Three-dimensional discrete element modeling and simulation method applicable to the motion and accretion of asteroids in rubble piles

Abstract

A three-dimensional discrete element modeling and simulation method applicable to asteroid motion and accretion is proposed. 1) Establishing a stochastic model: Input the mechanical parameters of asteroid fragments, apply the transformation formula to set the microscopic mechanical parameters of the particles, establish a random particle stacking model based on the geometric parameters, construct a microscopically random and macroscopically isotropic model by adjusting the normal distribution of particle diameter and random stacking, and apply gravity to the particles to make them stack naturally. 2) Establishing a numerical model of a "rubble pile" asteroid: Based on the asteroid's geometric parameters, use the spherical cutting function to obtain the asteroid's physical model, change the fracture force between elements to simulate the van der Waals adhesion effect between asteroid fragments, set the gravitational force between particles, and obtain a "rubble pile" asteroid model with specific geometric dimensions and mechanical properties. 3) Simulating asteroid motion and accretion evolution: Set the asteroid's spin axis and set different spin periods, and complete the simulation of the spin evolution process of the rubble pile asteroid.

Description

Technical Field

[0001] This invention relates to the field of asteroid motion simulation technology, and more specifically to a three-dimensional discrete element modeling and simulation method for the motion and accretion of rubble pile asteroids. Background Technology

[0002] The formation and evolution of the irregular shape and rotation period of boulder pile asteroids have become a hot topic of research for many scholars. However, due to the limitations of theoretical research methods, the dynamic processes between particles are simplified in the analysis, making it difficult to solve the problems of microscopic discreteness and discontinuity in boulder pile asteroids. Model experiments are also costly, time-consuming, difficult, and cannot be directly applied to asteroids. Using computer numerical simulation and other techniques to study the spin evolution of boulder pile asteroids has advantages such as ease of implementation, low cost, high efficiency, and repeatability. With the development of computing technology, particle mechanics simulation is widely used to simulate the orbital evolution of boulder pile asteroids. Among them, "hard sphere interaction" is usually used, which simulates the transmission of force through repeated instantaneous impacts. It cannot accurately describe stable and persistent particle contact, and therefore is not suitable for simulating dense particle flows, and the simulation accuracy is also limited. Discrete element method (DEM) is an effective means to simulate and observe the dynamic evolution of particle aggregates. Establishing a "rubble pile" asteroid model using discrete element method (DEM) suffers from theoretical and implementation complexities. Current models cannot fully address these issues, impacting the simulation of asteroid motion and accretion under complex conditions. Therefore, employing numerical modeling and simulation methods to analyze the motion and structural evolution of asteroids has significant practical implications. Summary of the Invention

[0003] The purpose of this invention is to provide a three-dimensional discrete element modeling and simulation method for the motion and accretion of "rubble pile" asteroids, solving the problems of high cost and long time consumption in model experiments and overcoming the limitations of theoretical research methods. Based on the fundamental principles of discrete element method, a discrete element model of a "rubble pile" asteroid with specific physical and mechanical properties is established and iterative calculations are performed. This method can realistically simulate the spin evolution process of "rubble pile" asteroids and realize the study of the influence mechanism of parameters such as spin period, volume density, and adhesion strength on planetary motion evolution.

[0004] To achieve the above objectives, this invention proposes a modeling and simulation method applicable to the motion and accretion of "rubble pile" asteroids, comprising the following steps:

[0005] (1) Establish a random model: Input the mechanical properties and geometric parameters of the asteroid fragments, establish a three-dimensional hexagonal densely packed square model according to the model and particle size, and apply the conversion formula to set the mechanical parameters of the particles; through the normal distribution of particle diameter adjustment and random stacking, construct a microscopically random and macroscopically isotropic model, apply gravity to the particles to make them stack naturally, and complete the compaction deposition process through gravity compaction, gradually reduce the gravity on the unit, and finally obtain a gravity-free particle random stacking model with specific mechanical properties and structure;

[0006] (2) Establish a "rubble pile" asteroid model with specific mechanical properties: Based on the weightless particle random stacking model established in step (1), according to the asteroid diameter, the asteroid geometric model is cut out using the sphere cutting function. The magnitude of the fracture force between discrete particles is adjusted according to the van der Waals adhesion force effect between particles. Gravitational force is applied to the particles to make the model similar to the mechanical properties of the "rubble pile" asteroid, thus obtaining a "rubble pile" asteroid model with specific size and mechanical properties.

