, using two-dimensional solid straight or curved models for geometric modeling of fiber reinforcement is more efficient in modeling and calculation, and converges more easily, facilitating rapid material design optimization and structural strength design. Third, using the planar circular arc method to simulate the real fiber morphology at the microscale can obtain fiber models with locally varying curvature characteristics, resulting in a more realistic model. Attached Figure Description

[0014] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0015] Figure 1 This is a flowchart of the fiber delivery process in an embodiment of the present invention. Figure 2 This is a schematic diagram of bending fiber modeling in an embodiment of the present invention. Figure 3 This is Example 1 of the finite element model (straight fiber) in the embodiments of the present invention. Figure 4 This is finite element model example 2 (bent fiber) in the embodiments of the present invention. Detailed Implementation

[0016] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0017] In this application, the aerogel composite material RVE model generated by this method satisfies the following conditions: (1) it satisfies the geometric periodic structure characteristics, which facilitates the application of periodic boundary conditions; (2) the fibers do not interfere and the spacing is controllable, and the fiber volume fraction or total number is controllable; (3) it can realize that the spatial distribution and geometric dimensions of the fibers follow a specific probability distribution; (4) a single bent fiber model composed of multiple arc segments with different curvatures is generated using the planar circular arc method. In the final generated RVE model, fibers with random characteristics are distributed within the matrix model. This patented method can realize the parameterized design of the RVE model and can generate specific models according to calculation requirements.

[0018] Reference Figure 1-4 The method for establishing an RVE model for aerogel composites considering the randomness of fiber characteristics includes the following steps: S1: Establish the base model, where the parameters of the base model include: the length a, width b, and height h of the RVE model; S2: Establish a fiber network model, wherein the parameters of the fiber network model include: spatial characteristic parameters including fiber origin coordinates, fiber tilt angle, fiber rotation angle and minimum fiber spacing in the matrix, as well as fiber number or fiber volume fraction; shape characteristic parameters including fiber length, fiber local curvature and fiber cross-sectional diameter. A fiber network model contains a certain number of individual fibers or a certain fiber volume fraction. A single fiber can be a straight fiber with no curvature change or a curved fiber with continuously changing curvature. S3: Assemble the overall model: Merge the generated fiber network model with the matrix model, embedding the fiber network into the matrix to form a composite material RVE model. Constraints and loads are then added for mesoscale mechanical and thermodynamic calculations.

[0019] As a preferred embodiment of this application, the specific steps in step S1 are as follows: The length, width, and height of the base model are determined to be a, b, and h, respectively. A base model with a cuboid spatial shape is generated. The entire base is the area where fibers are deployed. The base model can be meshed using three-dimensional solid elements.

[0020] In a preferred embodiment of this application, the specific steps for establishing the fiber network model in step S2 are as follows: (1) Determine the fiber delivery target, including the fiber quantity n or fiber volume fraction V. f； (2) Complete the establishment of a single fiber model, including straight fibers with no curvature change or curved fibers with constantly changing curvature; (3) Randomly place fibers in a spatial region that is the same size as the matrix model.

[0021] It should be further explained that the specific implementation process for randomly placing fibers within a spatial region of the same size as the matrix model is as follows: (1) Coordinate system: x-axis direction: (-a / 2, a / 2), y-axis direction: (-b / 2, b / 2), z-axis direction: (0, h); (2) Determine the fiber orientation restriction range, that is, determine the rotation angle restriction range (α). min α max ) and (β) min ,β max ); (3) Start deploying the first fiber: Randomly generate the coordinates of the fiber's starting point (limited to a spatial region of the same size as the matrix model) and the rotation angle (α). min α maxRandom values ​​within the range of (β) min ,β max (random values ​​within a range) (4) Generate a fiber (straight or curved) with random geometric features using the method described in the previous step. Place its starting point in the spatial region according to its coordinates, and then rotate it according to a random rotation angle. Specifically: The fiber rotation angle is determined by the rotation angle α in the xy plane and the rotation angle β in the yz plane:

[0022] For straight fibers: Given a randomly obtained fiber starting point coordinate (x1, y1, z1) and fiber length l0 within a spatial region, the fiber ending point can be calculated using rotation angles α in the xy plane and β in the yz plane.

