Porous medium modeling method based on Laguerre-Voronoi method

Abstract

The invention relates to a porous medium modeling method based on a Lagguerre-Voronoi method, and the method comprises the steps: firstly generating a group of sphere data with the sphere diameter in logarithmic normal distribution by utilizing MATLAB software; using LAMMPS software to randomly stack the group of spheres in the fixed cubic space to obtain the sphere center coordinate and diameter of each sphere; the method comprises the following steps: randomly stacking spheres, performing space division on the randomly stacked spheres by using a Lagguerre-Voronoi method to obtain a corresponding three-dimensional Lagguerre-Voronoi graph, retaining edges and vertexes of each sphere division space in the three-dimensional Lagguerre-Voronoi graph, and generating a porous medium skeleton based on the edges and vertexes of each sphere division space; and finally, establishing a porous medium model of a required framework section shape according to the porous medium framework. Compared with a commercially available commercial foam structure, the porous medium model established by the invention can reproduce an actual foam structure more truly, and internal pores have good performance in the aspects of disorder and connectivity.

Description

Technical Field

[0001] The present invention belongs to the technical field of the design of porous medium skeleton structures, and particularly relates to a method for modeling porous media based on the Laguerre-Voronoi space partitioning method. Background Technique

[0002] Porous medium materials (such as open-cell foamed metals, honeycombs, foamed ceramics, etc.) have been widely used in many fields such as aerospace, automotive manufacturing, construction, environmental protection, and energy storage due to their excellent mechanical properties, heat insulation, sound insulation, sound absorption, water absorption, etc. With the development of technology, more and more industrial and scientific fields have begun to focus on how to further optimize and design these foam materials to meet higher performance requirements.

[0003] Most of the existing methods for modeling porous media are based on simplified assumptions, often ignoring the microscopic structure and complex multi-scale characteristics of foam materials. These traditional methods usually focus on predicting macroscopic mechanical properties, but are often inaccurate in the detailed characterization of foam structures (such as pore structures, cross-sectional shapes and changes of skeletons, etc.), and it is difficult to reflect real physical phenomena. Summary of the Invention

[0004] The purpose of the present invention is to propose a method for modeling porous media by introducing the Laguerre-Voronoi space partitioning method in view of the limitations of the existing methods for modeling porous media, so as to obtain a more realistic and efficient porous medium model. To achieve the above purpose, the technical solution proposed by the present invention is: a method for modeling porous media based on the Laguerre-Voronoi method, comprising the following steps:

[0005] a) Using MATLAB software, generate a set of sphere data with the sphere diameters following a lognormal distribution;

[0006] b) Use LAMMPS software to randomly pack the set of spheres in step a) in a fixed cubic space to obtain the center coordinates and diameters of each sphere;

[0007] c) Use the Laguerre-Voronoi method to partition the space of the randomly packed spheres in step b) to obtain the corresponding three-dimensional Laguerre-Voronoi diagram, retain the edges and vertices of the space partitioned by each sphere in the three-dimensional Laguerre-Voronoi diagram, and generate a porous medium skeleton based on the edges and vertices of the space partitioned by each sphere;

[0008] d) Establish a porous medium model with the required cross-sectional shape of the skeleton according to the porous medium skeleton.

[0009] A further design of the above technical solution is that when generating a set of sphere data with the sphere diameters following a lognormal distribution in step a), the coefficient of variation of the sphere diameters is set to be equal to the coefficient of variation of the pore diameters.

[0010] When generating a set of sphere data with the sphere diameters following a lognormal distribution in step a), the coefficient of variation CV(d) and the average pore diameter E(d) of the sphere diameters can be preset. By adjusting these two parameters, effective control over the change in pore density of the porous medium can be achieved.

[0011] The cross-section of the porous medium skeleton generated in step c) is a conventional circular cross-section, a circular variable cross-section, a triangular cross-section, or a triangular variable cross-section.

