Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect
Abstract
:1. Introduction
2. Materials and Methods
2.1. Polyhedron Particle Generation Algorithm
2.2. Particle Abrasion Method
- 1.
- Calculate the new face point, noted as f-point, which is the average of all vertex positions of the defined face, according to Equation (4).
- 2.
- Calculate the new edge point, denoted as e-point, defined as the average of the two endpoints of the edge and the two f-points of the face sharing the edge, according to Equation (5).
- 3.
- Calculate the new vertex point, denoted as v1 point, defined as the vertex generated for each interior vertex of a given mesh; the new vertex is a linear combination of adjacent face points, adjacent edge midpoints, and vertices, calculated according to the equation:
2.3. Particle Shape Quantification
3. Numerical Simulations
3.1. Sample Preparation
3.2. Conventional Triaxial Test
4. Macroscopic Mechanical Response
4.1. Deviatoric Stress and Strain
4.2. Strength and Deformation
5. Meso Shear Properties
5.1. Coordination Number
5.2. Internal Sliding and Rotation
5.3. Fabric Anisotropy
- (1)
- Anisotropy evaluation method
- (2)
- Evolution of anisotropy
- (3)
- Stress–Force–Fabric relationship
6. Results
- A modeling method of randomly convex polyhedron particles was established. In addition, a method of generating different degrees of abrasion of the particles based on the corners and edges of the particles and the relative positions of the surfaces was established, which better reflects the abrasion process of the particles in their natural state. According to the results of the roundness index S3d, the particles have higher sphericity after abrasion. The particle abrasion function is derived from graphical and fundamental mechanical principles. However, it is necessary to couple it with the flow field to obtain a more detailed understanding of the particle abrasion mechanics.
- The macroscopic mechanical behavior of cohesionless granular materials is reproduced using traditional triaxial tests, including the nonlinear stress–strain relationship and dilatancy. With an increase in the degree of particle abrasion, the stiffness and macro shear strength of the material decrease, and the bulging deformation of the material is also restrained.
- The granular aggregate with a higher degree of abrasion has lower structural stability, a quicker decline in coordination number, and a lower average coordination number when achieving stability, according to microscopic analysis. At the initial loading stage, the granular material with a higher abrasion degree is more susceptible to relative rotation, while the granular aggregate with a lower abrasion degree is more susceptible to relative sliding. These micro mechanical phenomena can, to a certain extent, reveal the macro mechanical characteristics of granular materials.
- The major contribution to fabric anisotropy comes from normal contact force anisotropy, which is followed by contact normal anisotropy. The results of the S-F-F relationship for the four materials demonstrate that there is a good correspondence between the macro mechanical properties and the micro fabric of the materials and that this correspondence is independent of the particle abrasion level. The abrasion level has an inverse relationship with each fabric’s parameters. The additional constraint of the rubber mold will cause the internal friction angle of granular materials obtained from conventional triaxial tests to be overestimated even if the friction constraint between the particles and boundary is not taken into consideration.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Value |
---|---|
Particle density, ρ (kg/m3) | 2600 |
Particle coefficient of friction, μc | 0.5 |
Boundary–particle friction μb | 0.0 |
Particle normal stiffness, kn (N/m) | 1 × 108 |
Particle tangential stiffness, ks (N/m) | 5 × 107 |
Damping coefficient, dp | 0.3 |
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Hu, Z.; Zhang, J.; Tan, X.; Yang, H. Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect. Materials 2024, 17, 3947. https://doi.org/10.3390/ma17163947
Hu Z, Zhang J, Tan X, Yang H. Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect. Materials. 2024; 17(16):3947. https://doi.org/10.3390/ma17163947
Chicago/Turabian StyleHu, Zhengbo, Junhui Zhang, Xin Tan, and Hao Yang. 2024. "Modeling of the Particle Abrasion Process and a Discrete Element Method Study of Its Shape Effect" Materials 17, no. 16: 3947. https://doi.org/10.3390/ma17163947