A method and device for simulating the crushing of irregularly shaped particles

Abstract

A method and apparatus for simulating the crushing of irregularly shaped particles includes: generating an aggregate of irregularly shaped polyhedral particles and assigning initial strength attributes to each polyhedral particle; identifying potentially crushed polyhedral particles and labeling them as potentially integrally crushed and angularly crushed particles; identifying polyhedral particles about to break and labeling them as integrally crushed and angularly crushed particles; cutting and crushing the labeled integrally crushed and angularly crushed particles, and assigning initial strength attributes to the newly formed polyhedral sub-particles. Compared to traditional particle crushing simulation methods, the present invention not only simulates the crushing of irregularly shaped particles, but also allows the sub-particles to be crushed again. Its computational efficiency is far superior to traditional crushing simulation methods, and this crushing simulation method provides an effective technical means for further understanding the micromechanical mechanisms of particle crushing and the macromechanical behavior of crushable granular materials.

Description

Technical Field

[0001] The present invention relates to the technical field of particle crushing numerical simulation, and in particular to a method and device for simulating the crushing of irregularly shaped particles. Background Art

[0002] Granular materials have been widely used in geotechnical engineering fields such as roadbeds and ballasted roadbeds due to their affordability and ease of maintenance. However, when subjected to loads, particles may break, which not only changes the distribution of particles but also affects the overall mechanical properties of the material. Due to its unique advantages, discrete element methods are widely used in simulating the crushing of bulk materials. The existing particle crushing methods mainly include the replacement method and the bonded particle method. The replacement method is currently mainly used to simulate spherical particles and is not suitable for the crushing simulation of irregularly shaped particles. Although the bonded particle method is suitable for the crushing simulation of irregularly shaped particles, its sub-particles cannot be crushed again and the computational complexity is large. Therefore, it is necessary to establish an efficient simulation method for the crushing of irregularly shaped particles. Summary of the Invention

[0003] In order to solve the defects in the prior art, the present invention discloses a method for simulating the crushing of irregularly shaped particles, and its technical solution is as follows:

[0004] S1, generating irregular polyhedral particle aggregates and assigning initial strength attributes to each polyhedron;

[0005] S2, identifying potentially broken polyhedral particles and labeling them as potentially integrally broken and angularly broken particles;

[0006] S3, identifying polyhedral particles that are about to break and labeling them as overall broken and angular broken particles;

[0007] S4, performing cutting and crushing on the marked overall crushed and angular crushed particles, and assigning initial strength attributes to the newly formed polyhedral sub-particles.

[0008] Beneficial effects

[0009] (1) Particle crushing is divided into overall particle crushing and particle edge crushing. Particle crushing is achieved based on the particle cutting method, which can more realistically simulate the crushing problem of granular materials.

[0010] (2) The broken particles can be irregular in shape, and there is no overlap between the sub-particles formed after cutting, which will not cause calculation anomalies. The formed sub-particles can also be broken again, and the calculation efficiency is high. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A diagram of a polyhedral particle assembly according to the present invention;

[0012] Figure 2Figure 1 shows the particles of the present invention that are labeled as potentially broken overall and angularly broken;

[0013] Figure 3 Figure 1 shows the particles of the present invention labeled as overall crushing and angular crushing;

[0014] Figure 4 Schematic diagram of overall crushing and angular crushing cutting of the present invention;

[0015] Figure 5 This is a diagram of sub-particles formed after crushing according to the present invention;

[0016] Figure 6 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0017] A method for simulating the crushing of irregularly shaped particles, comprising the steps of:

[0018] S1: Generate irregular polyhedral particle aggregates. Based on the particle size range of the indoor test sample, generate multiple irregular polyhedral particle models that are consistent with the particle size range of the indoor test sample. Then, assign the overall crushing strength and angular crushing strength to the particles using equations (1) and (2), respectively.

[0019] E p0 =σ r d c (-ln(1-U(0,1))) 1 / m (1)

[0020] F0=σ r1 d -c1 (-ln(1-U(0,1))) 1 / m (2)

[0021] Where: σ r is the overall crushing characteristic energy value and c is the overall crushing effect parameter; d is the particle diameter; m is the Weibull modulus; U(0,1) is a random number uniformly distributed in the interval 0-1; σ r1 is the characteristic intensity of angular crushing and c1 is the angular crushing effect parameter.

