A method for creating a representative volume element of a composite material based on a minimum potential energy method

Abstract

The application discloses a composite material representative cell unit creation method based on a minimum potential method, relates to the technical field of composite materials, and comprises the following steps: generating a specific number of fibers randomly in the range of a matrix; when the fibers exceed the boundary of the matrix, creating a corresponding number of periodic mirror images at the corresponding positions of the matrix; constructing intersection potential functions, position potential functions and periodic potential functions of the arbitrary fibers, and obtaining total potential functions of all the fibers according to the intersection potential functions, the position potential functions and the periodic potential functions; and calculating the function values of the total potential functions, and creating a two-dimensional periodic representative cell unit of the composite material according to the center data of the multiple fibers when the function values are less than a critical value. The application provides the creation method of the composite material RVE based on the minimum potential method, and improves the problems of low fiber volume fraction and low execution efficiency of the existing method in creating the composite material RVE.

Description

Technical Field

[0001] This invention relates to the field of composite materials technology, and in particular to a method for creating representative bulk cells of composite materials based on the minimum potential energy method. Background Technology

[0002] Composite materials possess low density, excellent mechanical properties (high specific strength, specific stiffness, and low coefficient of thermal expansion, etc.) and physicochemical properties (excellent electrical and thermal conductivity, wear resistance, and vibration damping properties, etc.), leading to their widespread application in aerospace, automotive, and defense industries. Accurately predicting the thermo-mechanical properties of composite materials and establishing the mapping relationship between their microstructure and thermo-mechanical properties provides a theoretical basis for their engineering applications, theoretical guidance for their fabrication and molding, and also facilitates microstructure optimization. Therefore, it has significant scientific research value and engineering application value. The matrix materials of composite materials are divided into two main categories: metals and non-metals. Commonly used metal matrices include aluminum, magnesium, copper, titanium, and their alloys. Non-metallic matrices mainly include synthetic resins, rubber, ceramics, graphite, and carbon. Reinforcing materials mainly include glass fiber, carbon fiber, boron fiber, aramid fiber, silicon carbide fiber, asbestos fiber, whiskers, and metals.

[0003] Numerical methods can effectively consider the complex microstructure of composite materials and provide information on the microscopic deformation of each component of the composite material. Therefore, they are widely used in the research of predicting the thermo-mechanical properties of composite materials. In the process of predicting the thermo-mechanical properties of composite materials using numerical methods, it is first necessary to establish a representative volume element (RVE) that can accurately characterize the microstructure of the composite material. At present, the methods for creating composite material RVEs mainly include the following three categories: (1) non-contact fiber methods, including random sequential adsorption (RSA) method and molecular dynamics (MD) based methods, etc. (2) fiber intersection removal methods, mainly including methods based on numerical optimization algorithms. (3) methods based on image 3D reconstruction technology.

[0004] Image-based 3D reconstruction techniques require expensive and complex experimental equipment and specialized software, and the reconstruction process is highly complex, limiting their application scope. The RSA method generates composite RVEs with specific limits on fiber volume fraction, and its efficiency in creating composite RVEs with a large number of fibers is low, while also failing to control the fiber orientation distribution within the composite RVE. MD-based methods are numerically complex, and their creation efficiency is also low when the number of fibers is large; furthermore, they cannot control the fiber orientation distribution within the composite RVE. Summary of the Invention

[0005] This invention provides a method for creating representative bulk cells of composite materials based on the minimum potential energy method, which can solve the problems existing in the prior art.

[0006] This invention provides a method for creating representative bulk cells of composite materials based on the minimum potential energy method, comprising the following steps:

[0007] A specific number of fibers are randomly generated within the matrix, and data on the center of each fiber are recorded.

[0008] When the fiber extends beyond the boundary of the matrix, the number of periodic mirror images of the fiber is determined based on the extent to which the fiber extends beyond the matrix, and the offset vector corresponding to the periodic mirror image of the fiber is calculated.

[0009] Based on the number of periodic fiber mirror images and the offset vector corresponding to the periodic fiber mirror images, create a corresponding number of periodic fiber mirror images at the corresponding positions in the matrix, and record the center data of the periodic fiber mirror images.