[0012] When the cross-section of the skeleton is a conventional circular cross-section or a circular variable cross-section, the porous medium skeleton is imported into the SpaceClaim software for Boolean operations to obtain a porous medium model with the required conventional circular cross-section and circular variable cross-section skeletons.

[0013] When the cross-section of the skeleton is a triangular cross-section or a triangular variable cross-section, the porous medium skeleton is imported into the UG modeling software. The modeling of each skeleton is completed through the sweep command, and each skeleton is merged into a whole through the merge command to obtain a porous medium model with the required triangular cross-section and triangular variable cross-section skeletons.

[0014] After obtaining the corresponding three-dimensional Laguerre-Voronoi diagram in step c), the stacked spheres, the internal volume of the divided space corresponding to each sphere, and the interfaces between the spaces in the three-dimensional Laguerre-Voronoi diagram are deleted to obtain the edges and vertices of the divided spaces of each sphere. The edges and vertices of the divided spaces of each sphere are cylindricalized with a certain diameter to generate the porous medium skeleton material.

[0015] The generation process of the porous medium skeleton model with a circular variable cross-section is as follows: A quadratic function is used to fit the variation law of the radius of the skeleton cross-section. Six points on the outer contour line of the skeleton are selected, and the coordinates of these six points are calculated through the fitted quadratic function. The outer contour line of the skeleton is fitted using a spline curve. The fitted outer contour line of the skeleton is connected to the central axis of the skeleton to construct a closed plane. By rotating this closed plane 360° around the central axis of the skeleton, a single skeleton entity is generated, thus completing the modeling of the variable cross-section skeleton.

[0016] The generation process of the triangular and variable cross-section porous medium skeleton contour line is as follows: Set the three vertices of an equilateral triangle, then set a fitting point between every two vertices, and obtain the skeleton cross-section shapes of convex triangles, triangles, and concave triangles by fitting the three sides of the triangle with spline curves. Select six points on the outer contour line of the skeleton, and fit the three edges of the curvilinear triangle skeleton through the six points to form the contour line of a single variable cross-section porous medium skeleton.

[0017] The process of obtaining the porous medium skeleton through Boolean operations is as follows: When performing Boolean operations, a spherical node needs to be generated at the vertex of each foam skeleton. The diameter of the spherical node is larger than the diameter of the foam skeleton, and the nearby skeletons are connected using this node to form a solid porous medium.

[0018] The process of obtaining the three-dimensional Laguerre-Voronoi diagram by the Laguerre-Voronoi method is as follows: For any point r in the set M i , the weighting number r = {r 1 , r 2 , r 3 …, r n} forms a set. Then, the distance expression between any point p i in the set M and any other point q is:

[0019]

[0020] Then, the expression of the single partition space corresponding to the point p i is:

[0021] v L (p i ) = {pp ∈ R 3 , d L (p, p i ) < d L (p, p j ), i ≠ j}

[0022] Then, the expression of all partition spaces is:

[0023] V L (S, r) = {v L (p 1 ), v L (p 2 ), v L (p 3 ), … v L (p n )}

[0024] Based on the above rules, the fixed space partition is completed, and the three-dimensional Laguerre-Voronoi diagram can be obtained.

[0025] Compared with other existing modeling methods, the present method has the following advantages:

[0026] 1) The Laguerre-Voronoi method divides based on a point set in three-dimensional space, and can automatically determine physically meaningful Voronoi cells according to each generation point in the space (usually representing the center of pores), more accurately reflecting the geometric shape and distribution law of pores in porous media, being able to more realistically reproduce the actual foam structure, and having good performance in terms of disorder and connectivity of internal pores. This method is particularly suitable for dealing with porous media with complex morphology and irregular structure.

[0027] 2) The modeling method based on the Laguerre-Voronoi method can flexibly adjust various structural parameters during the modeling process, such as porosity, pore size distribution, pore morphology, and skeleton cross-sectional shape, etc. This flexible control ability enables designers to precisely achieve customized optimization of the performance of porous media.

