Periodic random growth porous model modeling method
The method addresses core connection and meshing issues in random porous structure modeling by using polyhedral primitives and normal direction growth, enhancing the accuracy and efficiency of porous structure representation.
Patent Information
- Application Number
- CN202310783266.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2023-06-29
- Publication Date
- 2024-12-31
AI Technical Summary
Existing three- and four-parameter modeling methods for random porous structures fail to account for core connections, leading to isolated solids and meshing difficulties, particularly with polyhedral primitives like spheres and rectangular polyhedrons.
A modeling method that uses polyhedral structures as solid primitives, employs normal directions for growth, and introduces additional parameters and algorithms to ensure core connections and periodicity, optimizing the generation of porous structures.
The method effectively connects isolated cores and facilitates meshing, resulting in a more accurate and efficient representation of porous materials with high porosity.
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Abstract
Description
Technical Field
[0001] The invention relates to a modeling method of a periodic random growth porous model based on a polyhedral structure that can fill a space only by translation, and belongs to the field of geometric structure modeling. Background Art
[0002] Porous materials have high specific strength and low thermal conductivity and are widely used in thermal protection and insulation. However, their complex and random structural characteristics bring great difficulties to the study of porous materials. With the development of numerical simulation technology, the models that can be targeted have evolved from models with regular shapes to models with random structures, including a large number of simulation studies of random porous structures. For random porous structure models, there are generally two modeling methods: 1. Randomly distributed closed-cell modeling; 2. Randomly grown open-cell modeling. The random growth open-cell modeling first started with the plane-based 8-way three-parameter modeling proposed in 2007, including nucleation rate Cd, growth probability Di and volume proportion P2. If a second growth phase is included, the additional parameters In,m are added to form four parameters. This three-parameter modeling method can be extended to three dimensions, and the growth direction has developed from 8 directions to 26 directions.
[0003] This type of three- or four-parameter modeling has two shortcomings. First, it does not involve the connection between the cores, which will lead to isolated solids, which is inconsistent with the actual situation. Second, taking three-dimensional as an example, this modeling method uses 26-way growth. If a sphere is used as a solid primitive, the convex surface of the sphere, especially the strange and narrow concave surface of the gas, will bring great difficulties to meshing. If a rectangular polyhedron is used as a solid primitive, it is inevitable that there will be situations such as linear growth and top growth that basically do not exist in reality.
[0004] In order to overcome the second difficulty mentioned above, a simple polyhedron that is easy to mesh and can fill the entire space only by translation is selected as a solid primitive, and only the normal direction of the polyhedron surface is selected as the growth direction to avoid line contact or even point contact growth of the polyhedron primitive. In response to the first difficulty, based on the structural characteristics of the polyhedron, the present invention improves the three-parameter method, adds four parameters and corresponding algorithms, realizes the connection of solid cores and the deletion of isolated solid cores, periodic porous structure modeling and other optimizations. Summary of the invention
[0005] The modeling process of the periodic random porous structure model is as follows: Figure 1 The text description is as follows.
[0006] Cores are randomly generated with a probability of C_P within the model boundary and stored in container 1 until the volume proportion of the set cores reaches C_V.
[0007] Determine the distance between the cores in the model. If the distance between a core and other cores is greater than C_D, delete the core. For the core with the closest distance and less than C_D in the eight regions divided by the three planes XY, YZ and XZ with the core as the origin, use the random shortest path method to generate a random shortest connected solid and store it in container 3. At the same time, the solid generated by the shortest random path can also be used to generate a porous structure model with extremely high porosity. Its structure diagram is shown in the figure below. Figure 1 shown.
[0008] Traverse the existing solid structure in container 1, use the core as the starting solid structure, and judge whether the adjacent unit on each surface is solid. If it is solid, skip it. If it is not solid, generate new primitives on the surface according to a certain probability G_P. When the primitive grows on the boundary, use a periodic algorithm to generate new primitives based on the corresponding surface, line or vertex on the surface, line or vertex. Traverse, judge and generate primitives for the existing solid with the new primitives again for an unlimited number of times until the solid volume reaches the specified volume proportion T_V.
[0009] In the previous traversal, after random growth around each solid, a volume ratio judgment is performed. When the volume ratio reaches CT_V, the solid in container 3 is merged into container 1 to participate in the subsequent rounds of traversal. When the volume reaches O_V, the starting point of the traversal no longer starts from the first solid in container 1, but from O_N. When the volume ratio reaches T_V, the traversal ends. BRIEF DESCRIPTION OF THE DRAWINGS
[0010] Figure 1 Schematic diagram of the modeling process of the periodic random porous model.
[0011] Figure 2 A porous model with extremely high porosity established based on the shortest random path method of cube unit solid core.