[0023] The spatial vector representation of a fiber is:

[0024] For curved fibers: the coordinates of the fiber's starting point are randomly obtained within the spatial region as (x1, y1, z1), and the coordinates of the fiber's starting point during the generation stage are... Therefore, the distance the fiber starting point moves can be obtained: Distance moved in the X direction:

[0025] Distance moved in the Y direction:

[0026] Distance moved in the Z direction:

[0027] During the generation phase, the coordinates of any point on the fiber can be represented as: The fiber is moved along the distance from the starting point, and the coordinates of any point on the fiber are obtained as follows: ,Right now:

[0028] At this point, the coordinates of the first point on the fiber are (x1, y1, z1). Then, the coordinates of any point on the fiber after rotation... It can be determined using the following formula: First, rotate within the yz plane:

[0029] Then rotate in the xy plane:

[0030] (5) Cut and move the fiber according to whether it exceeds the spatial area.

[0031] For straight fibers, the positional relationship between the fiber and the matrix can be determined by the coordinates of the fiber's starting and ending points: Case 1: If all fibers are located inside the matrix, proceed to the next step. Case 2: If the fiber portion extends beyond the matrix, the model needs to be cut, as follows: Let the fiber start point be: end: The intersection points between the fiber and the boundary are calculated using the fiber vector formula. and the boundary of the periodic model Corresponding point : When the fiber x-direction extends beyond the matrix:

[0032]

[0033] When the fiber's y-direction extends beyond the matrix:

[0034] When the fiber z-direction extends beyond the matrix:

[0035] Therefore, a fiber that extends beyond the matrix region can be... The fiber is divided into two fibers that satisfy the periodic boundary conditions of the model. and ,Right now:

[0036] For curved fibers, the positional relationship between the fiber and the matrix can be determined by using the coordinates of any point on the fiber: Case 1: If all fibers are located inside the matrix, proceed to the next step. Case 2: If the fiber portion extends beyond the matrix, the model needs to be cut, as follows: Determine that the fiber portion extends beyond the matrix:

[0037] For the portion extending beyond the cutting substrate, translation is performed as follows:

[0038] According to the above formula, if the coordinates of a fiber exceed the limit, it will be translated to move the excess fiber to the relative region of the model.

[0039] (6) Deploy the next fiber according to step (3) to step (5) and determine whether it interferes with the previously deployed fiber.

[0040] For straight fibers, vector representation can be used. Let's say k-1 fibers have already been deployed, and the k-th fiber is being deployed. If the fiber vector is represented in the form of , then there are a total of k vectors, represented as:

[0041] Where m1, m2, ..., m k-1 m k The value ranges from 0 to 1.

[0042] The minimum distance between the k-th fiber and the i-th fiber can be obtained by finding the extreme value of the following equation:

[0043] Where i is a positive integer between 1 and k-1, inclusive of 1 and k-1.

[0044] The minimum distance d between the k-th fiber and the i-th fiber can be obtained from the above formula. min Compare this minimum distance with the fiber spacing limit value min_d: when min_d <d min When the two fibers do not interfere, proceed to the next step and continue to determine whether the (i+1)th fiber interferes with the kth fiber; when min_d>d min When the two fibers interfere, the process returns to step (3) and the fibers are regenerated.

[0045] For curved fibers, interference can be determined by checking whether the minimum distance between any points on the two fibers exceeds a certain limit. The method is as follows: When the k-th fiber is deployed, determine whether it interferes with the (k-1)-th fibers already deployed. Both the k-th and i-th fibers (where i is a positive integer between 1 and k-1) consist of n nodes. The coordinates of the nodes on the k-th fiber are (xk1, yk1, zk1), (xk2, yk2, zk2), ..., (xkn, ykn, zkn). The coordinates of the nodes on the i-th fiber are (xi1, yi1, zi1), (xi2, yi2, zi2), ..., (xin, yin, zin). The distance between any two nodes on the two fibers can be expressed as:

[0046] Where 1 ≤ p, q ≤ n, and p and q are integers, and m is from 1 to n. 2Positive integers between 1 and n 2 .

