All granular systems, irrespective of whether conventional solid or a fluid matter, exhibit different properties because of the presence of particulate matter in the parallel plate of the granular flow frictional system. The shearing interface of the particulate matter with a granular media significantly affects many natural events and engineering applications, such as crustal movement, mud-rock flow, ore-rock crushing, grain processing, three-body friction, and abrasive flow machining [
]. The force chain networks produced by the granular systems under external load affect the movement and granular flow of the frictional systems, thereby affecting the quality of abrasive flow machining. This has attracted the attention of scholars globally.
The concept of particulate matter was proposed by French scientist Gennes, who is a 1991 Nobel laureate. In general, it refers to a large number of discrete particles forming a system, in which the particle size ranges between 1 μm and 2 μm [
]. According to the sparse degree of particle arrangement, a particle system can be divided into particle gas, particle fluid, and particle solid; the latter two belong to the dense particulate matter systems.
Bouchaud et al. [
] introduced the concept of force chains. The adjacent granules squeeze one another to form different force chain strengths under gravity or an external load. A force chain is the path on which the force passes along the granular contact network, while a contact network, in which some contact deformations are large and connected into a quasi-linear system, passes a significant force of gravity or a significant number of external loads to form strong force chains. The weak force chains are formed because of the weak contact deformation among granules and low external force. The strong force chains can bear load, and the direction of the weak force chains is perpendicular to the direction of the strong force chains to support the strong force chains and prevent breaking. However, changing the occlusion among granules enables the weak force chains to bear the load. The external load borne by the system is transmitted through the force chain network. The force chain network is formed by an external load acting on the particles that squeeze each other in the granular system. The force chains are extremely sensitive to changes in external load and geometric characteristics of the granular system. A slight change in the external load causes a large variation in the force chains of the same granular system [
]. Along with the formation of force chains, the geometric transition in force chain connectivity is also observed. The spatial distribution of force chains in the shear band exhibits two dominant length scales, i.e., force chains are separated by lateral support, on an average, by one particle diameter in one direction and two particle diameters in a second direction [
]. Gendelman et al. [
] presented a new formalism that employed the knowledge of the external forces and the orientations of contacts between particles (of any given size), to compute all interparticle forces. Using a geographical null model constrained by the particles’ contact network, Bassett et al. [
] extracted chain-like structures, which were the reminiscent of force chains, and proposed three diagnostics to measure these chain-like structures.
It is difficult to provide an exact description of the force chains because of the complex disordered characteristics of the internal force chains in the granular system. Many researchers use different methods to analyze force chains under different conditions. Force chains were observed to play an important role in the microstructure of granular materials. In statics, the buckling of force chains is mainly located inside the shear band [
]. The International Fine Powder Research Institute (IFPRI) had funded an extensive research on dry powder and granular flows, especially dense flows at relatively high shear rates, in which the effect of force chains and jamming interactions were investigated considering the flow, stress and packing dynamics [
]. Besides, some researchers analyzed granular flows using simulation methods. Guo and Curtis [
] focused on the modeling of complex granular flows employing the discrete element method (DEM) approach, where the DEM models were applied to study the flow behavior of aspherical, flexible, or cohesive particles, including particle breakage. Azéma and Radjai [
] analyzed inertial granular flows and observed that contact anisotropy, force chain anisotropy, and friction mobilization were related to contact network and force transmission. Booth et al. [
] proposed that a continuum of friction angles existed between single-grain and bulk friction angles due to the grain-to-grain force chains. Marteau and Andrade [
] measured the force chains in opaque granular matter under shear using digital image correlation (DIC) and granular element method (GEM) to understand the micromechanical response of a complex granular assembly applied to macroscopic strains and stresses. Nicot et al. [
] highlighted the crucial interplay between force chains and adjoining clustered structures (grain clusters in three-dimensional (3D) conditions and grain loops in two-dimensional (2D) conditions). Further, to have a better understanding of force transition and stability mechanism of granular materials on mesoscale, a series of photoelastic experiments were conducted. The formation and evolution of force chains in the particle flow processes were also observed [
A traditional fluid theory cannot be applied to granules because of the complex nature of granular matter. However, a force chain reflects the internal evolution of the granules under external conditions on mesoscale. The evolution of granular matter in a granular flow frictional system can be explored through the study of the mesoscale force chains, and the evolution of granules can be described from a new aspect based on the simulation advantages of the DEM or finite element method (FEM) models. Tordesillas et al. [
] observed that the stability of force chains was highly correlated with the strength and volume properties of the granular material. The buckling of force chains resulted in noninterference and formation of shear bands in the granular material. Moreover, the mechanical response of dense granular materials indented through the rigid flat punch was closely related to the force chains and the surrounding particle clusters based on the subsequent studies. Meng et al. [
