A geometric modeling method for the microstructure of planar particle-filled composite materials

Abstract

The present invention discloses a geometric modeling method for the microstructure of a planar particle-filled composite material, including: generating aggregates with a volume fraction of V ag , filling the aggregates non-intersectingly in the unit cell; generating random numbers and constructing a filler coordinate matrix G with a fixed angle; obtaining a filler coordinate matrix G θ with a random phase based on the filler coordinate matrix G; performing periodic construction based on the filler coordinates G θ with a random phase, and obtaining a G θ matrix by extending according to the G p positions; judging whether there is interference between different G p based on the G p matrix; judging whether the generated filler meets the specified mass fraction w p based on the G t matrix; writing an automatic modeling file based on the obtained filler coordinates. The established filler has a random distribution, a random phase, the filler size is normally distributed, there is no interference between them, it meets periodicity, and some fillers consider aggregation.

Description

Technical Field

[0001] The invention belongs to the field of geometric modeling of microstructures of planar particle-filled composite materials, and in particular relates to a geometric modeling method of microstructures of planar particle-filled composite materials. Background Art

[0002] Composite materials have the characteristics of low specific gravity, excellent conductivity, and high strength, so they have become a hot topic in research and application. Among them, finite element methods of composite materials have become an important means to study the mechanism of composite materials. In current theoretical methods such as finite element, the quality of the model determines the result of the calculation, so how to quickly and conveniently establish a geometric model has become an urgent problem to be solved.

[0003] The graphene flake model calculated by molecular dynamics is modeled using a self-avoiding random walk algorithm. Graphene is embedded in rubber and its position and direction are random. From its display, the model is periodic. To facilitate numerical calculations, the filler is simplified to two dimensions. However, the model has the following characteristics or limitations: it does not solve the problem of filler interference under high mass fractions, and does not consider the characteristics of filler normal distribution and agglomeration.

[0004] The current model of planar particle-filled composites has the following limitations:

[0005] 1. All models do not take into account the normal distribution characteristics of filler particle size, while filler particle size is actually normally distributed and particle size has a significant impact on the performance of filled composite materials.

[0006] 2. All models do not take into account the partial agglomeration of filler particles. However, particles in filled composite materials will inevitably undergo local agglomeration, which will greatly affect the performance of the composite materials. Summary of the invention

[0007] The purpose of the invention is to provide a method for geometric modeling of the microstructure of a planar particle-filled composite material to solve the problems existing in the above-mentioned prior art.

[0008] To achieve the above object, the present invention provides the following solution: A geometric modeling method for the microstructure of a planar particle-filled composite material, comprising:

[0009] Step 1: Generate volume fraction V ag agglomerates, so that the agglomerates are filled in the unit body without intersecting each other;

[0010] Step 2: Generate random numbers and construct a fixed-angle filler coordinate matrix G;

[0011] Step 3: Obtaining a random phase filler coordinate matrix G based on the filler coordinate matrix G θ ;

[0012] Step 4: Filling coordinates G based on the random phase θ Perform periodic construction and according to G θ Position expansion to obtain G p matrix;

[0013] Step 5: Based on the G p Matrix judgment different G p whether there is interference between them;

[0014] Step 6: Based on the G p The matrix determines whether the generated filler meets the specified mass fraction w t ;

[0015] Step 7: Write an automatic modeling file based on the obtained filler coordinates.

[0016] Preferably, the volume fraction of all aggregates in the unit volume V is specified ag , the number of aggregates in the unit body N ag , aggregate size A s ; Generate N with different rotation angles at a fixed position j Fillers, each piece is A s , generate random numbers to move the whole body, and determine whether it intersects with the generated agglomerates. If so, regenerate it; if not, generate the agglomerate until the volume fraction meets V ag , thus obtaining the volume fraction V ag Aggregates of

[0017] The volume fraction V ag According to the formula Calculated, a is the side length of the cube model of the representative volume unit, d is the thickness of the filler sheet, N j is the number of filler sheets in a single agglomerate.