[0047] Compare the distances d1, d2, ..., dm, ..., dn between any two nodes on the two fibers. 2 To obtain the minimum distance d min Compare this minimum distance with the fiber spacing limit value min_d: when min_d <d min When the two fibers do not interfere, proceed to the next step and continue to determine whether the (i+1)th fiber interferes with the kth fiber; when min_d>d min When the two fibers interfere, the process returns to step (3) and the fibers are regenerated.

[0048] (7) Termination of fiber delivery. Determine when to stop fiber delivery based on the fiber delivery target. If the target is the number of fibers, stop delivery once the target number is reached; if the target is the fiber volume fraction, calculate the volume fraction of the total volume of fibers already delivered. When the volume fraction of the total fiber volume reaches the target volume fraction, stop fiber delivery and complete the fiber network modeling. If the fiber number or volume fraction does not reach the delivery target, return to step two to continue fiber delivery.

[0049] The volume fraction can be determined by the following formula:

[0050] Straight fibers:

[0051] Bending fibers:

[0052] Where Vi represents the volume of a single fiber, vi represents the volume of each fiber arc segment, r is the radius of curvature of the arc segment, and d is the diameter of the fiber.

[0053] In a preferred embodiment of this application, the step of generating a single fiber in step S2 is as follows: (1) Determine the range of variation for fiber length, fiber curvature, and fiber diameter; (2) Straight fiber generation: The length l0 and diameter d of the fiber are generated using the Weibull distribution function. The starting point of the fiber is (0, 0) and the ending point is (0, l0). The fiber is modeled as a two-dimensional solid straight line. The diameter is defined by the cross-sectional properties of the model, thus obtaining a single fiber model. The probability density function of the Weibull distribution is:

[0054] Where x is a random variable, λ>0 is a scaling parameter, and k>0 is a shape parameter; (3) Generation of curved fibers: First, the total length l0 and diameter d of the fiber are generated using the Weibull distribution function. Then, the single curved fiber model is obtained using the planar circular arc method. A single curved fiber is composed of n circular arcs connected together. The number of circular arcs can be set manually. (4) For straight or curved fiber models, two-dimensional rod elements or beam elements can be used for mesh generation.

[0055] In a preferred embodiment of this application, the planar circular arc method used in generating the bent fibers is as follows: The range of length variation for each arc segment can be determined by the upper limit l0 / (n-1) and the lower limit l0 / n. The lengths of the first to n-1 arc segments can be determined using the Weibull distribution function. The length of the nth arc segment is determined by subtracting the sum of the lengths of the previous n-1 arc segments from the total length l0, thereby randomly distributing the total length to each arc segment. The curvature of each arc segment is randomly generated using the Weibull function.

[0056] To better understand, the following steps for generating bent fibers are further explained: The total length is randomly distributed across each arc segment.

[0057] The curvature of each arc segment can be randomly generated using the Weibull function.

[0058] The starting point of the first arc segment is (0, 0), and the ending point of the (n-1)th arc segment is the starting point of the nth arc segment. Adjacent arc segments are tangent (internal or external). First, the first arc segment is generated, then rotated to generate the second arc segment starting from the ending point of the first arc segment. The second arc segment is tangent to the first arc segment, and so on, until the final n connected arc segments constitute a single curved fiber. Details are as follows: In the xy-plane coordinate system, taking (x1, y1) = (0, 0) as the starting point of the fiber, the random length of the first arc (arc 1) is l1, the random curvature is k1, then the radius of curvature is r1 = 1 / k1, and the coordinates of the center of arc 1 are (Ox1, Oy1) = (0, r1): The arc angle is:

[0059] The coordinates of the midpoint of the arc are:

[0060] The coordinates of the endpoint of the arc are:

[0061] Before generating the second arc (arc 2), rotate arc 1: Rotate arc 1 around its center. Rotate the endpoint of the arc to point (0, 0). After rotation: The starting point of arc 1 is:

[0062] The midpoint of arc 1 is:

[0063] End point of arc 1:

[0064] The starting point of arc 2 is the ending point of arc 1. And it is the tangent point of two circular arcs, with a random length of l2 and a random curvature of k2. Then the radius of curvature is r2 = 1 / k2. We can obtain the coordinates of the center of arc 2, and then obtain the coordinates of the corresponding point on arc 2: The arc angle of arc 2 is:

[0065] Since the two arcs are tangent, the center of arc 2 has two possibilities. Let's assume the coordinates of the center of arc 2 are (Ox2, Oy2): If the two circular arcs are internally tangent and Oy2>0, then the center of arc 2 is: ; If the two circular arcs are externally tangent and Oy2 < 0, then the center of arc 2 is: .