[0007] (3) Simulation of asteroid spin process: Based on the "rubble pile" asteroid model with specific size and mechanical properties established in step (2). To achieve a quasi-static effect, a small angular acceleration is given to the model, gradually accelerating it to the set spin period. The asteroid spin evolution simulation is completed through iterative calculation using the discrete element method. By determining the main axis of rotation and setting the planetary spin period, a refined simulation of the spin evolution process of the "rubble pile" asteroid is achieved. The method of this invention can simulate the asteroid spin evolution process well. Further integration with real asteroid data is beneficial for in-depth and comprehensive exploration of the asteroid spin evolution destruction mechanism.

[0008] The beneficial effects of this invention are as follows: A three-dimensional compacted model with specific mechanical properties can be quickly established using conversion formulas; a "rubble pile" asteroid physical model can be rapidly constructed using a spherical cutting function on the compacted model; interparticle fracture forces and gravitational forces are set to simulate the mechanical interactions between asteroid fragments; and a small angular acceleration is applied to the model, gradually accelerating it to a set spin period to achieve a quasi-static effect. This invention uses discrete particles to construct the model, giving it a particle structure similar to a real "rubble pile" asteroid, which can realistically simulate the spin accretion phenomenon of asteroids. Furthermore, the spin period, adhesion strength, and bulk density can be adjusted within the model to study the influence mechanism of parameters such as spin period, bulk density, and adhesion strength on planetary motion evolution. Attached Figure Description

[0009] Figure 1 A flowchart illustrating the implementation of a three-dimensional discrete element modeling and simulation method for asteroid orbital evolution.

[0010] Figure 2This is a flowchart of the construction process for a zero-gravity isotropic random stacking model.

[0011] Figure 3 Flowchart for the construction and simulation of a numerical model of a rubble-heap asteroid. Detailed Implementation

[0012] To better understand the technical content of the present invention, specific embodiments are described below in conjunction with the accompanying drawings.

[0013] like Figure 1-3 As shown, according to a preferred embodiment of the present invention, a three-dimensional discrete element modeling and simulation method for the motion and accretion of asteroids in a rubble pile includes the following steps:

[0014] (1) Establishing a random model: Input the mechanical properties and geometric parameters of the asteroid fragments, establish a three-dimensional hexagonal close-packed cubic model based on the model and particle size, and apply the conversion formula to set the mechanical parameters of the particles; through adjustment of the normal distribution of particle diameter and random packing, construct a microscopically random and macroscopically isotropic model, apply gravity to the particles to allow them to pack naturally, and complete the compaction deposition process through gravity compaction, gradually reducing the gravity on the unit, and finally obtaining a gravity-free random particle packing model with specific mechanical properties and structure; such as Figure 1 The second image illustrates this; this example is a cube, the asteroid has a diameter of 1200m, and the cube's dimensions are 2000m.

[0015] (2) Establishing a "rubble pile" asteroid model with specific mechanical properties: Based on the overall isotropic random model established in step (1), the asteroid's geometric model is cut out using a spherical cutting function according to the asteroid's diameter (the spherical model in step 31, see step 31). Figure 1 (Figure 3) The magnitude of the fracture force between discrete particles is adjusted according to the van der Waals adhesion effect of asteroid fragments, and gravity is applied to the discrete particles to make the model similar to the mechanical properties of a "rubble pile" asteroid; thus, a "rubble pile" asteroid model with specific size and mechanical properties is obtained.

[0016] (3) Simulation of asteroid spin process: Based on the "rubble pile" asteroid model with specific size and mechanical properties established in step (2). To achieve a quasi-static effect, a small angular acceleration is given to the model, which is gradually accelerated to the set spin period. The asteroid spin evolution simulation is completed by iterative calculation using the discrete element method. Same as step 36, step 37 is the data extraction process;

[0017] refer to Figure 2 As shown, the implementation process of establishing the stochastic model in step (1) is as follows:

[0018] Step 20: Input the geometric parameters of the model and the physical and mechanical parameters of the asteroid fragments; as shown in the table below:

[0019]

[0020] Step 21: Establish a random stacking model based on the geometric parameters of the input model;

[0021] Step 22: Substitute the average mechanical parameters of the asteroid fragments into the conversion formula to obtain the corresponding interparticle mechanical parameters and set the bulk density of the particles; same as step 20.

[0022] Step 23: Let the average particle diameter be d, generate a normal distribution random array with a mean of 1, denoted as f(1), and adjust the particle diameter as: D1 = d * f(1). The standard deviation of the normal distribution array is determined according to the gradation requirements of the crushed stone, and is between 0.1 and 0.5. After the normal distribution operation, the total particle volume increases;

[0023] Step 24: Adjust the particle diameter by correcting the diameter D2: D2 = D1 / mean(f(1)) 3 ) 1 / 3 This ensures that the total volume of the particles remains constant; the mean in the formula is the average value.