[0028] 3) This method can quickly complete the establishment of a three-dimensional model of porous media, and can generate a porous media model through 3D printing technology, enabling practical engineering and technical applications and experimental research. Brief Description of the Drawings

[0029] Figure 1 is a three-dimensional model of porous media established according to the modeling method of the present invention.

[0030] Figure 2 is a schematic diagram of the modeling process for establishing porous media based on the Laguerre-Voronoi method.

[0031] Figure 3 is a flowchart for establishing porous media based on the Laguerre-Voronoi method.

[0032] Figure 4 is the Laguerre-Voronoi space division rule and three-dimensional Laguerre-Voronoi diagram.

[0033] Figure 5 is a schematic diagram of the formation of a circular variable cross-section skeleton.

[0034] Figure 6 is a schematic diagram of the formation of a triangular cross-section skeleton.

[0035] Figure 7 is a table of structural parameters of commercial porous materials.

[0036] Figure 8 is an analysis diagram of the actual porosity error.

[0037] Figure 9 It is the error analysis diagram of the actual specific surface area.

[0038] Figure 10 It is the structural comparison diagram of the porous medium established in the present invention and commercial porous materials. Specific embodiments

[0039] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0040] Embodiment 1

[0041] The modeling process of this embodiment is divided into three parts, and the process is as Figure 3 shown: (1) Complete the preselection of randomly packed spheres in MATLAB; (2) Use the classical molecular dynamics simulator LAMMPS to generate a set of randomly packed spheres: (3) Use the Laguerre-Voronoi method to divide the randomly packed spheres in a fixed space, and finally run the script in APDL to complete the establishment of the porous medium model.

[0042] In order to construct a porous medium model that conforms to the structural parameters of actual porous materials, this embodiment is based on the Laguerre-Voronoi space division method and formulates a porous structure modeling method based on the Laguerre-Voronoi method. The Laguerre-Voronoi method is a weighted Voronoi space division method, and its division rule is as Figure 4 shown. Specifically, for any point r i in the set M, the weighting numbers r = {r 1 , r 2 , r 3 …, r n} form a set. Then, the distance expression between any point p i and any other point q in the set M is:

[0043]

[0044] Then, the expression of the single division space corresponding to the point p i is:

[0045] v L (p i ) = {pp ∈ R 3 , d L (p, p i ) < d L (p, p j ), i ≠ j} Formula (2)

[0046] Then, the expression of all division spaces is:

[0047] V L (S,r)={v L (p 1 ),v L (p 2 ),v L (p 3 ),…v L (p n )}Formula (3)

[0048] By completing the fixed space division based on the above rules, the three-dimensional Laguerre-Voronoi diagram can be obtained.

[0049] Based on the Laguerre-Voronoi space partitioning method, the modeling design method of this embodiment is as follows: First, according to the average pore size E(d) and pore size variation coefficient CV(d) of commercial porous materials, as follows Figure 7 As shown in the figure, sphere data conforming to the normal distribution are generated in MATLAB. Then, the molecular dynamics code is written using LAMMPS software to control a certain number of spheres to be randomly stacked in a fixed cubic space to simulate the random distribution of pores in real porous materials. Finally, the script file of the Laguerre-Voronoi space partitioning method is run in the APDL software to complete the spatial partitioning of randomly stacked spheres in a fixed space, and the edges and vertices of the space partitioned by each sphere are retained. Based on these edges and vertices, the conventional circular section and variable section porous media models are established; for triangular section and variable section skeletons, the APDL script is used to generate the porous media skeleton contour line, and the required porous media model is established after being imported into the three-dimensional modeling software. The program is written using the command flow language of the APDL software to complete the Laguerre-Voronoi method partitioning and establish the porous media model and export it to the .iges file format. Files in this format are easy to convert to other three-dimensional drawing software and have strong convertibility. At the same time, it is easy to import into analysis software such as WorkBench and Fluent, which is convenient for model research and analysis.