[0012] Figure 3 6-way growth of cubic unit and periodic random porous model of cubic solid unit.
[0013] Figure 4 The structure of the hexagonal prism unit and its 8-way growth diagram.
[0014] Figure 5 The structure of the rhombic dodecahedron unit cell and its 12-way growth diagram. Implementation
[0015] The modeling method described in the present invention is slightly different depending on the structure of the solid element. Their common feature is that the entire space can be filled by simply translating the surface normal, specifically including a cuboid, a hexagonal prism and a rhombic dodecahedron. The side length of the polyhedron in the scheme can be any value. Specific implementation method one:
[0017] The side lengths a, b and c of the rectangular unit are positive integers. The side lengths LX, LY and LZ of the model are positive integer multiples of a, b and c respectively. Initially, all units are assumed to be gas. Until the volume proportion of the solid core reaches C_V, the coordinates corresponding to each unit are traversed in a loop with (a, 0, 0), (b, 0, 0) and (c, 0, 0) as the unit interval and direction. The three coordinate values of X, Y and Z of each unit interval have two positive and negative options. The three unit intervals have two positive and negative movement options, a total of 6 movement directions, and one by one correspond to the normal directions of the 6 faces of the rectangular solid primitive. For each traversed coordinate, determine whether the unit is solid. If it is gas, generate a random number. If the random number is less than the nucleation probability C_P, generate a solid primitive of the same size as the rectangular unit to fill the unit and mark the unit as solid, and put it into container 1 as a solid core.
[0018] Take the coordinates of each solid core in container 1 as their respective origins, establish a coordinate system equivalent to the cuboid, and use the three planes XY, YZ and XZ to divide the space with each core as the origin into eight regions. Traverse each solid core in container 1 to find the minimum distance to other cores in the eight regions. If the minimum distance is less than C_D, the coordinate combination of the two cores is loaded into container 2. If all the minimum distances are greater than C_D, the solid core is deleted from container 1.
[0019] All coordinate combinations in container 2 are traversed, and the difference between the coordinates of the two cores in each combination in the X, Y and Z directions is divided by a, b and c respectively to get the number of times that can be increased or decreased in the three directions. A direction is randomly selected from the three directions of X, Y and Z to add a solid primitive, and the coordinates of the solid primitive are recorded in container 3 until the number of times in each direction is exhausted, and the random shortest path between the two cores is completed.
[0020] Before the solid volume percentage reaches T_V, the existing solids in container 1 are traversed. Determine in turn whether the nearest unit in the normal direction of each surface of each solid is a solid. If it is a gas, generate a random number. If the generated random number is less than the growth probability G_P, fill the unit with a solid primitive, mark the unit as a solid, and put it into container 1 for subsequent rounds of traversal. After completing the judgment in six directions, enter the analysis of the next existing solid. If the solid primitive is filled on the boundary, a periodic modeling algorithm is used. The algorithm is divided into three situations: if the primitive appears at the vertex, a solid primitive is also filled in the other 7 vertices; if it appears at the edge, a solid primitive is filled in the position corresponding to the 3 parallel edges; if the primitive appears on the surface, a solid primitive is filled in the corresponding parallel surface. At the same time, the corresponding marking of the units in the three situations is completed.
[0021] In the previous traversal, after random growth around each solid, a volume ratio judgment is performed. When the volume ratio reaches CT_V, the core connection part is merged into the solid to participate in the next round of traversal. When the volume reaches O_V, the starting point of the traversal no longer starts from the first solid in container 1, but from O_N. When the volume ratio reaches T_V, the traversal ends. The growth diagram of the cube unit in the rectangular unit and the generation of the cube unit periodic random porous model are shown in Figure 3 As shown in the figure, some isolated solids are on the boundary, which are generated by the periodic modeling method. They can be connected to the solid at the other end of the parallel surface through the periodic boundary conditions and are no longer isolated. Specific implementation method 2:
[0023] The side lengths a and b of the hexagonal prism unit are positive integers, and the side lengths LX, LY and LZ of the cuboid model are positive integer multiples of 2a, a×sqrt3 (sqrt3 is the square root of 3, and sqrt2 is the square root of 2) and b, respectively. All units are initially assumed to be gas. Until the volume proportion of the solid core reaches C_V, the coordinates corresponding to each unit are cyclically moved and traversed with (3 / 2×a, sqrt3×a / 2, 0), (0, a×sqrt3, 0) and (0, 0, b) as the unit interval and direction. The three coordinate values of X, Y and Z of each unit interval have two positive and negative options, so the first unit interval has 4 moving directions, and the second and third unit intervals have two moving directions each, for a total of 8 moving directions, which correspond to the normal directions of the 8 faces of the hexagonal solid primitive. For each coordinate traversed, determine whether the unit is solid. If it is gas, generate a random number. If the random number is less than the nucleation probability C_P, generate a solid primitive of the same size as the hexagonal unit to fill the unit and mark the unit as solid, and put it into container 1 as a solid core.