[0010] Based on multiple fiber center data and periodic mirror center data of fibers, intersecting potential energy function, position potential energy function and periodic potential energy function are constructed;

[0011] The overall potential energy function is obtained from the intersection potential energy function, the position potential energy function, and the periodic potential energy function.

[0012] Calculate the value of the overall potential energy function and compare it with the set critical value;

[0013] When the function value is less than the critical value, a two-dimensional periodic representative cell unit of the composite material is created based on multiple fiber center data.

[0014] Preferably, determining the number of periodic mirror images of fibers based on the extent to which the fibers extend beyond the matrix specifically includes the following steps:

[0015] If the fiber extends beyond one surface of the matrix, i.e. η k =1, then n p =1, ΔL p＝1 =δL k k∈{1,2,3,4};

[0016] If the fiber extends beyond both surfaces of the matrix simultaneously, i.e. η k =1 and η l =1, then n p =3, ΔL p＝1 =δL k ,ΔL p＝2 =δL l ,ΔL p＝3 =δL k +δL lk,l∈{1,2,3,4},k<l,k≠l-2;

[0017] Where k represents the first face, l represents the second face, and n p η represents the number of periodic mirror images of the fiber. k η represents the intersection of the fiber with the first surface of the matrix. l This indicates the intersection of the fiber with the second surface of the matrix, k = 1, 2, 3, and 4, representing the left, lower, right, and upper surfaces of the matrix, respectively. δL1 = (-L, 0), δL2 = (0, -L), δL3 = (L, 0), δL4 = (0, L), where L is the side length of the matrix, and ΔL... p The offset vector represents the periodic mirror image.

[0018] Preferably, the offset vector of the periodic mirror image of the fiber is calculated using the following formula:

[0019] r p =r-ΔL p

[0020] In the formula, r and r p ΔL represents the center of the fiber and its periodic mirror image, respectively. p The offset vector represents the periodic mirror image.

[0021] Preferably, the intersection potential energy function is shown in the following equation:

[0022]

[0023] in,

[0024] ψ ij =max(-k) ij ,0)

[0025] k ij =||r i -r j ||-d

[0026] In the formula, r i and r j It is the center of fibers i and j, k ij It is the minimum distance between two fibers i and j, ψ ij d is the maximum intersection distance between two fibers i and j, and d is the diameter of the fiber;

[0027] The potential energy function at the location is shown in the following equation:

[0028]

[0029] In the formula, It is the minimum distance between fiber i and the substrate surface;

[0030] The periodic potential energy function is shown in the following equation:

[0031]

[0032] In the formula, φ ij It is the distance between fiber i and its periodic mirror image p;

[0033] The overall potential energy function is shown in the following equation:

[0034]

[0035] In the formula, N is the total number of fibers.

[0036] Preferably, the minimum distance between fiber i and the substrate surface is obtained based on the distance between any fiber i and the substrate surface. Specifically, the following steps are included:

[0037] If r1 i <-d / 2, If r1 i >L+d / 2, In other cases

[0038] like like In other cases

[0039] The minimum distance between fiber i and the substrate surface is:

[0040]

[0041] In the formula, r1 i It is the x-coordinate of the center of fiber i. It is the y-coordinate of the center of fiber i. It is the x-coordinate of the minimum distance vector between fiber i and the substrate surface. D is the y-coordinate of the minimum distance vector between fiber i and the matrix surface. i It is the minimum distance vector between fiber i and the substrate surface.

[0042] Preferably, the distance φ between the first fiber i and its periodic mirror image p is obtained based on the number of any fiber i and its periodic mirror images. ij Specifically, it includes the following steps:

[0043] When n p =1:

[0044] If r1 i <d I / 2, then P1 i,1 =L-(r1)p -r1 i ),

[0045] like but

[0046] If r1 i >L1-d I / 2, then P1 i,1 =(r1) i -r1 p )-L,

[0047] like Then P1 i,1 =r1 i -r1 p ,

[0048] When n p =3 hours:

[0049] If r1 i <d I / 2 and but

[0050]

[0051] If r1 i >L1-d I / 2 and but

[0052]

[0053] If r1 i <d I / 2 and but

[0054]

[0055] If r1 i >L1-d I / 2 and but

[0056]

[0057] The distance between fiber i and its periodic mirror image p is:

[0058] φ ij =‖P i,j ||

[0059] In the formula, P1 i,1 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P1, r1 P It is the x-coordinate of the center of the periodic mirror image P of fiber i. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P1, where P1 i,2 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P2. It is the y-coordinate of the center of the periodic mirror image P of fiber i. It is the x-coordinate of the center of the periodic mirror image P1 of fiber i. It is the y-coordinate of the center of the periodic mirror image P1 of fiber i, where P1 i,2 It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P1 i,3 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P i，j It is the distance vector between fiber i and its periodic mirror image P.