[0066] Once the tangency method is determined, the midpoint (x4, y4) and the endpoint (x5, y5) of arc 2 can be obtained.

[0067] The midpoint of arc 2 is:

[0068] End point of arc 2:

[0069] Before generating the third arc (arc 3), rotate the already generated arc model again by an angle of _____. Update the coordinates of all points: The starting point of arc 1 is:

[0070] The midpoint of arc 1 is:

[0071] End point of arc 1 (i.e., start point of arc 2):

[0072] The midpoint of arc 2 is:

[0073] End point of arc 2:

[0074] Similarly, by directly rotating or according to the coordinates of the feature points of each arc segment, several connected arc segments can be obtained. The curved fiber is modeled using a two-dimensional solid curve, and the diameter is defined by the cross-sectional properties of the model. Thus, the generation of a single curved fiber can be completed.

[0075] In a preferred embodiment of this application, the specific steps for assembling the overall model in step S3 are as follows: The generated fiber network model is merged with the matrix model. The matrix model is meshed using 3D solid elements, while the fiber network model is meshed using 2D rod or beam elements. The fiber network is embedded into the matrix to form a composite material RVE model. Constraints and loads are then added for calculation. The entire model exhibits periodic structural characteristics.

[0076] It should be noted that the above modeling process can be implemented by writing text in Python and automatically generating it in Abaqus software, or it can be further developed into a plugin and used in conjunction with the software.

[0077] In this application, the bending fiber can also be generated using the planar broken line method, which uses multiple straight line segments with different directions connected together to form the bending fiber; Two-dimensional solid fiber models can be replaced with three-dimensional solid fiber models, which can represent cross-sectional shapes and dimensions, but require high mesh quality and have low computational efficiency. The distribution of fiber length, diameter, curvature, etc., can be replaced with random values ​​or other probability distributions, such as normal distribution.

[0078] To better understand the technical solution of this application, the following examples will be used to further illustrate it.

[0079] Example 1: Finite element model of aerogel composite material RVE (straight fiber): In this example, the fiber volume fraction is used as the termination criterion. The target fiber volume fraction is Vf=2%, and the fiber length varies from 5 to 10 mm. The shape parameter k=2 of the Weibull distribution function controlling the fiber length is calculated, and the scaling factor λ≈1.76. The fiber diameter varies from 0.5 to 0.6 mm, and the shape parameter k=2 of the Weibull distribution function controlling the fiber diameter is calculated, and the scaling factor λ≈0.0284. The proposed aerogel composite RVE model is a cube with side lengths a=b=h=100 mm. Fibers are randomly placed in the matrix model with a pitch angle of ±30° to the xy plane and a minimum fiber spacing of 0.25 mm. Random fibers are generated sequentially until the randomly generated fibers meet the fiber volume fraction requirement. The following conditions are judged for the randomly generated fibers: (1) The spacing between fibers meets the minimum spacing requirement; (2) The fibers meet the geometric periodicity structural characteristics in the RVE model; (3) The fiber volume fraction meets the requirement (Vf≥2%). In this example, under the above conditions, the volume fraction is 2.01%, and a total of 1007 fibers are generated.

[0080] Example 2: Finite element model of aerogel composite material RVE (bent fiber): In this example, the fiber count is used as the termination criterion, with a target fiber count of 500. The fiber length varies from 20 to 40 mm. The Weibull distribution function shape parameter k=2 is calculated to control the fiber length, with a scaling factor λ≈8.4. Each fiber consists of two arc segments, and the fiber curvature varies from 0 to 0.005 mm. -1 The shape parameter k=1 of the Weibull distribution function controlling the fiber diameter was calculated, with a scaling factor λ≈0.000353. The fiber diameter range was 0.5~1mm. The shape parameter k=2 of the Weibull distribution function controlling the fiber diameter was calculated, with a scaling factor λ≈0.159. The proposed aerogel composite material RVE model is a cube with a side length of a=b=h=100mm. Fibers are randomly placed in the matrix model with a pitch angle of ±10° to the xy plane and a minimum fiber spacing of 0.25mm. Random fibers are generated sequentially until the number of randomly generated fibers meets the fiber requirement. The following conditions are judged for the randomly generated fibers: (1) The spacing between fibers meets the minimum spacing requirement; (2) The fibers meet the geometric periodic structure characteristics in the RVE model; (3) The number of fibers meets the requirement (n=500). In this example, under the above conditions, a total of 500 fibers were generated, with a volume fraction of 7.43%.