[0018] Preferably, the random number needs to initialize the random number seed over time and meet the uniformity requirement, and regenerate if it does not meet the uniformity requirement;

[0019] According to the random number, a random number G is obtained. 1 (x 1 ,y 1 , z 1 ), use it as a filler vertex coordinate to construct the other three vertex coordinates G 2 (x 1 +b x ,y 1 , z 1 ), G 3 (x 1 +bx ,y 1 +b x , z 1 ), G 4 (x 1 ,y 1 +b x , z 1 ), b x is a random number with a normal distribution, and its normal distribution is b x ~N(u,σ 2 ), where the mean u is the side length of the filler and the standard deviation σ 2 It is used to control the distribution of the filler side length. Finally, it is integrated together to obtain the filler coordinate matrix G (G 1 ; G 2 ; G 3 ; G 4 ).

[0020] Preferably, a random number θ(U 1 , V 1 , W 1 ), θ represents the rotation angle of the filler along the Cartesian three coordinate systems (X, Y, Z); G θ Determined by the aircraft attitude angle, θ is regarded as the aviation random attitude angle, from which the coordinate transformation matrix can be obtained. According to the coordinate transformation matrix and the filler coordinate matrix G, the filler rotated coordinate G can be obtained θ , thereby obtaining the packing coordinate matrix G of the random phase θ .

[0021] Preferably, the periodic construction and the expansion obtain G p The matrix needs to determine whether the filler is at the unit body boundary at this time. If it is not at the boundary, it will be judged differently. p If there is interference between the steps, if it is at the boundary, the location of the filler should be determined, and the corresponding copy translation should be performed according to its location, and the copy should be moved to the corresponding position of the unit body to obtain the G p , the G p Contains the G θ and the packing coordinate matrix after copying the translation.

[0022] Preferably, the determination of different G p The process of whether there is interference between them includes repeating steps 2, 3, and 4 to obtain the coordinates G of a new filler. p-x+1 , use the separating axis algorithm to detect whether the two fillings intersect. If it is determined that the two fillings intersect, discard the current random number, take the next random number and repeat steps 4 and 5. If it is determined that the two fillings do not intersect, generate the current filling image and save the coordinates.

[0023] Preferably, the separating axis algorithm sets an arbitrary projection axis to transform the coordinates of all vertices of the first filler G p-1 Project the projection axis and obtain the projection matrix T 1 , fill all vertices G in the second sheet p-2 Project the projection axis respectively to obtain the projection construction matrix T 2 , and so on, fill the xth piece with all vertex coordinates G p-x Project the projection axis to obtain the projection construction matrix T x , and so on, finally we get the matrix T x+1 , and then perform T 1 , T 2 …T x With T x+1 The judgment rule is whether MAX{T x}>=MIN{T x+1}, while MIN{T x}<=MAX{T x+1}, if both conditions are met at the same time, they are judged to intersect on this projection axis, and the projection axis should be changed for detection again. If both conditions are met on all the set projection axes, they are judged to intersect. Otherwise, as long as the two conditions are not met at the same time on any projection axis, the two packings are judged not to intersect.

[0024] Preferably, the determination of whether the generated filler meets the specified mass fraction w t The process includes repeating steps 5 and 6 until a specified number of filler sheets with periodic translation are obtained, according to Calculate the composite mass fraction, ρ 1 is the packing density, ρ 0 is the matrix density, a is the side length of the cubic model of the representative volume unit, d is the thickness of a single-layer filler sheet, and n is the number of filler sheets. If the mass fraction does not meet the requirements, repeat steps 4 and 5. If the mass fraction meets the requirements, exit the loop and proceed to step 7.

[0025] Preferably, the automatic modeling file written based on the obtained filler coordinates requires that all saved filler coordinates be written in the macro command format of the 3D modeling software, and a loop program be constructed to automatically establish points for all planar filler coordinates, and then a loop program be constructed to connect every four points, and a loop program be constructed to stretch every four lines into a curved surface to establish a square unit body with a side length of a, and a loop program be constructed to forcibly remove all filler parts outside the unit body, and the filler inside the unit body will be retained to obtain a geometric model of the microstructure of the planar filler composite material.