[0024] Step 25: Reduce the particle diameter to increase the mobility of the particles and the entire system, with a reduction ratio between 1.2 and 1.5;

[0025] Step 26: Assign a random initial velocity to the particles. The maximum particle velocity shall not exceed maxV = 0.01·d / dT, where dT is the simulation time step, determined by the particle mass (M). p ) and normal stiffness coefficient (K) n Determine: dT = 0.02π·sqrt(M) p / K n );

[0026] Step 27: Restore the particle diameter to the original size D2, apply gravity to the particles to allow them to accumulate naturally, and complete the compaction deposition process.

[0027] Step 28: Gradually reduce the gravity acting on the unit. A total of five gravity reduction steps were performed, with each step reducing the unit's gravity by 1 / 5. The calculation was iterated 200 times until the gravity acting on the particles in the stacked model was reduced to 0. Iterative calculation is a fundamental calculation in discrete element method (DEM) computation. Iterative calculation refers to the iterative cycle of [force -> acceleration -> velocity -> particle displacement].

[0028] In step 22, the average mechanical parameters of the asteroid fragments are substituted into the conversion formula to obtain the corresponding inter-particle mechanical parameters and the particle bulk density is set. The unit model and conversion formula in this embodiment are as follows: the model particle units consider both positive and tangential forces, determined by five parameters: the positive stiffness coefficient (K...n ), Tangential stiffness coefficient (K) s ), interparticle failure displacement (X) b ), interparticle shear strength (Fs0) and interparticle friction coefficient (μ) p A three-dimensional discrete element model was established based on the average mechanical parameters of asteroid fragments, including five macroscopic mechanical parameters: Young's modulus (E), Poisson's ratio (v), tensile strength (T), etc. u ), compressive strength (C) u ) and friction coefficient (μ i The mechanical parameters between particles are determined by the following conversion formula:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] In the formula, d represents the particle diameter; the three-dimensional closely packed discrete element model established by this formula possesses specific mechanical properties. I is an intermediate variable, calculated based on the macroscopic friction coefficient, and then the interparticle friction coefficient is calculated based on I.

[0035] Next, refer to Figure 3 The illustrated process for constructing a specific-sized "rubble pile" asteroid model is based on... Figure 2 The established stochastic model is implemented as follows:

[0036] Step 31: Use the function cutSphereObj to cut out a sphere with a diameter of 1.2km from the random stacking model established in step (1); that is, the sphere cutting function in (2) cuts out the asteroid geometric model.

[0037] Step 32: Set the fracture force between units to simulate this adhesion force and introduce an adhesion coefficient c to represent the adhesion strength between asteroid particles. In the numerical simulation, the fracture force of the unit is multiplied by c to characterize the adhesion force. In this embodiment, c is taken as 1.

[0038] Step 33: Add inter-unit gravitational force to the particle, the gravitational force F of unit t. t Determined according to the following formula:

[0039]

[0040] Where G is the gravitational constant, with a value of 6.67 × 10⁻⁶.-11 N·m 2 ·kg 2 m i m t For the masses of elements i and t, r it This represents the distance between the two units.

[0041] Step 34: Establish a cubic frame with a side length of 10km centered on the model. When the particles fly beyond this distance, motion calculations will no longer be performed.

[0042] Steps 35-36 are for setting the running parameters of the model.

[0043] Step 35: Move the asteroid's center of mass to the origin of the coordinate system, and set the z-axis as the spin axis so that it spins around the principal axis;

[0044] Step 36: To achieve a quasi-static effect while setting the asteroid spin period, the particle angular acceleration is set to 8.73 × 10⁻⁶. -5 rad·s -1 It continues to accelerate until the simulation time reaches 35,000 seconds.

[0045] Step 37: Output simulation snapshots at different iteration times, and compare the changes in asteroid geometric and physical parameters such as the semi-axis length under different models to reveal the spin simulation patterns of the asteroid. For ease of explanation, only the physical quantity of the semi-axis length is listed for explanation, along with its formula:

[0046]

[0047]

[0048]

[0049] Where a, b, and c are the semi-axis lengths in different directions; X, Y, and Z are the particle coordinate arrays.

[0050] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Those skilled in the art can make various modifications and refinements without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention shall be determined by the claims.