[0050] Based on the above modeling ideas, the following steps need to be determined in the process of constructing a porous media model using the Laguerre-Voronoi space partitioning method:

[0051] Step 1: Preselection of random filling spheres;

[0052] In order to ensure that the generated sphere diameter conforms to the log-normal distribution characteristics and effectively control the pore size distribution characteristics, it is assumed that the coefficient of variation of the sphere diameter is equal to the coefficient of variation of the pore size. Based on this assumption, the coefficient of variation of the sphere diameter CV(d) and the average pore size E(d) are pre-set in the program design. By adjusting these two parameters, the pore density change of the porous medium can be effectively controlled. Specifically:

[0053] The volume distribution of randomly packed spheres is preselected using a lognormal distribution, and the probability density function of the lognormal distribution is expressed by the following formula:

[0054]

[0055] where: and σ are two parameters related to the expected value E(x) and variance Var(x) of the sphere volume, and their relationship can be expressed by the following relational formula:

[0056]

[0057] The coefficient of variation of the sphere volume CV(x) is expressed as the ratio of the standard deviation SD(x) to the expected value E(x):

[0058] CV(x) = SD(x) / E(x) Formula (7)

[0059] SD(x) = √Var(x) 1 / 2 Formula (8)

[0060] To better analyze the porous medium structure, the coefficient of variation of the sphere diameter CV(d) preset in modeling step a) is replaced by the coefficient of variation of the sphere volume CV(V) g , that is, the value of the coefficient of variation remains unchanged in the program, and the sphere volume is used instead of the sphere diameter. Their relationship expression is as follows:

[0061] V = πd g 3 ³ / 6 Formula (9)

[0062] Step 2: Formation of the variable cross-section of the skeleton;

[0063] The change in the radius of the skeleton cross-section conforms to the following expression:

[0064] R(x) = a×x 2 +R s Formula (10)

[0065] where R(x) is the radius of the skeleton cross-section at different positions; x is the axial position of the skeleton where the cross-section of the skeleton is located. When the value of x is 0, this cross-section is the middle cross-section of the skeleton; R s is the radius of the middle cross-section of the skeleton.

[0066] Let the ratio of the radius R s of the middle cross-section of the skeleton to the radius R ns of the two end cross-sections of the skeleton be S, then:

[0067] S = R s / R ns Formula (11)

[0068] Let the length of the skeleton be lenl. Substitute the points (0, SR ns ) and (0.5lenl, R ns ) into Equation (10), and the expression for the change in the cross-sectional radius of the skeleton can be obtained:

[0069]

[0070] The modeling scheme is to take six points on the outer contour line of the skeleton and use a spline curve to fit the outer contour line of the skeleton. The six points taken are located at the axial positions of the skeleton as -0.5lenl, -0.3lenl, -0.1lenl, 0.1lenl, 0.3lenl, and 0.5lenl respectively. Substitute them into Equation (12) to obtain the cross-sectional radii at the corresponding positions, which are R ns , (9 + 16S)R ns / 25, (1 + 24S)R ns / 25, (1 + 24S)R ns / 25, (9 + 16S)R ns / 25, and R ns . Thus, the coordinates of these six points can be obtained. Then, obtain the middle axis of the skeleton, connect the outer contour line of the skeleton with the middle axis of the skeleton to form a closed plane, and rotate this plane 360° around the axis to form a single skeleton entity, completing the modeling of the variable cross-sectional skeleton.