] studied the distribution of granular flow lubrication, evolution law of force chains, their dynamic state, and distribution probability of the force chain distribution characteristics by establishing the granular flow lubrication model on friction of parallel surfaces under sliding conditions based on the DEM model. Sun and Wang [
] observed that the direction of the strong force chains coincided with the direction of large external load through the discrete simulation of coplanar sphere centers of 12 000 of 2D equidistant granules, which were in static stacking. Wang et al. [
] established a parallel-plate shear cell to simulate the shearing of an infinite parallel plate. The change in the relevant parameters and the shear dilatancy can be divided into plastic strain, macroscopic failure, and granular recombination stages. Moreover, the force chain direction and the load behavior are described by the force chains ratio of the
component to the
component, load distribution curve, and force chains pattern. Before that, they studied the mechanical properties and the force chain variations of the granular flow in the friction pair gap to simulate the Taylor-Couette shear model using DEM [
]. Bai et al. [
] investigated the complex granular flow and mixing in a cylindrical bladed mixer (CBM) by the continuum approach of Eulerian FEM. The method is verified by comparing various features of the solid flows reproduced by FEM, such as the formation of heaps, recirculating flow around blades, and spatial distributions of velocities, along with those reproduced by DEM. Meng and Liu [
] analyzed the average velocity, velocity fluctuation, regional partition, and self-diffusion characteristics of the dense shear-granular flow in a parallel plate. Cai et al. [
] studied some interesting features of 2D granular shearing flow by molecular dynamic approach for a specific granular system. Wang et al. [
] simulated the Taylor-Couette shear model using DEM to study the mechanical properties and force chain changes in the granular flow in friction pair clearance. Chang et al. [
] designed and developed a friction equipment to study the frictional behavior between work piece surface and granular matter. Further, the velocity, attack angle, surface morphology, and particle size were considered in the experiments to reveal the effects of these input parameters on the force transmission behavior. Wang et al. [
] used a multi-scale method based on coupling the FEM with DEM to model the shear process of two parallel plates with solid particles between first-body deformation and third-body rheology in a three-body interface to account for the interaction of them. Wang et al. [
] simulated the Taylor-Couette shear model using DEM to study mechanical properties and force chain changes in the granular flow in friction pair clearance. Meng et al. [
] analyzed the effects of upper plate friction coefficient on macroscopic granular flows, mesoscopic force distributions, macroscopic stress-strain responses, and evolutions of super-strong force chains using a discrete element analytical model that used the PFC2D software with an average solid fraction of 0.80.
Elkholy and Khonsari [
] used steel balls with a particle diameter of 3 mm as the third body, and shearing tests were performed using shear devices with different friction surface roughnesses. The shear force between the upper and lower plates and the displacement of the lower plate toward
axis were tested. The test showed that the displacement of the lower plate in the
axis was related to the surface roughness of the upper and lower plates, normal load applied to the upper plate, and rotation speed. They also compared the experimental results with simulation results and observed a good agreement between the two.
] established a parallel-plate shearing model using DEM to observe the movement of the particles between the upper and lower plates through the shearing motion of the upper and lower plates. The results of the study showed that the shear dilatancy caused by the three-body particles was the main cause of the frictional interface displacement.
Granular flow is a complex and enormous system. Many scholars have explored the characteristics of granular matter through a variety of experiments and methods from different aspects. However, many unique phenomena and mechanical properties of the granular matter are determined by the complex dynamic response of the force chain network, and very few studies on the factors that affect the force chain characteristics have been performed. In this study, a parallel plate granular flow system is constructed to simulate the force chains of granules based on the DEM model. The pattern of force chains is observed under the influence of load. The load and distribution rates of the weak force chains are analyzed based on the overall motion and shear dilatancy stages, respectively, as well as the direction of the strong-weak force chains to observe the change in the internal force chains characteristics of the granular system with its parameters.
Based on the aforementioned existing research work, this study further develops the parallel-plate granular flow model of a frictional system based on DEM, aiming to simulate the abrasive flow machining process, provide a method to analyze the force chains in granular flow, and clarify important relationships between the force chains and processing conditions. The remainder of this study is organized as follows. Section
briefly introduces the simulation model and related parameters. Section
is composed of four parts: part 1 analyzes the distribution and load rates of the weak force chains changing with parameters, such as load, speed, friction coefficient, and number of granular layers; changes in the force chain direction are studied in part 2; shape of force chains changing with load in different stages are analyzed in part 3; and finally, the shear dilatancy stage changing with various parameters are analyzed in part 4. Section
is the test verification of this study. Section
concludes this study.