[0026] The technical effects of the present invention are:

[0027] The established fillers have random distribution and random phase, the filler sizes are normally distributed, they do not interfere with each other, they satisfy periodicity, and some fillers are considered to be agglomerated.

[0028] The normal distribution and agglomeration characteristics can be set arbitrarily. The normal distribution can be controlled by the mean value and variance, and the agglomeration degree can be set by relevant parameters.

[0029] This method is not limited to MATLAB. Any high-level language can be used to implement the method. Similarly, any 3D modeling software can be used to implement modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0031] Figure 1 It is a flow chart of the geometric modeling process of the planar particle-filled composite material in an embodiment of the present invention;

[0032] Figure 2 A geometric model diagram of a composite material with uniform particle size and no agglomeration in an embodiment of the present invention;

[0033] Figure 3 This is an example diagram of the normal distribution random number distribution generated in the embodiment of the present invention;

[0034] Figure 4 It is a geometric model diagram of normal distribution of particle size and no agglomeration in an embodiment of the present invention;

[0035] Figure 5 It is a geometric model diagram of a composite material with normal distribution of particle size and no agglomeration in an embodiment of the present invention;

[0036] Figure 6 It is a geometric model diagram of normal distribution of particle size and local agglomeration in an embodiment of the present invention;

[0037] Figure 7 Schematic diagram of the composite material geometry with normal distribution of particle size and local agglomeration in an embodiment of the present invention. DETAILED DESCRIPTION

[0038] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, this embodiment provides an automated geometric modeling method for a planar particle-filled composite material microstructure, comprising the following steps:

[0040] 1. Generate volume fraction V ag Agglomerates. Specify the volume fraction V of all aggregates in the unit volume ag , the number of aggregates in the unit body N ag , aggregate size A s According to the formula a is the side length of the cubic model of the representative volume unit, d is the thickness of the filler sheet, N j is the number of filler sheets in a single agglomerate, obtained by calculation. Generate N at different rotation angles at a fixed position j Fillers, each piece is A s , generate random numbers to move the whole body, repeat the above steps, and determine whether it intersects with the generated agglomerates. If it intersects, regenerate it. If it does not intersect, generate the agglomerate again until the volume fraction meets V ag . The V ag is a real number greater than 0 and less than 1, N ag is an integer greater than 0, A s The size range is (0~a), a is a real number greater than 0, and d is a real number greater than 0. The single agglomerate is composed of N j The filler is composed of N j The larger the value, the greater the degree of agglomeration of the aggregates. j Calculated by the formula.

[0041] 2. Generate random numbers and construct a fixed-angle filler coordinate matrix G. Initialize the random number seed over time and generate random numbers that meet the uniformity requirements. If the uniformity requirements are not met, regenerate them. Take the random number G 1 (x 1 ,y 1 , z1 ), use it as a filler vertex coordinate to construct the other three vertex coordinates G 2 (x 1 +b x ,y 1 , z 1 ), G 3 (x 1 +b x ,y 1 +b x , z 1 ), G 4 (x 1 ,y 1 +b x , z 1 ), where b x is a random number with a normal distribution, and its normal distribution is b x ~N(u,σ 2 ), where the mean u is the side length of the filler and the standard deviation σ 2 It is used to control the distribution of the filler side length. Finally, it is integrated together to obtain the matrix G(G 1 ; G 2 ; G 3 ; G 4 ). a is a real number greater than 0, the random number ranges from (0 to a), u is a real number greater than 0, σ 2 is a real number greater than 0. The random number uniformity test is completed by the frequency statistical test method.

[0042] 3. G is randomly rotated to obtain the filler coordinate matrix G of the random phase θ . Take a random number θ(U 1 , V 1 , W 1 ), θ represents the rotation angle of the filler along the Cartesian three coordinate system (X, Y, Z). G can be determined according to the aircraft attitude angle θ , taking θ as the aviation random attitude angle, the coordinate transformation matrix can be obtained. According to this matrix and the filler G coordinate matrix, the filler rotated coordinate G can be obtained. θ , at this time, a random phase filler is obtained. The value of θ is in the range of (0~π),

[0043] 4. Complete the periodic construction according to G θ Position expansion to obtain G p After completing step 3, it should be determined whether the filler is at the unit cell boundary. If not, proceed to step 5. Otherwise, it should be determined where it is at the boundary, and the corresponding copy and translation should be performed according to its position, and the copy should be moved to the corresponding position of the unit cell. Multiple translations should be performed at the edges and corners. The corresponding filler coordinates will be represented by G θChange to G p , G p Contains G θ And the filler coordinate matrix after copying and translation. Whether the filler is at the boundary and the position at the boundary are determined by coordinate judgment.