[0071] Example 2

[0072] This example is a porous medium model with a conventional circular cross-section. Please refer to Figure 1 (a) as shown. The specific implementation steps are as Figure 2 shown and are explained in detail as follows:

[0073] (1) Preselect spheres with a normal distribution;

[0074] Perform normal distribution processing on the diameters of the preselected spheres using the normal distribution equation described in Step 1 of Example 1, as Figure 2 (a) shown. Use MATLAB software for data generation and processing. By adjusting the coefficient of variation of the sphere diameter CV(d) and the average pore diameter E(d), porous media with different pore densities can be generated. For example, for a porous medium with 10 PPI, CV(d) is 0.28 and E(d) is 3.53, as Figure 6 shown.

[0075] (2) Randomly pack the spheres in a fixed space;

[0076] Write the sphere radius and normal distribution probability generated in the above steps into the program for randomly packing spheres, and use the LAMMPS software to execute this program to control a certain number of spheres to randomly pack within a fixed cubic space, as shown in Figure 2 (b). Before executing the program, parameters such as the length, width, and height of the cube can be adjusted to change the size of the fixed space.

[0077] (3) Use the Laguerre-Voronoi space partitioning method to partition the randomly packed spheres;

[0078] To implement the Laguerre-Voronoi space partitioning, a set M of the center coordinates of all packed spheres and the corresponding set r of radii need to be provided, and its space partitioning method is as shown in Figure 4 (a). After deriving these data from the above two steps, write them into the script of the space partitioning method and run it in the APDL software to perform the partitioning of the spheres within the fixed space. When all the spheres are partitioned, a three-dimensional Laguerre-Voronoi diagram can be obtained, as shown in Figure 4 (b). Then, delete the packed spheres, the internal volume of the partitioning space corresponding to each sphere, and the interfaces between the spaces in the three-dimensional Laguerre-Voronoi diagram, and only retain the edges and vertices of the partitioning spaces of each sphere, as shown in Figure 2 (d).

[0079] (4) Generate a porous medium model;

[0080] Import the model file generated in the previous step into ANSYS, and perform cylindrification with a certain diameter on the retained edges to generate the porous medium skeleton material, as shown in Figure 2 (e) and (f).

[0081] Import the porous medium model into the SpaceClaim software for Boolean operations. The specific steps are as follows: When performing Boolean operations, a spherical node needs to be generated at the vertex of each foam skeleton. The diameter of the spherical node is slightly larger than the diameter of the foam skeleton, and this node is used to connect the nearby skeletons. When all the spherical nodes are generated and the connection is completed, the entire structure forms a unified solid porous medium.

[0082] (5) Verification of the porous medium model;

[0083] Under different pore density and porosity conditions, perform error analysis on the actual porosity and the expected porosity, as well as the actual specific surface area and the expected specific surface area of the established model, as shown in Figure 8 and Figure 9As shown. At the same time, the established porous medium model was 3D printed using the material of tin bronze alloy CuSn10, and it was compared with the commercially available copper foam manufactured by the electrodeposition method, as Figure 10 shown. The results show that the relative errors between the actual porosity and the expected porosity are all less than ±5%, and the relative errors between the actual specific surface area and the expected specific surface area are all less than 21%. Although there are certain errors in the three-dimensional porous medium model established by the present invention, it can better present the structure of the actual foam.

[0084] Example 3

[0085] This example is a porous medium model with a circular variable cross-section skeleton. Please refer to Figure 1 (b) shown. Its specific modeling steps are the same as steps (1) and (2) of the porous medium with a circular cross-section skeleton in Example 2, but are different in steps (3) and (4). The specific differences are as follows:

[0086] (3) Use the Laguerre-Voronoi space division method to divide randomly packed spheres;

[0087] For the modeling of the variable cross-section skeleton, it is necessary to follow the method in step 2 of Example 1, use a simplified quadratic function to fit the variation law of the cross-section radius of the skeleton, determine 6 points on the outer contour line, calculate the coordinates of these six points through the fitted quadratic function, use a spline curve to fit the outer contour line of the skeleton, and rewrite the program in combination with the central axis of the skeleton. When running this program in APDL software, a closed plane is formed by connecting the outer contour line of the skeleton and the central axis of the skeleton, and then the closed plane is rotated 360° around the central axis to generate a single skeleton entity, thus completing the modeling of the variable cross-section skeleton, as Figure 5 (b) shown. In addition, by adjusting the key point positions of the quadratic function curve fitting (such as Figure 5 (a) shown), the shape of the skeleton cross-section can be flexibly changed to generate a porous medium skeleton model with different variable cross-section characteristics.

