МОДЕЛИРОВАНИЕ МЕТОДОМ ДИСКРЕТНЫХ ЭЛЕМЕНТОВ ПРОЦЕССА ВЫСОКОСКОРОСТНОГО ВЗАИМОДЕЙСТВИЯ ГРАНУЛИРОВАННОЙ СРЕДЫ И СТЕРЖНЯ С ПОЛУСФЕРИЧЕСКИМ ОГОЛОВКОМ

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions. The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes. Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior. In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media. In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity. Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

The dynamic behavior of granular media subjected to projectile impact was numerically investigated using a discrete element method (DEM). Specifically, the effects of the impact angle on the dynamic phenomena of projectile and granular media were examined. In general, after impact, a projectile either penetrates, rebounds, or moves horizontally depending on the impact angle of the projectile. The velocity histories of projectiles after impact for penetration and rebound differed. The impact angle did not affect drag force histories. The drag force histories of projectiles had ƒ-0.4 and ƒ-2.7 spectra. We have presented the probability distribution of the scattered velocity of granular media. When projectiles rebounded from granular media, the angle distribution of scattered granular media in the horizontal plane was butterfly-like. The impact angle did not affect the angle distribution of scattered granular media in the vertical plane. The granular media scattered in an elevation angle region of 40-60° regardless of the impact angle.

Numerical simulation of particle flow behavior in a screw conveyor using the discrete element method

We present a simulation scheme for solving high‐viscosity fluid and particle dynamics in a coupled computational fluid dynamics and discrete element method (CFD‐DEM) framework. This simulation scheme is intended to be used for geodynamical magmatic studies such as crystal settling at the melting roof of a magma chamber. The high‐viscosity fluid is treated by the Stokes‐flow approximation, where the fluid interacts with particles via the drag force in a cell‐averaged manner. The particles are tracked with contact forces by DEM. To efficiently solve such Stokes‐DEM coupled equations, we propose two key techniques. One is formulation of particle motion without the inertial term, allowing a larger time step at higher viscosities. The other is a semi‐implicit treatment of the cell‐averaged particle velocity in the fluid equation to stabilize the calculation. We simulate the settling particles in strongly viscous fluids in three dimensions and compare the results with the experimental and theoretical results. Our solution strategy is found to be robust and successfully captures the collective behavior of the particles. The simulation method presented here will be useful in various fields interested in long‐term dynamics of high‐viscosity granular media.

A study of influence of gravity on bulk behaviour of particulate solid

Granular lubrication is a promising extreme environment lubrication candidate. Lubricated by granular media, the startup dynamic process of a plain journal is significant to the mechanical performance, which is not well investigated yet. A research model focusing on the startup process of a granular flow lubrication bearing is constructed by the discrete element method. The granules filled in slim gaps extrude and collide with each other, which transfers the force to the shaft and causes instability to the shaft movement. During the movement from rest to stable running position, repeated position mutations of the shaft were found to occur. The variations in axis resistance torque and average unbalanced force are indistinctive, whereas those in average contact force, coordination number, and slip ratio are apparent. In this process, the force interacts within the inner granular assembly, which results in the formation of a force chain network. The breakage and reconstruction of this network can be used to analyze the movement and force variation characteristics. The movement and load tend to stabilize after a certain running period. The results provide a deeper understanding of the unique behavior of the granular-lubricated bearing induced by granular media.

We analyse the applicability of a number of graph community detection algorithms for detection of particle groups involved in collective motion in stirred granular media. The approach is based on the “velocity similarity graph”, when identification of particle groups moving in a coordinated manner is reduced to the problem of “community detection” in graph analysis. The algorithms and techniques developed for community detection in graphs can be thereby applied for identification of particle groups involved in coordinated motion in granular matter. We illustrate this approach by an example of granular media filled in a rotating cylinder. However, different community detection algorithms provide significantly different results. Comparison of the output of different algorithms, as well as interpretation of their physical meaning, provide insights that can contribute to developing both the graph algorithms as well as novel methods for granular media analysis.Given the fuzzy definition of “communities” in graphs, in particular as applied to larger-scale structures in granular media, application of other types of algorithms is considered. Currently, many software packages are available for simulation of granular matter based on the discrete element method (DEM). Simulations based on this method produce the data for individual particles. Additional processing of this data, enabling to identify the structures consisting of multiple particles moving in a coordinated matter, would extend the analysis based on simulations, thereby increasing the applicability and value of DEM simulations for both realistic predictions of behaviour of granular media, as well as enhancing physical insights into the mechanisms underlying the macroscopic behaviour.

Two key mechanical processes exist in the formation of powder compacts. These include the complex kinematics of particle rearrangement as the powder is densified and particle deformation leading to mechanical failure and fragmentation. Experiments measuring the time varying forces across a densifying powder bed have been performed in powders of microcrystalline cellulose with mean particle sizes between 0.4 and 1.2 mm. In these experiments, diagnostics measured the applied and transmitted loads and the bulk powder density. Any insight into the particle behavior must be inferred from deviations in the smoothly increasing stress-density compaction relationship. By incorporating a window in the compaction die body, simultaneous images of particle rearrangement and fracture at the confining window are captured. The images are post-processed in MATLAB® to track individual particle motion during compression. Complimentary discrete element method (DEM) simulations are presented and compared to experiment. The comparison provides insight into applying DEM methods for simulating large or permanent particle deformation and suggests areas for future study.