Claims

1. A three-dimensional discrete element modeling and simulation method suitable for asteroid motion and accretion, characterized in that, Includes the following steps: (1) Establish a random model: Input the mechanical parameters of the asteroid fragments, apply the conversion formula to set the micromechanical parameters of the particles, establish a random particle stacking model based on the geometric parameters, construct a micro-random and macro-isotropic model by adjusting the normal distribution of particle diameter and random stacking, apply gravity to the particles to make them stack naturally, complete the compaction deposition process through gravity compaction, gradually reduce the gravity on the unit, and finally obtain a gravity-free random particle stacking model with specific mechanical properties and structure; (2) Establish a numerical model of a "rubble pile" asteroid: Based on the weightless random stacking model established in step (1), according to the asteroid's geometric parameters, the physical model of the asteroid is obtained by using the sphere cutting function. The fracture force between units is changed to simulate the van der Waals adhesion effect between asteroid fragments. The gravitational force between particles is set so that the mechanical properties of the model are similar to those of the asteroid, and a "rubble pile" asteroid model with specific geometric dimensions and mechanical properties is obtained. (3) Simulate asteroid motion and accretion evolution: Based on the "rubble pile" asteroid model with specific geometric dimensions and mechanical properties established in step (2), set the asteroid spin axis and set different spin periods, and simulate the spin evolution process of the "rubble pile" asteroid through iterative calculation using the discrete element method; The specific steps for establishing the random stacking model in step (1) are as follows: Step 20: Input the geometric parameters of the model and the physical and mechanical parameters of the asteroid fragments; Step 21: Establish a random stacking model based on the geometric parameters of the input model; Step 22: Substitute the average mechanical parameters of the asteroid fragments into the conversion formula to obtain the corresponding interparticle mechanical parameters and set the bulk density of the particles; Step 23: Adjust the particle diameter to match the original set diameter. d The mean is 0.1, and the distribution follows a normal pattern. The standard deviation of the normal distribution is determined according to the gradation requirements of the crushed stone, and is between 0.1 and 0.

5. d Between these points, after the normal distribution operation, the total particle volume increases; Step 24: Adjust the particle diameter by correcting the diameter: D 2= D 1 / mean( f (1) 3 ) 1 / 3 This ensures that the total volume of the particles remains unchanged. Step 25: Reduce the particle diameter to increase the mobility of the particles and the entire system, with a reduction ratio between 1.2 and 1.5; Step 26: Assign a random initial velocity to the particles, with the maximum particle velocity not exceeding [the specified value]. maxV =0.01 ·d / dT , in dT To simulate the time step, the particle mass is used. M p and positive stiffness coefficient K n Sure: dT =0.02π · sqrt( M p / K n ); Step 27: Restore the particle diameter d to its original size. D 2. Gravity is applied to the particles to allow them to accumulate naturally; finally, two gravity compaction processes are applied to complete the compaction and deposition process. Step 28: Gradually reduce the gravity acting on the unit; A total of five gravity reduction steps were performed, with each step reducing the unit gravity by 1 / 5 and iterating 200 times to reduce the gravity on the particles of the stacked model to 0. The conversion formula in step (1) is as follows: The model particle units are considered to have both positive and tangential forces, determined by five parameters: positive stiffness coefficient... K n Tangential stiffness coefficient K s Interparticle failure displacement X b Interparticle shear strength Fs 0 and interparticle friction coefficient μ p A three-dimensional discrete element model was established based on the average mechanical parameters of shale, including five macroscopic mechanical parameters: Young's modulus. E Poisson's ratio v ,tensile strength T u Compressive strength C u and coefficient of friction μ i , The implementation steps for establishing the numerical model and simulation of the rubble pile asteroid in steps (2) and (3) are as follows: Step 31: Use the sphere cutting function cutSphereObj to cut out the asteroid geometric model from the weightless random stacking model established in step (1); Step 32: Set the fracture force between units and introduce the adhesion coefficient c to simulate the van der Waals adhesion force between asteroid fragments; Step 33: Set up the gravitational force between units; Step 34: Establish a virtual cubic frame centered on the Earth model. Once a particle flies out of this frame, no further calculations will be performed on the particle. Step 35: Move the asteroid's center of mass to the origin of the coordinate system, and set the z-axis as the spin axis so that it spins around the principal axis; Step 36: To achieve a quasi-static effect, the asteroid model is accelerated to rotate in the form of angular acceleration until it reaches the preset spin period; Step 37: Through continuous iterative calculations, detect the changes in asteroid half-axis length, average filling rate, and average spin velocity under different spin periods, iteration times, volume densities, and adhesion strengths; Step 38: Output the simulation results of the asteroid spin evolution destruction of the rubble pile.

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