CN114154384A

CN114154384A - Random filling algorithm for spherical particles in three-dimensional cubic space

Info

Publication number: CN114154384A
Application number: CN202111460282.XA
Authority: CN
Inventors: 付远; 邱伊健; 张友亮
Original assignee: Institute of Applied Physics of Jiangxi Academy of Sciences
Current assignee: Institute of Applied Physics of Jiangxi Academy of Sciences
Priority date: 2021-12-03
Filing date: 2021-12-03
Publication date: 2022-03-08

Abstract

The invention provides a structural algorithm for generating random spherical particle filling distribution with a certain volume fraction in a three-dimensional cubic space model. The algorithm can provide a very effective numerical modeling means in the research fields of space environment, deep space exploration, deduction of interplanetary celestial body interaction, geotechnical mechanics, sand storm dynamic analysis and the like. The spatial model generated by the algorithm can benefit the research field from numerical modeling. The algorithm first creates a fixed number of particles with zero volume in a single cube. Each particle has a random velocity vector. The sphere then begins to move, increasing in radius according to the growth law. The objective of the algorithm is to calculate the time at which one of the following events occurs, collision between two spherical particles (algorithm 2) or collision between one spherical particle and at least one cell face (algorithm 3). If two particles collide, their respective new velocities are calculated using the kinetic energy principle (algorithm 4). At the same time, to meet the periodicity requirements of the algorithm, the sphere on one spatial boundary surface is periodically copied to the opposite spatial surface (algorithm 5). And finally, when the volume fraction reaches the expected value, the algorithm is ended.

Description

Random filling algorithm for spherical particles in three-dimensional cubic space

Technical Field

The invention relates to a construction method of a structure model applied to the research fields of space environment, deep space exploration, deduction of interplanetary celestial body interaction, geotechnical mechanics, sand storm dynamic analysis and the like.

Background

Determination of the effectiveness of a spatial structure is a classical solid mechanics problem. The homogenization model uses information about the properties, geometry, and spatial distribution of the constituent phases to estimate or constrain the performance of the spatial structure. The method comprises a self-consistent scheme, a mori-tanaka (mt) model and the like, and the general self-consistent format is provided. Although the predictive capabilities of these models may be implemented numerically by many people. However, to the knowledge of the inventors, no research has focused on performing a systematic and thorough evaluation of existing homogeneous models. Therefore, the microstructure range for which the homogenization model provides a prediction of a given accuracy is not strictly defined. Comprehensive performance assessment requires the establishment of an important database of "accurate" performance. To reduce the investment of modeling, it is significant to develop a robust and fully automated process to build the database.

The main object of the present invention is to propose a fully automatic modeling tool for constructing and verifying a complex homogenization spatial model of randomly distributed spherical particles (fig. 1).

Disclosure of Invention

The algorithm described in the present invention first creates a fixed number of particles with zero volume in a single cube. Each particle has a random velocity vector. The sphere then begins to move, increasing in radius according to the growth law. The objective of the algorithm is to calculate the time at which one of the following events occurs, collision between two spherical particles (algorithm 2) or collision between one spherical particle and at least one cell face (algorithm 3). If two particles collide, their respective new velocities are calculated using the kinetic energy principle (algorithm 4). At the same time, to meet the periodicity requirements of the algorithm, the sphere on one spatial boundary surface is periodically copied to the opposite spatial surface (algorithm 5). And finally, when the volume fraction reaches the expected value, finishing the algorithm of the main program.

Drawings

FIG. 1 shows a particle filling model constructed by the algorithm.

Fig. 2 is a schematic diagram of velocity vector update of two colliding spherical particles.

Figure 3 is a mirror image two-dimensional schematic of a particle.

Detailed Description

Algorithm 1 shows the main routine for invoking algorithms 2-5. In addition, the following paragraphs detail various subroutines. A detailed description is given so that other researchers can replicate the code. In the description of the algorithm, the convention is adopted that symbols with subscripts represent unique physical attributes (e.g., a) of each spherical particle, unless otherwise specified_i) With superscript notation representing physical particle characteristics from one calculation step to another (e.g. R)ⁿ）。

Inter-particle collision detection

The particle collision detection in the algorithm adopts a binary algorithm. Before this algorithm is given, the following description is needed: the collision time t between two particles i and j should satisfy the following equation:

（1）

wherein:

（1a）

(1b)

equation 1 yields a one-dimensional quadratic equation for t, which is of the form:

（2）

wherein:

(2a)

(2b)

（2c）。

algorithm 2 presents the various algorithm steps for determining the time to next collision of two spherical particles.