[0060] Preferably, the first derivative of the intersection potential energy function with respect to multiple fiber centers is calculated;

[0061] Calculate the second derivative of the position potential energy function with respect to multiple fiber centers;

[0062] Calculate the third derivative of the periodic potential energy function with respect to multiple fiber centers;

[0063] Calculate the total derivative of the overall potential energy function with respect to multiple fiber centers based on the first, second, and third derivatives;

[0064] When the function value is greater than the critical value, the center of all fibers is updated by the total derivative, and then the intersection potential energy function, position potential energy function and periodic potential energy function are reconstructed for the next round of calculation.

[0065] Preferably, the first derivative is calculated using the following formula:

[0066]

[0067] The second derivative is calculated using the following formula:

[0068]

[0069] The third derivative is calculated using the following formula:

[0070]

[0071] Preferably, the total derivative is calculated using the following formula:

[0072]

[0073] In the formula, This is the gradient operator.

[0074] Preferably, the center of all fibers is updated using the following formula:

[0075]

[0076] In the formula, r i,n and r i,n+1 Let τ be the fiber center before and after the update, respectively, and let τ∈[0,1] be the time step.

[0077] Compared with the prior art, the beneficial effects of the present invention are:

[0078] This invention proposes a method for creating periodic RVEs of composite materials based on the minimum potential energy method. This method compares the sum of multiple potential energy functions of the fiber with a set critical value, and can be applied to create two-dimensional periodic RVEs of continuous fiber reinforced composite materials. This improves the problems of low fiber volume fraction and low execution efficiency in existing methods for creating composite material RVEs. Attached Figure Description

[0079] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0080] Figure 1 A flowchart of a method for creating representative bulk cells of composite materials based on the minimum potential energy method according to the present invention;

[0081] Figure 2 This is a schematic diagram of multiple fibers randomly generated within the matrix in an embodiment of the present invention;

[0082] Figure 3 This is a periodic mirror diagram illustrating the fiber creation beyond the matrix boundary in an embodiment of the present invention;

[0083] Figure 4 This is a schematic diagram of the fiber generation function in an embodiment of the present invention;

[0084] Figure 5 This is a schematic diagram of fiber center data generated in an embodiment of the present invention. Detailed Implementation

[0085] 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.

[0086] Reference Figure 1 This invention provides a method for creating representative cell units of composite materials based on the minimum potential energy method. This method can simply and efficiently create two-dimensional periodic RVEs of composite materials with a very high fiber volume fraction (>70%), specifically including the following steps:

[0087] Step 1: Within the matrix range [0,L]×[0,L], randomly generate a specific number N (corresponding to a given fiber volume fraction v1), allowing multiple fibers to intersect. Record the center data of multiple fibers.

[0088] Step 2: Refer to Figure 2 and Figure 3 If the fiber extends beyond the matrix boundary, a corresponding number of periodic mirror images are created at the corresponding locations on the matrix. The corresponding locations of the periodic mirror images are calculated using the following formula:

[0089] r p =r-ΔL p

[0090] In the formula, r and r p ΔL represents the center of the fiber and its periodic mirror image, respectively. p The offset vector represents the periodic mirror image.

[0091] The number of periodic mirror images of fibers is determined based on how far the fibers extend beyond the matrix, specifically including the following situations:

[0092] If the fiber extends beyond one surface of the matrix, i.e. η k =1, then n p =1, ΔL p＝1 =δL k k∈{1,2,3,4}. If the fiber simultaneously extends beyond two surfaces of the matrix, i.e. η k =1 and η l =1, then n p =3, ΔL p＝1 =δL k ,ΔL p＝2 =δL l ,ΔL p＝3 =δL k +δL l k,l∈{1,2,3,4},k<l,k≠l-2.