[0088] (4) Generate a porous medium model;

[0089] In the last step of modeling, four entities will be obtained by running the rotation command in ANSYS software. Therefore, it is necessary to merge the four entities obtained in a single cycle into one entity through the volume merge command to generate a unified circular variable cross-section skeleton porous medium model, as Figure 1 (b) shown.

[0090] Example 4

[0091] This example is a porous medium model with a triangular variable cross-section skeleton. Please refer to Figure 1As shown in (c), the specific modeling steps are the same as steps (1) and (2) of the circular cross-section skeleton porous medium in the first embodiment, but are different in steps (3) and (4). The specific differences are as follows:

[0092] (3) Use the Laguerre-Voronoi space partitioning method to partition randomly packed spheres;

[0093] When generating the triangular variable cross-section skeleton, directly generating a curved-edge triangular variable cross-section skeleton using ANSYS software will cause serious deformation of the model. Therefore, this process cannot be directly completed through this software. For this reason, this embodiment uses APDL command stream programming to implement the construction of the contour line of the curved-edge triangular variable cross-section skeleton.

[0094] First, set the three vertices of an equilateral triangle, and then set a fitting point between every two vertices. The skeleton cross-section shapes of convex triangles, triangles, and concave triangles are obtained by fitting the three sides of the triangle with spline curves. In the program, by controlling the position parameters of the fitting points, the concavity and convexity of the skeleton cross-section can be precisely adjusted. At the same time, using the variable cross-section establishment rule in step 2 of the previous step, the three edges of the curved-edge triangular skeleton are fitted through 6 points, and finally the contour line of a single variable cross-section porous medium skeleton is formed.

[0095] Based on the above method, modify the APDL command stream program. After the Laguerre-Voronoi space partitioning method is completed, generate the corresponding contour line of the curved-edge triangular variable cross-section skeleton, as Figure 1 shown in (c).

[0096] (4) Generate a porous medium model;

[0097] Since only the contour line of the skeleton is generated in step (3), in order to complete the construction of the porous medium model, a three-dimensional modeling software is also needed. Export the skeleton contour line as an.iges format, and then complete the modeling of each skeleton through the sweep command in the UG NX software, as Figure 6 shown.

[0098] The technical solutions of the present invention are not limited to the above embodiments. All technical solutions obtained by using equivalent replacement methods fall within the scope of protection required by the present invention.

Claims

1. A porous media modeling method based on the Laguerre-Voronoi method, characterized in that: The steps include: a) Using MATLAB software, generate a set of sphere data with a log-normal distribution of sphere diameter; b) using LAMMPS software to randomly stack a group of spheres in step a) in a fixed cubic space to obtain the coordinates and diameter of the center of each sphere; c) using the Laguerre-Voronoi method to perform spatial division on the randomly stacked spheres in step b) to obtain a corresponding three-dimensional Laguerre-Voronoi diagram, retaining the edges and vertices of the space divided by each sphere in the three-dimensional Laguerre-Voronoi diagram, and generating a porous medium skeleton based on the edges and vertices of the space divided by each sphere; d) Establishing a porous medium model with a desired skeleton cross-sectional shape according to the porous medium skeleton.

2. The porous media modeling method based on the Laguerre-Voronoi method according to claim 1, characterized in that: When generating a set of sphere data with sphere diameters showing a log-normal distribution in the step a), the coefficient of variation of the sphere diameter is set equal to the coefficient of variation of the pore size.