[0022] S2, identify the potentially broken polyhedral particles and mark them as potential overall broken and angular broken particles. Every 200 steps, all polyhedral particles are traversed, and the shape change strain energy Eq of each polyhedral particle is calculated by formula (3), and the volume change strain energy Ep of each polyhedral particle is calculated by formula (4). At the same time, all contact forces F on each polyhedron are obtained through the built-in algorithm of the software. i .

[0023]

[0024] Where: σ1, σ2, and σ3 are the maximum, intermediate, and minimum principal stresses of the particle, respectively; V is the particle volume; v is the Poisson's ratio of the material; E is the elastic modulus of the material; and G is the shear modulus of the material.

[0025] Substitute the Eq and Ep of each polyhedral particle into formula (5). If formula (5) is satisfied, the polyhedral particle is marked as a potential integrally broken particle. For polyhedral particles that do not satisfy formula (5), compare whether there is a contact force F greater than 0.9 times the self-edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle mass center is greater than the particle equivalent radius R. equ (R equ The radius of the spherical particle with the same volume as the irregular particle), as shown in formula (6), will mark the particle as a potential angular broken particle.

[0026]

[0027] F>0.9·F0 and dis>R equ (6)

[0028] Where: f d is the contact surface curvature coefficient; a and b are the crushing parameters; dis is the distance between the coordinate point of the contact force and the particle mass center; R equ is the equivalent radius of the particle.

[0029] S3, identify the polyhedron particles that are about to break and mark them as overall broken and angular broken particles. Calculate again for 200 steps, traverse the particles marked as potential overall broken and angular broken particles, calculate the shape change strain energy Eq of each polyhedron particle by formula (3), calculate the volume change strain energy Ep of each polyhedron particle by formula (4), and obtain all contact forces F on each polyhedron through the built-in algorithm of the software i , substitute Eq and Ep marked as potential overall broken particles and angular broken particles into formula (7). If formula (7) is satisfied, the polyhedron particle is marked as an overall broken particle, and the maximum contact force F of the particle is recorded. max For polyhedral particles that do not satisfy formula (7), compare whether there is a contact force F greater than its own edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle mass center is greater than R equ , as shown in formula (8), the particle is marked as an angular broken particle, and the contact force F and the particle long axis direction n are recorded. la .

[0030]

[0031] F>F0 and dis>R equ (8)

[0032] After all the particles marked as potential overall broken particles and angular broken particles have been traversed, all the labels of potential overall broken particles and angular broken particles are cleared.

[0033] S4, perform cutting and crushing on the marked overall crushed and angular crushed particles, and assign initial strength attributes to the newly formed polyhedron sub-particles. Traverse the particles marked as overall crushed particles in sequence, first perform the first cutting on the particles, and the normal vector n of the first cutting plane is n = σ1 × F max , and the cutting point passes through F max After the first cut, if the particle has n remaining particles greater than 0.5·F max The contact force F i (Except F max The particle will be cut n times later, and the normal vector n of the cutting plane i =F i ×(P0-P i ), where P0 is the coordinate of the particle's center of mass, P i is the contact force F i The particles marked as angular broken particles are traversed in sequence, and the particles are cut into angular broken pieces. The normal vector of the cutting plane is the direction of the long axis of the particle n. la The initial strength properties are assigned to the sub-particles formed by overall crushing and angular crushing cutting, and the overall crushing strength E p0 As shown in formula (1), the angular crushing strength F0 is shown in formula (2). Clear all labels of overall crushed and angular crushed particles. Stop loading when the preset calculation termination condition is reached.

[0034] Example

[0035] A first aspect of the present invention provides a method for simulating the crushing of irregularly shaped particles. Specifically, the method comprises:

[0036] Step S1: Generate an irregularly shaped polyhedron particle aggregate and assign an initial strength attribute to each polyhedron.

[0037] Specifically, a cylindrical wall is first generated in the discrete element particle flow (PFC) software, and then polyhedral particles are generated inside the rectangular wall. Then, the iterative cycle is repeated until the unbalanced stress ratio is less than 1e-5, so that the overlap between particles is fully rebounded. Then, the overall crushing strength and angular crushing strength are assigned to each particle using equations (1) and (2). Finally, a loading plate is generated on the topmost particle, and the final model is as follows: Figure 1 shown.

[0038] Step S2: Identify potentially broken polyhedral particles and mark them as potentially broken overall and broken corner particles.