[0093] Where k represents the first face, l represents the second face, and η k This indicates the intersection situation between the fiber and the k-th surface of the matrix (intersection η). k =1, otherwise η k =0), η l The numbers represent the intersection of the fiber with the second surface of the matrix, k = 1, 2, 3 and 4, representing the left, lower, right and upper surfaces of the matrix, respectively, δL1 = (-L, 0), δL2 = (0, -L), δL3 = (L, 0), δL4 = (0, L).

[0094] Step 3: Refer to Figure 4 Construct the intersection potential energy function between any two fibers i and j, and calculate the gradient of the intersection potential energy function with respect to the center of fiber i.

[0095] For the two fibers i and j in the matrix (the centers are r respectively) i and r j First, calculate the minimum distance between them:

[0096] k ij =||r i -r j ||-d

[0097] Then, calculate the maximum intersection distance between them:

[0098] ψ ij =max(-k) ij ,0)

[0099] Therefore, the cross-link potential energy function between the two fibers is defined as:

[0100]

[0101] The derivative of the intersection potential energy function with respect to the center of fiber i is:

[0102]

[0103] Step 4: Construct the position potential function of any fiber i, and calculate the gradient of the position potential function with respect to the center of fiber i.

[0104] Consider fiber i (center is The distance between the fiber and the surface of the substrate is:

[0105] (1) If r1 i <-d / 2, If r1 i >L+d / 2, In other cases

[0106] (2) If like In other cases

[0107] In the formula, r1 i It is the x-coordinate of the center of fiber i. It is the y-coordinate of the center of fiber i. It is the x-coordinate of the minimum distance vector between fiber i and the substrate surface. It is the y-coordinate of the minimum distance vector between fiber i and the substrate surface.

[0108] Therefore, the minimum distance between fiber i and the matrix surface is D i Let be the minimum distance vector between fiber i and the substrate surface. Then the position potential energy function of fiber i is defined as:

[0109]

[0110] The derivative of the position potential energy function with respect to the center of fiber i is:

[0111]

[0112] Step 5: Construct the periodic potential function of any fiber i, and calculate the gradient of the periodic potential function with respect to the center of fiber i.

[0113] For fiber i and its periodic mirror image p (centered at...) The center vector between them is:

[0114] (1) When n p =1:

[0115] If r1 i <d I / 2, then P1 i,1 =L-(r1) p -r1 i ),

[0116] like Then P1 i,1 =r1 i -r1 p ,

[0117] If r1 i >L1-d I / 2, then P1 i,1 =(r1) i -r1 p )-L,

[0118] like Then P1 i,1 =r1 i -r1 p ,

[0119] (2) When n p =3 hours:

[0120] If r1 i <d I / 2 and but

[0121]

[0122] If r1 i >L1-d I / 2 and but

[0123]

[0124] If r1 i <d I / 2 and but

[0125]

[0126] If r1 i >L1-d I / 2 and but

[0127]

[0128] Therefore, the distance between fiber i and its periodic mirror image p is:

[0129] φ ij =‖P i,j ||

[0130] In the formula, P1 i,1 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P1, r1 P It is the x-coordinate of the center of the periodic mirror image P of fiber i. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P1, where P1 i,2 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P2. It is the y-coordinate of the center of the periodic mirror image P of fiber i. It is the x-coordinate of the center of the periodic mirror image P1 of fiber i. It is the y-coordinate of the center of the periodic mirror image P1 of fiber i, where P1 i,2 It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P1 i,3 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P i，j It is the distance vector between fiber i and its periodic mirror image P.

[0131] The periodic potential energy function of fiber i is defined as:

[0132]

[0133] The derivative of the periodic potential energy function with respect to the center of fiber i is:

[0134]

[0135] Step 6: Calculate the overall potential energy function Ψ of all fibers and its derivative (gradient) with respect to the fiber center.

[0136]

[0137] and

[0138]

[0139] Step 7: Calculate the overall potential energy function and compare it with the set critical value. When the function value is less than the critical value, end the process and record the center of all fibers, such as... Figure 5 As shown. Based on the generated fiber center data, a two-dimensional periodic RVE of the composite material is created.