[0044] 5. Repeatedly generate G p And judge different G p Repeat steps 2, 3, and 4 to obtain the coordinates G of a new piece of filler. p-x+1 . Use the separation axis algorithm to detect, set the projection axis arbitrarily, and convert the coordinates of all vertices of the first filler G p-1 Project the projection axis and obtain the projection matrix T 1 , fill all vertices G in the second sheet p-2 Project the projection axis respectively to obtain the projection construction matrix T 2 , and so on, fill the xth piece with all vertex coordinates G p-x Project the projection axis to obtain the projection construction matrix T x , and so on, finally we get the matrix T x+1 , and then perform T 1 , T 2 …T x With T x+1 The judgment rule is whether MAX{T x}>=MIN{T x+1}, while MIN{T x}<=MAX{T x+1}, if both conditions are met at the same time, then the intersection is determined on this projection axis, and the projection axis should be changed for detection again. If both conditions are met on all set projection axes, then the two are determined to intersect. Otherwise, as long as the two conditions are not met at the same time on any projection axis, then the two fillers are determined to be non-intersecting. If the two fillers are determined to intersect, the current random number is discarded, and the next random number is taken to repeat steps 4 and 5. If the two fillers are determined to be non-intersecting, the current filler image is generated and the coordinates are saved. The first piece of filler needs to be judged with all agglomerates to see if there is an intersection. It can only be generated if there is no intersection. When generating the second piece of filler, it needs to be detected with the first piece and agglomerates. When generating the third piece, it needs to be detected with the first two pieces and agglomerates. At the same time, the third piece can be generated if there is no intersection. By analogy, when generating the xth piece, it needs to be detected with the first x-1 pieces and agglomerates respectively. At the same time, the xth piece can be generated if there is no intersection. There are two types of projection axis selection. One is the absolute coordinate system, which can be selected as

[001] ,

[110] , [11 / 100], etc. The second type is the local coordinate system vector formed by the filler side length. It can be seen that the selection of projection axes is arbitrary and endless. At the same time, the number of projection axes determines the quality of detection capabilities.

[0045] 6. Determine whether the generated filler meets the specified mass fraction w t Repeat steps 5 and 6 until a specified number of filler sheets with periodic translation are obtained. The composite material mass fraction, ρ 1 is the packing density, ρ 0 is the matrix density, a is the side length of the cubic model of the representative volume unit, d is the thickness of a single-layer filler sheet, n is the number of filler sheets, if the mass fraction does not meet the requirements, repeat steps 4 and 5, if the mass fraction meets the requirements, exit the loop and proceed to step 7. t is a real number greater than 0 and less than 1, d is a real number greater than 0, and n is an integer greater than 0. The number of fillers is unknown, but the side length of the filler is a random number that can be calculated each time it is generated. As long as the mass fraction is given, the number of fillers can be solved.

[0046] 7. Automatic modeling file writing. All the saved filler coordinates are written in the macro command format of the 3D modeling software, and a loop program is constructed to automatically establish points for all planar filler coordinates. Then a loop program is constructed to connect every four points, and every four lines are constructed to stretch into a surface, and a square unit body with a side length of a is constructed. A loop program is constructed to forcibly remove all filler parts outside the unit body, and the filler inside the unit body will be retained to obtain a geometric model of the microstructure of the planar filler composite material. Complete the writing of the macro file format according to the command format of the 3D modeling software, which will obtain a script file, and then directly run the script file in the modeling software to complete the modeling. Specific embodiment 1

[0048] 1. Form agglomerates. ag =0, that is, no aggregates are generated.