[0081] 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 establishing an RVE model for aerogel composites considering the randomness of fiber characteristics, characterized in that, Includes the following steps: S1: Establish the base model, where the parameters of the base model include: the length a, width b, and height h of the RVE model; S2: Establish a fiber network model, wherein the parameters of the fiber network model include: spatial feature parameters and shape feature parameters; Spatial characteristic parameters include fiber origin coordinates, fiber tilt angle, fiber rotation angle, and minimum fiber spacing within the matrix, as well as fiber number or fiber volume fraction. Shape characteristic parameters include fiber length, local curvature of the fiber, and diameter of the fiber cross section; The fiber network model contains a certain number or volume fraction of individual fibers. The specific steps for generating a single fiber are as follows: (1) Determine the range of variation for fiber length, fiber curvature, and fiber diameter; (2) Straight fiber generation: The length l0 and diameter d of the fiber are generated using the Weibull distribution function. The starting point of the fiber is (0, 0) and the ending point is (0, l0). The fiber is modeled as a two-dimensional solid straight line. The diameter is defined by the cross-sectional properties of the model, thus obtaining a single fiber model. The probability density function of the Weibull distribution is: ； Where x is a random variable, λ>0 is a scaling parameter, and k>0 is a shape parameter; (3) Generation of curved fibers: First, the total length l0 and diameter d of the fiber are generated using the Weibull distribution function. Then, the single curved fiber model is obtained using the planar circular arc method. A single curved fiber is composed of n circular arcs connected together. The number of circular arcs can be set manually. The planar circular arc method is as follows: During the bending fiber generation process, the length variation range of each arc segment can be determined by the upper limit l0 / (n-1) and the lower limit l0 / n. The lengths of the first to n-1 arc segments can be determined using the Weibull distribution function. The length of the nth arc segment is determined by subtracting the sum of the lengths of the previous n-1 arc segments from the total length l0, thereby randomly distributing the total length to each arc segment. The curvature of each arc segment is randomly generated using the Weibull function. (4) For straight or curved fiber models, two-dimensional rod elements or beam elements can be used for mesh generation; S3: Assemble the overall model: Merge the generated fiber network model with the matrix model, embedding the fiber network into the matrix to form a composite material RVE model. Constraints and loads are then added for mesoscale mechanical and thermodynamic calculations.

2. The method for establishing an RVE model for aerogel composite materials considering the randomness of fiber characteristics according to claim 1, characterized in that, The specific steps for establishing the matrix model in step S1 are as follows: The length, width, and height of the base model are determined to be a, b, and h, respectively. A base model with a cuboid spatial shape is generated. The entire base is the area where fibers are deployed. The base model can be meshed using three-dimensional solid elements.

3. The method for establishing an RVE model for aerogel composite materials considering the randomness of fiber characteristics according to claim 1, characterized in that, The specific steps for establishing the fiber network model in step S2 are as follows: (1) Determine the fiber delivery target, including the fiber quantity n or fiber volume fraction V. f ; (2) Complete the establishment of a single fiber model, including straight fibers with no curvature change or curved fibers with constantly changing curvature; (3) Randomly place fibers in a spatial region that is the same size as the matrix model.

4. The method for establishing an RVE model for aerogel composite materials considering the randomness of fiber characteristics according to claim 1, characterized in that, The specific steps for assembling the overall model in step S3 are as follows: The generated fiber network model is merged with the matrix model. The matrix model is meshed using three-dimensional solid elements, while the fiber network model is meshed using two-dimensional rod or beam elements. The fiber network is embedded into the matrix to form a composite material RVE model. Constraints and loads are then added for calculation.

Images