[0039] Specifically, 200 steps are calculated to traverse all polyhedral particles. The shape change strain energy Eq of each polyhedral particle is calculated by formula (3), and the volume change strain energy Ep of each polyhedral particle is calculated by formula (4). At the same time, all contact forces F on each polyhedron are obtained through the built-in algorithm of the software. i Substitute the Eq and Ep of each polyhedral particle into formula (5). If formula (5) is satisfied, the polyhedral particle is marked as a potential integrally broken particle. For polyhedral particles that do not satisfy formula (5), compare whether there is a contact force F greater than 0.9 times the self-edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle center of mass is greater than the particle equivalent radius R. equ (R equ The radius of the spherical particle with the same volume as the irregular particle) is shown in formula (6), and the particle is marked as a potential angular broken particle, such as Figure 2 .

[0040] Step S3: identifying polyhedral particles that are about to be broken and marking them as whole-broken particles and angular-broken particles.

[0041] Calculate again for 200 steps, traverse the particles marked as potential overall broken particles and angular broken particles, calculate the shape change strain energy Eq of each polyhedron particle by formula (3), calculate the volume change strain energy Ep of each polyhedron particle by formula (4), and obtain all contact forces F on each polyhedron by the built-in algorithm of the software i , substitute Eq and Ep marked as potential overall broken particles and angular broken particles into formula (7). If formula (7) is satisfied, the polyhedron particle is marked as an overall broken particle, and the maximum contact force F of the particle is recorded. max For polyhedral particles that do not satisfy formula (7), compare whether there is a contact force F greater than its own edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle mass center is greater than R equ , as shown in formula (8), the particle is marked as an angular broken particle, and the contact force F and the particle long axis direction n are recorded. la ,like Figure 3 After all the particles marked as potential overall broken particles and angular broken particles have been traversed, all the labels of potential overall broken particles and angular broken particles are cleared.

[0042] Step S4: Cut and crush the marked overall crushed and angular crushed particles, and assign initial strength attributes to the newly formed polyhedron sub-particles. Traverse the particles marked as overall crushed particles in sequence, and first cut the particles for the first time. The normal vector n of the first cutting plane is n = σ1 × F max , and the cutting point passes through Fmax After the first cut, if the particle has n remaining particles greater than 0.5·F max The contact force F i (Except F max The particle will be cut n times later, and the normal vector n of the cutting plane i =F i ×(P0-P i ), where P0 is the coordinate of the particle's center of mass, P i is the contact force F i The particles marked as angular broken particles are traversed in sequence, and the particles are cut into angular broken pieces. The normal vector of the cutting plane is the direction of the long axis of the particle n. la ,like Figure 4 The initial strength properties are assigned to the sub-particles formed by overall crushing and angular crushing cutting, and the overall crushing strength E p0 As shown in formula (1), the angular crushing strength F0 is shown in formula (2). Clear all labels of overall broken and angular broken particles. Stop loading when the preset calculation termination condition is reached. The sub-particles formed after the final crushing are as follows Figure 5 .

[0043] The method presented in this paper addresses the issues of conventional particle crushing simulation methods, which restrict the crushed particles to spherical shapes, prevent the subsequent fragmentation of fragments, and impose high computational complexity. Compared to conventional particle crushing simulation methods, this method not only simulates the crushing of irregularly shaped particles but also allows for the fragmentation of fragments. Its computational efficiency is significantly higher than that of conventional particle crushing simulation methods, providing an effective technical means for further understanding the micromechanical mechanisms of particle crushing and the macromechanical behavior of crushable granular materials.