[0049] 2. Generate random numbers and construct a fixed-angle filler coordinate G matrix. Generate a (10000, 3) matrix in the range (-50, 50) for uniformity testing. The particle side length is 25, and the first row of the above matrix is ​​taken to construct the G matrix.

[0050] 3. The matrix G is randomly rotated to obtain the filler coordinate matrix G of the random phase θ Generate a (10000, 3) matrix in the range (0, 180), perform a uniformity test, and take the first row as the rotation angle of the filler. Based on this angle and G, we can get G θ matrix.

[0051] 4. Build periodicity, G θ Position expansion to get matrix G p According to G θ The position of G is copied and translated accordingly.p-1 matrix.

[0052] 5. Determine the mutual interference of fillers. Take the second row of the random number matrix and follow the above steps to get G p-2 , using the separation axis algorithm to determine G p-1 With G p-2 The mutual interference between them is determined. If there is no mutual interference, the coordinates of this filler are saved. The mutual interference of all fillers can be obtained by analogy until step 6 is satisfied.

[0053] 6. Determine whether the specified quality score w is met t Repeat step 5 until the specified number of filler sheets is obtained. The composite mass fraction can be calculated, where is an unknown number, which can be generated in real time based on b x Calculate the number of fillers n, a = 100, ρ 0 =1.02,ρ 1 =2.2, d=0.34, w t Set to 4.5%. If the mass fraction does not meet the requirements, repeat the above steps. If the mass fraction meets the requirements, exit the loop and proceed to step 7.

[0054] 7. Write the automatic modeling file. Write it according to the command of CATIA automatic modeling, build a loop to import all coordinates, stretch after connecting, and finally establish the geometric model of the microstructure filled with plane shape, such as Figure 2 .

[0055] Embodiment 2:

[0056] 1. Form agglomerates. ag =0, that is, no aggregates are generated.

[0057] 2. Generate random numbers and construct a G matrix of filler coordinates with a fixed angle. Generate a (10000, 3) matrix in the range of (-50, 50) for uniformity test. Generate a particle side length matrix with a normal distribution, that is, a random number (250, 1) matrix with a normal distribution mean of 25 and a standard deviation of 10. Take the first row of the above two matrices to construct the G matrix. The normal distribution is as follows: Figure 3 shown.

[0058] 3. The matrix G is randomly rotated to obtain the filler coordinate matrix G of the random phase θ Generate a (10000, 3) matrix in the range (0, 180), perform a uniformity test, and take the first row as the rotation angle of the filler. Based on this angle and G, we can get G θ matrix.

[0059] 4. Build periodicity, G θPosition expansion to get matrix G p According to G θ The position of G is copied and translated accordingly. p-1 matrix.

[0060] 5. Determine the mutual interference of fillers. Take the second row of the random number matrix and follow the above steps to get G p-2 , using the separation axis algorithm to determine G p-1 With G p-2 The mutual interference between them is determined. If there is no mutual interference, the coordinates of this filler are saved. The mutual interference of all fillers can be obtained by analogy until step 6 is satisfied.

[0061] 6. Determine whether the specified quality score w is met t Repeat steps 4 and 5 until the specified number of packing sheets is obtained, and calculate according to the formula, where a = 100, ρ 0 =1.02,ρ 1 =2.2, d=0.34, w t If the mass fraction does not meet the requirements, repeat the above steps. If the mass fraction meets the requirements, exit the loop and proceed to step 7. Figure 4 Normally distributed filler flakes are visible at 4%wt.

[0062] 7. Write the automatic modeling file. Write it according to the command of CATIA automatic modeling, build a loop to import all coordinates, stretch after connecting the lines, and finally establish the geometric model of the microstructure filled with plane shape.

[0063] Embodiment 3:

[0064] 1. Generate volume fraction V ag Aggregates. ag = 0.8%, set the number of aggregates N ag is 2, the aggregate size is A s is 20. According to the formula a=100,d=0.34,N can be calculated j Generate N random rotation angles at the origin of the coordinate axis j Fillers, each with a size of 20, generate random numbers to move them as a whole, repeat the above steps, and determine whether they intersect with the generated agglomerates. If they intersect, regenerate them; if not, generate the agglomerates until the volume fraction meets 0.8%.