[0024] With the coordinates of each solid core in container 1 as their respective origins, a coordinate system equivalent to the rectangular parallelepiped model is established, and the space with each core as the origin is divided into eight regions using the three planes XY, YZ and XZ. Each solid core in container 1 is traversed to find the minimum distance to other cores in the eight regions. If the minimum distance is less than C_D, the coordinates of the two cores are combined and loaded into container 2. If all the minimum distances are greater than C_D, the solid core is deleted from container 1.
[0025] Traverse all coordinate combinations in container 2, divide the difference between the coordinates of the two cores in the X, Y and Z directions of each combination by 3 / 2×a, a×sqrt3, and b respectively, to get the number of times that can be increased or decreased in the three directions, and randomly select a direction that matches the two cores from the eight directions (3 / 2×a, sqrt3×a / 2,0), (0, a×sqrt3, 0) and (0, 0, b) to add a solid primitive, and record the coordinates of the solid primitive in container 3 until the number of times in each direction is exhausted, and the random path between the two cores is completed.
[0026] Before the solid volume percentage reaches T_V, the existing solids in container 1 are traversed. Determine in turn whether the nearest unit in the normal direction of each surface of each solid is a solid. If it is a gas, generate a random number. If the generated random number is less than the growth probability G_P, fill the unit with a solid primitive, mark the unit as a solid, and put it into container 1 for subsequent rounds of traversal. After completing the judgment in twelve directions, enter the analysis of the next existing solid. If the solid primitive is filled on the model boundary, a periodic modeling algorithm is used. The algorithm is divided into three situations: if the primitive appears at the vertex, a solid primitive is also filled in the other 7 vertices; if it appears at the edge, a solid primitive is filled in the position corresponding to the 3 parallel edges; if the primitive appears on the surface, a solid primitive is filled in the corresponding parallel surface. At the same time, the corresponding marking of the units in the three situations is completed.
[0027] In the previous traversal, after random growth around each solid, a volume ratio judgment is performed. When the volume ratio reaches CT_V, the core connection part is merged into the solid to participate in the next round of traversal. When the volume reaches O_V, the starting point of the traversal no longer starts from the first solid in container 1, but from O_N. When the volume ratio reaches T_V, the traversal ends. The structure and growth diagram of the hexagonal prism unit is shown in Figure 4 shown. Specific implementation method three:
[0029] The side length of the rhombic dodecahedron unit is a×sqrt3, where a is a positive integer. The side lengths of the cuboid model LX, LY and LZ are positive integer multiples of 2a, 2a×sqrt2 and 2a×sqrt2 respectively. All units are initially assumed to be gas. Until the volume proportion of the solid core reaches C_V, the coordinates corresponding to each unit are looped through with (2a, a×sqrt2, a×sqrt2), (0, 2a×sqrt2, 0) and (0, 0, 2a×sqrt2) as the unit interval and direction. The three coordinate values of X, Y and Z of each unit interval have two positive and negative options. Therefore, the first unit interval has 8 movement directions, and the second and third unit intervals have two movement options each, for a total of 12 movement directions, which correspond to the normal directions of the 12 faces of the rhombic dodecahedron solid primitive. For each coordinate traversed, determine whether the unit is solid. If it is gas, generate a random number. If the random number is less than the nucleation probability C_P, generate a solid primitive of the same size as the rhombic dodecahedron unit to fill the unit and mark the unit as solid, and put it into container 1 as a solid core.
[0030] With the coordinates of each solid core in container 1 as their respective origins, a coordinate system equivalent to the rectangular parallelepiped model is established, and the space with each core as the origin is divided into eight regions using the three planes XY, YZ and XZ. Each solid core in container 1 is traversed to find the minimum distance to other cores in the eight regions. If the minimum distance is less than C_D, the coordinates of the two cores are combined and loaded into container 2. If all the minimum distances are greater than C_D, the solid core is deleted from container 1.
[0031] Traverse all coordinate combinations in container 2, divide the difference between the coordinates of the two cores in the X, Y and Z directions of each combination by 2a, a×sqrt2, and a×sqrt2 respectively, to get the number of times that can be increased or decreased in the three directions, and randomly select a direction that matches the two cores from the twelve directions (2a, a×sqrt2, a×sqrt2), (0, 2a×sqrt2, 0) and (0, 0, 2a×sqrt2) to add a solid primitive, and record the coordinates of the solid primitive in container 3 until the number of times in each direction is exhausted, and the random path between the two cores is completed.