[0140] Step 8: If the function value is greater than the given critical value, update the center of all fibers:

[0141]

[0142] Where r i,n and r i,n+1 Let τ be the fiber center before and after the update, respectively, where τ∈[0,1] is the time step. Then return to step 3 for a new round of iteration.

[0143] Example

[0144] Taking continuous carbon fiber reinforced resin matrix composites as an example, the fibers are unidirectionally distributed with randomly distributed center points, and the fiber diameter is 10 μm. Based on the method proposed in this invention, two-dimensional periodic RVEs with a high fiber volume fraction in composite materials can be efficiently created. The steps are as follows:

[0145] Step 10: Randomly generate 96 fibers (corresponding to 75% fiber volume fraction) within the matrix range [0, 100 μm] × [0, 100 μm] (intersection is allowed).

[0146] Step 11: If the fiber extends beyond the boundary of the matrix, create the corresponding number of periodic mirrors at the corresponding positions on the matrix.

[0147] Step 12: Calculate the intersection potential energy function between any two fibers and its derivative with respect to the fiber center.

[0148] Step 13: Calculate the position potential energy function of any fiber and its derivative with respect to the fiber center.

[0149] Step 14: Calculate the periodic potential energy function of the fiber and its derivative with respect to the fiber center.

[0150] Step 15: Calculate the overall potential energy function of all fibers and its derivative with respect to the fiber center.

[0151] Step 16: If the total potential energy function Ψ of all fibers is greater than the given critical value, update the center of all fibers, then return to step 12 for the next round of update iterations until the total potential energy function Ψ is less than the given critical value. If the total potential energy function Ψ of all fibers is less than the given critical value, end the process and record the center of all fibers.

[0152] Step 17: Based on the generated fiber center data, create a two-dimensional periodic RVE for the composite material.

[0153] This invention proposes a method for creating two-dimensional periodic resonant fibers (RVEs) in continuous fiber-reinforced composite materials based on the gradient descent algorithm, namely the minimum potential energy method. This method first generates fibers with a given volume fraction (intersections are allowed) within the matrix. Then, based on the degree of fiber intersection, the degree of fiber extension beyond the matrix, and the degree of periodic mirror deviation, a potential energy function is established that characterizes the degree of intersection, extension beyond the matrix, and periodic mirror deviation of all fibers. Finally, the gradient descent algorithm is used to continuously adjust the positions of the corresponding fibers until the potential energy function approaches zero. The composite material RVE creation method based on the minimum potential energy method can simply and efficiently create two-dimensional periodic RVEs in composite materials with very high fiber volume fractions (>70%).

[0154] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0155] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for creating representative volumetric units of composite materials based on the minimum potential energy method, characterized in that, Includes the following steps: A specific number of fibers are randomly generated within the matrix, and data on the center of each fiber are recorded. When the fiber extends beyond the boundary of the matrix, the number of periodic mirror images of the fiber is determined based on the extent to which the fiber extends beyond the matrix, and the offset vector corresponding to the periodic mirror image of the fiber is calculated. Based on the number of periodic fiber mirror images and the offset vector corresponding to the periodic fiber mirror images, create a corresponding number of periodic fiber mirror images at the corresponding positions in the matrix, and record the center data of the periodic fiber mirror images. Based on multiple fiber center data and periodic mirror center data of fibers, intersecting potential energy function, position potential energy function and periodic potential energy function are constructed; The overall potential energy function is obtained from the intersection potential energy function, the position potential energy function, and the periodic potential energy function. Calculate the value of the overall potential energy function and compare it with the set critical value; When the function value is less than the critical value, a two-dimensional periodic representative cell unit of the composite material is created based on multiple fiber center data.

2. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 1, characterized in that, The number of periodic mirror images of fibers is determined based on the extent to which the fibers extend beyond the matrix. This involves the following steps: If the fiber extends beyond one surface of the matrix, i.e. η k =1, then n p =1, ΔL p＝1 =δL k k∈{1,2,3,4}; If the fiber extends beyond both surfaces of the matrix simultaneously, i.e. η k =1 and η l =1, then n p =3, ΔL p＝1 =δL k ,ΔL p＝2 =δL l ,ΔL p＝3 =δL k +δL l k,l∈{1,2,3,4},k<l,k≠l-2; Where k represents the first face, l represents the second face, and n p η represents the number of periodic mirror images of the fiber. k η represents the intersection of the fiber with the first surface of the matrix. l This indicates the intersection of the fiber with the second surface of the matrix, k = 1, 2, 3, and 4, representing the left, lower, right, and upper surfaces of the matrix, respectively. δL1 = (-L, 0), δL2 = (0, -L), δL3 = (L, 0), δL4 = (0, L), where L is the side length of the matrix, and ΔL... p The offset vector represents the periodic mirror image.

3. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 2, characterized in that, The offset vector of the periodic mirror image of the fiber is calculated using the following formula: r p =r-ΔL p In the formula, r and r p ΔL represents the center of the fiber and its periodic mirror image, respectively. p The offset vector represents the periodic mirror image.

4. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 3, characterized in that, The intersection potential energy function is shown in the following equation: in, ψ ij =max(-k ij ,0) k ij =‖r i -r j ‖-d In the formula, r i and r j It is the center of fibers i and j, k ij It is the minimum distance between two fibers i and j, ψ ij d is the maximum intersection distance between two fibers i and j, and d is the diameter of the fiber; The potential energy function at the location is shown in the following equation: In the formula, It is the minimum distance between fiber i and the substrate surface; The periodic potential energy function is shown in the following equation: In the formula, φ ij It is the distance between fiber i and its periodic mirror image p; The overall potential energy function is shown in the following equation: In the formula, N is the total number of fibers.

5. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 4, characterized in that, The minimum distance between fiber i and the substrate surface is obtained based on the distance between any fiber i and the substrate surface. Specifically, the following steps are included: like like In other cases like like In other cases The minimum distance between fiber i and the substrate surface is: In the formula, It is the x-coordinate of the center of fiber i. It is the y-coordinate of the center of fiber i. It is the x-coordinate of the minimum distance vector between fiber i and the substrate surface. D is the y-coordinate of the minimum distance vector between fiber i and the matrix surface. i It is the minimum distance vector between fiber i and the substrate surface.

6. The method for creating representative volumetric units of composite materials based on the minimum potential energy method as described in claim 5, characterized in that, The distance φ between the first fiber i and its periodic mirror image p is obtained based on the number of any fiber i and its periodic mirror images. ij Specifically, it includes the following steps: When n p =1: like but like but like but like but When n p =3 hours: like and but like and but like and but like and but The distance between fiber i and its periodic mirror image p is: f ij =‖P i,j ‖ In the formula, P1 i,1 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P1, r1 P It is the x-coordinate of the center of the periodic mirror image P of fiber i. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P1, where P1 i,2 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P2. It is the y-coordinate of the center of the periodic mirror image P of fiber i. It is the x-coordinate of the center of the periodic mirror image P1 of fiber i. It is the y-coordinate of the center of the periodic mirror image P1 of fiber i, where P1 i,2 It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P1 i,3 It is the x-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P3. It is the y-coordinate of the distance vector between fiber i and its periodic mirror image P2, P i，j It is the distance vector between fiber i and its periodic mirror image P.

7. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 6, characterized in that, It also includes the following steps: Calculate the first derivative of the intersection potential energy function with respect to multiple fiber centers; Calculate the second derivative of the position potential energy function with respect to multiple fiber centers; Calculate the third derivative of the periodic potential energy function with respect to multiple fiber centers; Calculate the total derivative of the overall potential energy function with respect to multiple fiber centers based on the first, second, and third derivatives; When the function value is greater than the critical value, the center of all fibers is updated by the total derivative, and then the intersection potential energy function, position potential energy function and periodic potential energy function are reconstructed for the next round of calculation.

8. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 7, wherein the first derivative is calculated by the following formula: The second derivative is calculated using the following formula: The third derivative is calculated using the following formula:

9. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 8, characterized in that, The total derivative is calculated using the following formula: In the formula, This is the gradient operator.

10. The method for creating representative bulk cells of composite materials based on the minimum potential energy method as described in claim 9, characterized in that, Update the center of all fibers using the following formula: In the formula, r i,n and r i,n+1 Let τ be the fiber center before and after the update, respectively, and let τ∈[0,1] be the time step.

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