[0065] 2. Generate random numbers and construct a G matrix of filler coordinates with a fixed angle. Generate a (10000, 3) matrix in the range of (-50, 50) for uniformity test. Generate a particle side length matrix with a normal distribution, that is, a random number (250, 1) matrix with a normal distribution mean of 15 and a standard deviation of 10. Take the first row of the above two matrices to construct the G matrix.

[0066] 3. The matrix G is randomly rotated to obtain the filler coordinate matrix G of the random phase θ Generate a (10000, 3) matrix in the range (0, 180), perform a uniformity test, and take the first row as the rotation angle of the filler. Based on this angle and G, we can get G θ matrix.

[0067] 4. Build periodicity, G θ Position expansion to get matrix G p According to G θ The position of G is copied and translated accordingly. p-1 matrix.

[0068] 5. Determine the mutual interference of fillers. Take the second row of the random number matrix and follow the above steps to get G p-2 , using the separation axis algorithm to determine G p-1 With G p-2 The mutual interference between them is determined. If there is no mutual interference, the coordinates of this filler are saved. The mutual interference of all fillers can be obtained by analogy until step 6 is satisfied.

[0069] 6. Determine whether the specified quality score w is met t Repeat steps 4 and 5 until the specified number of filler sheets is obtained. The composite mass fraction can be calculated, where is an unknown number, which can be generated in real time based on b x Calculate the number of fillers n, a = 100, ρ 0 =1.02,ρ 1 =2.2, d=0.34, w t If the mass fraction does not meet the requirement, repeat the above steps. If the mass fraction meets the requirement, exit the loop and proceed to step 7.

[0070] 7. Write the automatic modeling file. Write it according to the command of CATIA automatic modeling, build a loop to import all coordinates, stretch after connecting, and finally establish the geometric model of the microstructure filled with plane shape, such as Figure 5-7 .

[0071] The present invention is not limited to the above-mentioned embodiments. In the technical method disclosed in the present invention, technicians in this field can make some substitutions and deformations of its technical features based on the technical content disclosed therein without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A geometric modeling method for the microstructure of planar particle-filled composite materials. It is characterized in that include: Step 1: Generate volume fraction V ag agglomerates, so that the agglomerates are filled in the unit body without intersecting each other; Step 2: Generate random numbers and construct a fixed-angle filler coordinate matrix G; Step 3: Obtaining a random phase filler coordinate matrix G based on the filler coordinate matrix G θ ; Step 4: Filling coordinates G based on the random phase θ Perform periodic construction and according to G θ Position expansion to obtain G p matrix; Step 5: Based on the G p Matrix judgment different G p whether there is interference between them; Step 6: Based on the G p The matrix determines whether the generated filler meets the specified mass fraction w t ; Step 7: Write an automatic modeling file based on the obtained filler coordinates; Specify the volume fraction V of all aggregates in the unit cell ag , the number of aggregates in the unit body N ag , the size of each filler in the agglomerate is A s ; Generate N with different rotation angles at a fixed position j Fillers, each piece is A s , generate random numbers to move the whole body, and determine whether it intersects with the generated agglomerates. If so, regenerate it; if not, generate the agglomerate until the volume fraction meets V ag , thus obtaining the volume fraction V ag Aggregates of The volume fraction V ag According to the formula Calculated, a is the side length of the cube model of the representative volume unit, d is the thickness of the filler sheet, N j is the number of filler sheets in a single agglomerate.

2. A geometric modeling method for a microstructure of a planar particle-filled composite material according to claim 1, Features: The random number seed must be initialized over time and meet the uniformity requirement. If it does not meet the uniformity requirement, it must be regenerated; According to the random number, a random number G is obtained. 1 (x 1 ,y 1 , z 1 ), use it as a filler vertex coordinate to construct the other three vertex coordinates G 2 (x 1 +b x ,y 1 , z 1 ), G 3 (x 1 +b x ,y 1 +b x , z 1 ), G 4 (x 1 ,y 1 +b x , z 1 ), b x is a random number with a normal distribution, and its normal distribution is b x ~N(u,σ 2 ), where the mean u is the side length of the filler and the standard deviation σ 2 It is used to control the distribution of the filler side length; finally, it is integrated together to obtain the filler coordinate matrix G (G 1 ; G 2 ; G 3 ; G 4 ).