3. The porous media modeling method based on the Laguerre-Voronoi method according to claim 1, characterized in that: In the step a), the coefficient of variation CV(d) of the sphere diameter and the average pore diameter E(d) can be preset. By adjusting these two parameters, the change of the pore density of the porous medium can be effectively controlled.

4. The porous media modeling method based on the Laguerre-Voronoi method according to claim 2, characterized in that: The skeleton cross section of the porous medium skeleton generated in step c) is a conventional circular cross section, a circular variable cross section, or a triangular cross section or a triangular variable cross section; When the skeleton cross section is a conventional circular cross section or a circular variable cross section, the porous medium skeleton is imported into the SpaceClaim software for Boolean operation to obtain the required porous medium model of the conventional circular cross section and the circular variable cross section skeleton; When the skeleton cross section is a triangular cross section or a triangular variable cross section, the porous medium skeleton is imported into the UG modeling software, the modeling of each skeleton is completed through the sweep command, and each skeleton is merged into a whole through the merge command to obtain the porous medium model of the required triangular cross section and triangular variable cross section skeleton.

5. The porous media modeling method based on the Laguerre-Voronoi method according to claim 4, characterized in that: After the corresponding three-dimensional Laguerre-Voronoi diagram is obtained in step c), the stacked spheres, the internal volume of the divided space corresponding to each sphere, and the interfaces between the spaces in the three-dimensional Laguerre-Voronoi diagram are deleted to obtain the edges and vertices of the spaces divided by each sphere, and the edges and vertices of the spaces divided by each sphere are cylindricalized with a certain diameter to generate a porous medium skeleton material.

6. The porous media modeling method based on the Laguerre-Voronoi method according to claim 5, characterized in that: The generation process of the circular variable-section porous media skeleton model is as follows: use a quadratic function to fit the changing law of the skeleton cross-sectional radius, select six points on the skeleton outer contour line, calculate the coordinates of these six points through the fitted quadratic function, use a spline curve to fit the skeleton outer contour line, connect the fitted skeleton outer contour line with the skeleton's central axis, construct a closed plane, and generate a single skeleton entity by rotating the closed plane 360° around the skeleton's central axis, thereby completing the modeling of the variable-section skeleton.

7. The porous media modeling method based on the Laguerre-Voronoi method according to claim 6, characterized in that: The skeleton contour line generation process of triangular and variable-section skeleton porous media is as follows: set up three vertices of an equilateral triangle, then set up a fitting point between every two vertices, fit the three sides of the triangle through a spline curve to obtain the skeleton cross-sectional shapes of convex triangles, triangles and concave triangles, select six points on the outer contour line of the skeleton, and fit the three edges of the curved triangle skeleton through the six points to form the contour line of a single variable-section porous media skeleton.

8. The porous media modeling method based on the Laguerre-Voronoi method according to claim 7, characterized in that: The process of obtaining the porous medium skeleton through Boolean operation is as follows: when performing Boolean operation, a spherical node needs to be generated at the vertex of each foam skeleton. The diameter of the spherical node is larger than the diameter of the foam skeleton. The node is used to connect the nearby skeletons to form a solid porous medium.

9. The porous media modeling method based on the Laguerre-Voronoi method according to claim 1, characterized in that: The process of obtaining the three-dimensional Laguerre-Voronoi diagram by the Laguerre-Voronoi method is as follows: for any point r in the set M i , weighted number r = {r1, r2, r3…, r n } form a set, then any point p in the set M i The distance expression between any other point q is: d L (p i ,q)={[d V (p i ,q)] 2 -r i 2 } 12 Then point p i The corresponding single partition space expression is: v L (p i )={pp∈R 3 ,d L (p,p i )<d L (p,p j ),i≠j} Then the expressions for all partition spaces are: V L (S,r)={v L (p1),v L (p2),v L (p3),…v L (p n )} By completing the fixed space division based on the above rules, the three-dimensional Laguerre-Voronoi diagram can be obtained.

Images