[0032] Before the solid volume percentage reaches T_V, the existing solids in container 1 are traversed. Determine in turn whether the nearest unit in the normal direction of each surface of each solid is a solid. If it is a gas, generate a random number. If the generated random number is less than the growth probability G_P, fill the unit with a solid primitive, mark the unit as a solid, and put it into container 1 for subsequent rounds of traversal. After completing the judgment in twelve directions, enter the analysis of the next existing solid. If the solid primitive is filled on the model boundary, a periodic modeling algorithm is used. The algorithm is divided into three situations: if the primitive appears at the vertex, a solid primitive is also filled in the other 7 vertices; if it appears at the edge, a solid primitive is filled in the position corresponding to the 3 parallel edges; if the primitive appears on the surface, a solid primitive is filled in the corresponding parallel surface. At the same time, the corresponding marking of the units in the three situations is completed.
[0033] In the previous traversal, after random growth around each solid, a volume ratio judgment is performed. When the volume ratio reaches CT_V, the core connection part is merged into the solid to participate in the next round of traversal. When the volume reaches O_V, the starting point of the traversal no longer starts from the first solid in container 1, but from O_N. When the volume ratio reaches T_V, the traversal ends. The structure of the rhombic dodecahedron unit and the schematic diagram of the growth of the rhombic dodecahedron are shown in Figure 5 shown.
Claims
1. A random growth method of porous models based on translation filling space, the algorithm features include the following contents: Set parameters such as the model boundary length and primitive side length, nucleation probability C_P, nucleus volume proportion C_V, primitive growth probability G_P, nucleus spacing C_D, connection proportion CT_V, optimization parameter O_V and volume proportion T_V; randomly generate nuclei within the model boundary with the probability of C_P and store them in container 1 until the set nucleus volume proportion reaches C_V; determine the distance between nuclei in the model, if the distance between a nucleus and other nuclei is greater than C_D, delete the nucleus, for the nucleus with the closest distance and less than C_D in the eight areas divided by the three planes XY, YZ and XZ with the nucleus as the origin, use the random shortest path method to generate random shortest connected solids and store them in container 3; traverse the existing solid structure in container 1, with the nucleus as the starting solid structure, determine whether the adjacent space of each surface is solid, if it is solid, skip it, if not, generate new primitives on the surface with a certain probability G_P, and record the current volume N_V of the solid. When a primitive grows on a boundary, a periodic algorithm is used to generate a new primitive based on the corresponding surface, line or vertex on the surface, line or vertex. The existing solid with the new primitive is traversed, judged and generated again for an unlimited number of times until the solid volume reaches the specified volume ratio T_V; in the previous traversal, a volume ratio judgment is performed after each random growth around the solid, and when the volume ratio reaches CT_V, the solid in container 3 is merged into container 1 to participate in subsequent rounds of traversal. When the volume reaches O_V, the starting point of the traversal no longer starts from the first solid in container 1, but from O_N. When the volume ratio reaches T_V, the traversal ends.
2. According to claim 1, the isolated solids which are too far away from other cores and not connected thereto are deleted from the container 1 and no longer participate in the subsequent growth of solid elements.
3. According to claim 1, the solid primitive between two core pairs with a distance less than C_D grows randomly from the starting core to the target core, and the growth direction is the normal direction of the polyhedron surface. If the growth direction is not parallel to the X, Y and Z directions, then when a certain coordinate of the primitive is equal to that of the target core, it grows forward in a fluctuating manner. For example, when the Y coordinate value of the primitive is equal to that of the target core, a movement value in the Y direction is randomly increased or decreased, and the next movement in the Y direction is opposite to the movement direction to ensure that the shortest growth path is achieved.
4. According to claim 1, the internuclear distance and the internuclear ratio jointly construct the number, distribution and connection structure of the solid cores of the porous model, and are also used to generate a porous structure model when the porosity is extremely high.
5. According to claim 1, when the volume ratio reaches CT_V, the solid in container 3 is incorporated into container 1 to participate in subsequent rounds of traversal. The value of CT_V is between C_V and T_V, which is used to adjust and control the thickness of the connected part of the solid, thereby regulating the overall structure of the porous model.
6. According to claim 1, when the volume ratio reaches O_V, only the solids after the O_Nth solid in the container 1 are traversed, and the traversal of the solids whose surface normals are all solid is reduced to improve the solid generation efficiency, O_N=O_V×N_V2 / T_V. If a small amount of gas is mixed in the solids before the O_Nth solid, it is used to simulate the pores left when the pores are closed and no new solid primitives are allowed to be generated.
7. This growth model is used for polyhedral primitives that can fill the entire space by translation alone, including cuboid, hexagonal prism and rhombic dodecahedron primitives, where: The cuboid structure contains not only the geometric structure but also cuboid mesh elements that can be used directly in simulations.