[0044] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions merely illustrate the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for simulating the crushing of irregularly shaped particles, characterized by: S1, generating an aggregate of irregular-shaped polyhedral particles and assigning initial strength properties to each irregular-shaped polyhedral particle; The initial strength properties are divided into overall crushing strength and angular crushing strength, that is, each particle has two strengths; the overall crushing strength E p0 As shown in formula (1), the edge crushing strength F0 is shown in formula (2): E p0 σ r d c (-ln(1-U(0,1))) 1 / m (1) F0=σ r1 the -c1 (-ln(1-U(0,1))) 1 / m (2) σ r is the overall crushing characteristic energy value and c is the overall crushing effect parameter; d is the particle diameter; m is the Weibull modulus; U(0,1) is a random number uniformly distributed in the interval 0-1; σ r1 is the characteristic intensity of angular crushing and c1 is the parameter of angular crushing effect; S2, identify potentially broken polyhedral particles and mark them as potentially broken overall and angular particles: S2-1, every 200 calculation steps, traverse all polyhedral particles, calculate the shape change strain energy Eq of each polyhedral particle by formula (3), calculate the volume change strain energy Ep of each polyhedral particle by formula (4), and obtain all contact forces F on each polyhedron through the built-in algorithm of the software i ; σ1, σ2, σ3 are the maximum, intermediate, and minimum principal stresses of the particle; V is the particle volume; v is the Poisson's ratio of the material; E is the elastic modulus of the material; G is the shear modulus of the material; S2-2, substitute the Eq and Ep of each polyhedral particle into (5). If they meet the requirements, the polyhedral particle is marked as a potential overall crushing particle. For polyhedral particles that do not meet the requirements of Eq (5), compare whether there is a contact force F greater than 0.9 times the self-edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle center of mass is greater than the particle equivalent radius R. equ , the R equ The radius of the spherical particle with the same volume as the irregular particle is marked as a potential angular broken particle; and E p ≥0.9·f d ·E p0 (5) F>0.9·F0 and dis>R equ (6) f d is the contact surface curvature coefficient, a and b are the crushing parameters; dis is the distance between the coordinate point of the contact force and the particle mass center, R equ is the particle equivalent radius; S3, identifying polyhedral particles that are about to break and marking them as overall broken and angular broken particles; S4, performing cutting and crushing on the marked overall crushed and angular crushed particles, and assigning initial strength attributes to the newly formed polyhedral sub-particles.

2. The irregular-shaped particle crushing simulation method according to claim 1 is characterized in that the S1 step further includes the following content: based on the particle size range of the indoor test sample, generating multiple irregular polyhedron particle models that are consistent with the particle size range of the indoor test sample.

3. The irregular-shaped particle crushing simulation method according to claim 1, wherein, in step S3, identifying the polyhedral particles to be crushed comprises the following steps: S3-1, calculate again for 200 steps, traverse the particles marked as potential overall broken particles and angular broken particles, calculate the shape change strain energy Eq of each polyhedron particle by formula (3), calculate the volume change strain energy Ep of each polyhedron particle by formula (4), and at the same time obtain all contact forces F on each polyhedron through the built-in algorithm of the software i ; S3-2, substitute the Eq and Ep of the particles marked as potential overall broken particles and angular broken particles into formula (7). If formula (7) is satisfied, the polyhedron particle is marked as an overall broken particle, and the maximum contact force F of the particle is recorded. max For polyhedral particles that do not satisfy formula (7), compare whether there is a contact force F greater than its own edge crushing strength F0, and whether the distance dis between the coordinate point of the contact force F and the particle mass center is greater than R equ , as shown in formula (8), the particle is marked as an angular broken particle, and the contact force F and the particle long axis direction n are recorded. la ; Japanese E p ≥f d E p0 (7) F>F0 and dis>R equ (8) S3-3, after all the particles marked as potential overall broken particles and angular broken particles have completed the operation of S3-2, clear all the labels of the potential overall broken particles and angular broken particles.

4. The irregular-shaped particle crushing simulation method according to claim 3, wherein in step S4, the cutting and crushing of the marked integrally crushed and angularly crushed particles comprises the following steps: S4-1, traverse the particles marked as whole broken particles in turn, first cut the particles for the first time, the normal vector of the first cutting plane is n = σ1 × F max , and the cutting point passes through F max Coordinate point; after the first cutting, if the particle has n remaining particles greater than 0.5·F max The contact force F i , except F max In addition, the particle will be cut n times later, and the normal vector n of the cutting plane i =F i ×(P0-P i ), where P0 is the coordinate of the particle's center of mass, P i is the contact force F i coordinates of S4-2, traverse the particles marked as angular broken particles in turn, and perform angular broken cutting on the particles. The normal vector of the cutting plane is the direction of the long axis of the particle n la ; S4-3, after completing the operations of S4-1 and S4-2, assign initial strength attributes to the sub-particles formed by overall crushing and angular crushing cutting, and the overall crushing strength E p0 As shown in formula (1), the angular crushing strength F0 is shown in formula (2), clearing all labels of overall broken and angular broken particles; S4-4, continue calculation, call S2-1 to S4-3 at the same time, and stop loading when the loading meets the termination condition.

5. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is executed, the device where the non-volatile storage medium is located is controlled to execute the method according to any one of claims 1 to 4.

6. An electronic device, characterized in that: The method comprises a processor and a memory; the memory stores computer-readable instructions, and the processor is used to execute the computer-readable instructions, wherein the computer-readable instructions execute the method according to any one of claims 1 to 4 when executed.

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