The signature of shear-induced anisotropy in granular media

We used the discrete element method (DEM) to understand the underlying attenuation mechanism in granular media, with special applicability to the measurements of the so-called effective mass developed earlier. We considered that the particles interacted via Hertz-Mindlin elastic contact forces and that the damping was describable as a force proportional to the velocity difference of contacting grains. We determined the behavior of the complex-valued normal-mode frequencies using (1) DEM, (2) direct diagonalization of the relevant matrix, and (3) a numerical search for the zeros of the relevant determinant. All three methods were in strong agreement with each other. The real and the imaginary parts of each normal-mode frequency characterized the elastic and the dissipative properties, respectively, of the granular medium. We found that as the interparticle damping [Formula: see text] increased, the normal modes exhibited nearly circular trajectories in the complex frequency plane, and that for a given value of [Formula: see text], they all lay on or near a circle of radius [Formula: see text] centered on the point [Formula: see text] in the complex plane, where [Formula: see text]. We found that each normal mode became critically damped at a value of the damping parameter [Formula: see text], where [Formula: see text] was the (real-valued) frequency when there was no damping. The strong indication was that these conclusions carried over to the properties of real granular media whose dissipation was dominated by the relative motion of contacting grains. For example, P- or S-waves in unconsolidated dry sediments can be expected to become overdamped beyond a critical frequency, depending upon the strength of the intergranular damping constant.

A new derivative of the particle‐based discrete element method (DEM) for computationally modeling the mechanics of granular materials is suggested. In contrast to the conventional DEM, the new stress‐based discrete element method (SDEM) presented here is formulated using a macroscopic parameterization, lending itself well for structural geomodeling for which the Mohr‐Coulomb constitutive relation is the underlying model assumption. In SDEM, consistency exists between the macroscopic properties of a particle assembly and the microscopic parameters specified for each particle, unlike for the standard DEM for which microscopic and macroscopic properties can at best be calibrated through troublesome testing experiments. Importantly, this consistency allows for modeling realistically unforced formation and growth of faults and shear zones, with orientations as predicted by Mohr‐Coulomb theory and in agreement with general observations. By measuring the virtual deformation of spherical elastic particles rather than just virtual particle overlaps, this new formulation introduces strain rate and stress tensors at the particle level. Strain rates are obtained by adopting interpolation techniques from the methodology of meshless continuum methods like smoothed particle hydrodynamics, while the appealing discrete kinematic of DEM, including inherent dilatation effects and stick‐slip instabilities, is preserved as particles interact by finite contact forces. The SDEM theory, the computational strategy, and test examples are presented here. In the companion paper, SDEM computational “sandbox‐type” models illustrate the method's potential for contributing insight into the dynamics and kinematics of more advanced geomechanical processes.

This work presents a 3D extension of the deformable discrete element method (DDEM) developed previously for 2D problems. The 3D formulation employs spherical particles. The particle deformation is made up of a global and local deformation mode. The global mode is assumed to be produced by uniform stress due to the contact forces. Particle deformability yields a nonlocal contact model, in which one contact between particles is influenced by contacts with other particles. It also leads to the formation of new contacts in the particle assembly. The DDEM affects the behavior of the granular material at the macroscopic level and gives new possibilities in material modeling by the discrete element method (DEM). The new algorithm is verified on a unconfined uniaxial compression test of a cuboid specimen discretized with equal‐size bonded particles aligned in a simple cubic pattern using an analytical solution. Enhanced modeling capabilities are presented by simulating cylindrical specimens discretized with a nonuniform size of bonded particles. The micro–macro relationships for elastic parameters are obtained. It is shown that the DDEM extends the range of the Poisson's ratio achievable with the DEM. Additional simulations are performed to determine the stability limits of the DDEM.

Theoretical and experimental investigation on nonlinear dynamic of grain-beam system

An Efficient Algorithm for Operating on Large Numbers of Aggregate Particles with Applications to Simulating the Dynamics of Irregularly Shaped Grains

Application of discrete element method (DEM) to keel penetration in granular media is investigated. The basic relations for visco‐elastic granular media composed of spherical particles are presented, together with 5th order Gear predictor‐corrector scheme for time‐integration. The background version of DEM and numerical time integration algorithm are developed and implemented into DEMMAT code. The implementation of time‐integration algorithm is verified by simple tests concerning particle‐particle, particle‐wall interactions, for which analytical expressions exist. By limiting the size of the media domain, the three‐dimensional problem is reduced to particular case presented as two‐dimensional domain of spherical particles. The variation of keel reaction and distribution of the particle forces due to different material properties are investigated. First Published Online: 14 Oct 2010