Detecting collisions of spherical particles with cubic model space walls

The collision time between each spherical particle i and its non-intersecting cubic space must be calculated. The collision time between the spherical particle i and the spatial wall is given by equation 3:

(3)

。

where the sums represent the mth order terms of the vector sum, respectively. The collision time of the particle with the wall of the cubic model space is given in equation 3, where X is the position₁=0,X₂=0 and X₃The planes of =0 correspond to k =1, k =2, and k =3, respectively, and are located at X₁=L,X₂=L,X₃The planes of = L correspond to K =4, K =5, and K =6, respectively. While algorithm 3 gives the steps required to calculate the time for the next collision between the spherical particle and the cubic space wall.

Updating of particle velocity after impact

Fig. 2 shows two colliding spherical particles. Their velocity before impact is divided into two parts, one parallel and one perpendicular to the line connecting their centers. These vertical portions remain during the collision. Under the influence of the rate of increase of the radius of addition, the parallel components are interchanged. And calculating the speed of the ball after collision by adding new parallel components and vertical components. Details of the post-crash velocity solution are given in algorithm 4.

。

Creating periodic mirror images of spherical particles as they collide with cubic model space walls

When a spherical particle i collides with one or more cube model space walls, periodic mirror images of the sphere must be formed on opposite sides of the cube (plane X)₁=0 opposing face X₁= L, plane X₂=0 opposing face X₂= L, plane X₃=0 opposing face X₃= L). The number of periodic spheres depends on the number of faces that intersect the spherical particle i. Each periodic particle has a position vector

And a velocity vector

. Each periodic particle has the same initial velocity as particle i, but its final velocity is offset by a vector. . The values of a, b and c are in the range, and the specific value depends on which surface the spherical particles are mirrored on. The algorithm 5 is specifically described in detail.

。

Periodic mirroring of particles

FIG. 3 shows a mirror image of two particles a and b, with arrow 1 indicating an arbitrary particle a in plane X_iMirror image of =0, arrow 2 indicates that any particle a is in plane X_iMirror image of L, and in order to meet the period boundary conditions, the mirrored images are complementary (both are pieced together to complete the grain image). For the same reason, arrowThe head 3 identifies any particle b in the plane X_jMirror image of =0, arrow 4 indicates arbitrary particle b at plane X_jMirror image of L.

Claims

1. An algorithm for randomly filling spherical particles in a three-dimensional cubic space is characterized in that the algorithm comprises 1-5 steps in total, wherein the algorithm 1 is a main control program which controls the whole operation of the program, and the algorithms 2, 3, 4 and 5 are subprograms in the main program and are used for detecting the collision among the spherical particles, the collision between the spherical particles and the wall surface of the cubic space, the update of the speed and the position state of the spherical particles after the collision and the generation algorithm of the mirror image of the spherical particles on the wall surface.

2. A main control program as claimed in claim 1, characterized in that the algorithm first creates a fixed number of particles with zero volume in a single cube, each particle having a random velocity vector, and then the sphere starts to move with increasing radius according to the growth law; the objective of the algorithm is to calculate the time at which one of the following events occurs: collisions between two spherical particles or between one spherical particle and at least one cell face; if two particles collide, their respective new velocities are calculated using the kinetic energy principle, and, in order to meet the periodic requirements of the algorithm, the sphere on one spatial boundary surface is periodically copied to the opposite spatial surface, and finally when the volume fraction reaches the desired value V^eWhen so, the main program algorithm ends.

3. Algorithm 2 according to claim 1, characterized in that a binary algorithm is used, and the minimum time for the next collision of two spherical particles is calculated and determined.

4. Algorithm 3 in accordance with claim 1, characterized in that the minimum time for collision between a spherical particle and at least one cell face is calculated and determined.

5. Algorithm 4 according to claim 1, characterized in that the velocity update algorithm after collision of spherical particles is determined.

6. Algorithm 5 according to claim 1, characterized in that the mirror image generation algorithm is determined after collision of the spherical particles with the wall surface.