3. A geometric modeling method for a microstructure of a planar particle-filled composite material according to claim 1, Features: Take a random number θ(U 1 , V 1 , W 1 ), θ represents the rotation angle of the filler along the Cartesian three coordinate systems (X, Y, Z); G θ Determined by the aircraft attitude angle, θ is regarded as the aviation random attitude angle, from which the coordinate transformation matrix can be obtained. According to the coordinate transformation matrix and the filler coordinate matrix G, the filler rotated coordinate G can be obtained θ , thereby obtaining the packing coordinate matrix G of the random phase θ .

4. A geometric modeling method for a microstructure of a planar particle-filled composite material according to claim 1, Features: The periodic construction and the expansion yield G p The matrix needs to determine whether the filler is at the unit body boundary at this time. If it is not at the boundary, it will be judged differently. p If there is interference between the steps, if it is at the boundary, the location of the filler should be determined, and the corresponding copy translation should be performed according to its location, and the copy should be moved to the corresponding position of the unit body to obtain the G p , the G p Contains the G θ and the packing coordinate matrix after copying the translation.

5. The geometric modeling method of the microstructure of a planar particle-filled composite material according to claim 1, Features: The judgment is different p The process of whether there is interference between them includes repeating steps 2, 3, and 4 to obtain the coordinates G of a new filler. p-x+1 , use the separating axis algorithm to detect whether the two fillings intersect. If it is determined that the two fillings intersect, discard the current random number, take the next random number and repeat steps 4 and 5. If it is determined that the two fillings do not intersect, generate the current filling image and save the coordinates.

6. A geometric modeling method for a planar particle-filled composite material microstructure according to claim 5, Features: The separating axis algorithm sets an arbitrary projection axis and fills all the vertex coordinates G in the first piece. p-1 Project the projection axis and obtain the projection matrix T 1 , fill all vertices G in the second sheet p-2 Project the projection axis respectively to obtain the projection construction matrix T 2 , and so on, fill the xth piece with all vertex coordinates G p-x Project the projection axis to obtain the projection construction matrix T x , and so on, finally we get the matrix T x+1 , and then perform T 1 , T 2 …T x With T x+1 The judgment rule is whether MAX{T x }>=MIN{T x+1 }, while MIN{T x }<=MAX{T x+1 }, if both conditions are met at the same time, they are judged to intersect on this projection axis, and the projection axis should be changed for detection again. If both conditions are met on all the set projection axes, they are judged to intersect. Otherwise, as long as the two conditions are not met at the same time on any projection axis, the two packings are judged not to intersect.

7. The geometric modeling method of a planar particle-filled composite material microstructure according to claim 1, Features: The method of judging whether the generated filler meets the specified mass fraction w t The process includes repeating steps 5 and 6 until a specified number of filler sheets with periodic translation are obtained, according to Calculate the composite material mass fraction, b x is a random number with normal distribution representing the side length of the packing, ρ 1 is the packing density, ρ 0 is the matrix density, a is the side length of the cubic model of the representative volume unit, d is the thickness of a single-layer filler sheet, and n is the number of filler sheets. If the mass fraction does not meet the requirements, repeat steps 4 and 5. If the mass fraction meets the requirements, exit the loop and proceed to step 7.

8. The geometric modeling method of a planar particle-filled composite material microstructure according to claim 1, Features: The automatic modeling file written based on the obtained filler coordinates requires that all saved filler coordinates be written in the macro command format of the 3D modeling software, and a loop program be constructed to automatically establish points for all planar filler coordinates. A loop program is then constructed to connect every four points, and a loop program is constructed to stretch every four lines into a surface to establish a square unit body with a side length of a. A loop program is constructed to forcibly remove all filler parts outside the unit body, and the filler inside the unit body will be retained to obtain a geometric model of the microstructure of the planar filler composite material.

Images