Analysis of grinding media motion behavior in a vertical spiral stirred mill based on discrete element method

The numerical modelling of particulate processes in environmental science increasingly requires an ability to represent the properties of individual natural particles. Considerable advances have been made in discontinuum modelling using spheres to represent particles. In this paper, we discuss recent developments that illustrate a way forward for tackling the complexity of realistically shaped bodies such as those exhibited by rock fragments. To address the validation of such approaches, we present a comparison of cube-packing experiments and their equivalent numerical simulation. Sensitivity to initial conditions, highlighted for non-spherical bodies, enters the discussion of problems with validation of numerical simulation. The algorithmic details behind these advances in modelling large systems of realistically shaped particles are summarized in our companion paper in this volume.

A new discrete element-embedded finite element method for transient deformation, movement and heat transfer in packed bed

In this work, we review three kinds of numerical algorithms, namely the discrete element method (DEM), the coupling discrete element and finite element method (DEM/FEM) and the cohesive zone model (CZM), for the impact fracture simulations of automotive laminated glass. Based on the non-continuum theory, the DEM is capable of modeling the impact fracture phenomenon. However, this method is very time-consuming. To remedy this shortcoming, we have been devoted to combining the discrete element method and the finite element method. Another notable work is to simulate the impact fracture behaviors by using the CZM. Some future works concerning this research aspect are also presented.

Simulation of fracturing processes in porous rocks can be divided into two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures or (ii) modeling the rock by a discrete (or discontinuous) approach that describes the material directly as a collection of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified so that they reproduce the discretization of a first-order finite element method (FEM) for linear elasticity. This provides an expression of the virtual forces in terms of general Hook’s macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in a reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it enables a direct coupling between (M)DEM and domains modeled by a grid made of polyhedral cells. Thus, this approach makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate the simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented using the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work provides a more uniform approach and extends these previous works to general polyhedral grids for the non-fracturing domain.

In discrete element methods (DEM, [2] and [4]) the simulated bodies are typically assumed to be infinitely rigid in order to reduce the computational cost. However, there are multibody systems where it is useful to take into account the deformability of the simulated bodies in order to enable the evaluation of their stress and strain distributions. This paper focuses on the simulation of systems of multiple deformable bodies using a combination of discrete and finite element methods (FEM), with some simplifying assumptions that are necessary to make the solution of the problem feasible. In traditional mixed FE formulations the contact effects can be taken into account using Lagrange multipliers methods and keeping the contact surfaces and forces as unknowns together with the unknown displacements. This approach results in huge systems of highly nonlinear coupled equations due to geometric as well as boundary nonlinearities. Furthermore, the parts of the bodies that may come in contact, typically, have to be identified before performing the simulation. However, no prior knowledge of the upcoming contacts is available in the multibody systems under consideration. Considering the excessive computational requirements, due to the huge number of degrees-of-freedom (DOF) and the high nonlinearities of the coupled systems of equations, it is unrealistic to solve problems involving many interacting bodies using such classical contact FE approaches. Simulations of deformable bodies with reasonable computational cost are enabled by incorporating FEM in DE analyses using certain assumptions that uncouple the contact interactions from the equations of dynamic equilibrium. In particular, the DEM are employed to identify, at each simulation step, the bodies in contact and determine the contact forces. Then, either a FE or a DE formulation is used at the individual body level to describe the equations of motion, depending

Scaled-up rice grain modelling for DEM calibration and the validation of hopper flow

This paper carries out a survey on available methods for micromechanical modelling on asphalt mixture. Focus is placed on models based on different concepts as well as different computational methods in numerical implementation. The major topics covered include: models based on discrete element method, micromechanical finite element models, disturbed state concept, the discontinuous deformation analysis method, integration of mechanics on different scales, etc. A brief description of some fundamental algorithms in discrete element and finite element methods are also included due to the modelling accuracy and thus wide interest in them. Simple case studies are included to illustrate the methods in discussion wherever space allows.

Simulation of fracturing processes in porous rocks can be divided in two main branches: (i) modeling the rock as a continuum enhanced with special features to account for fractures, or (ii) modeling the rock by a discrete (or discontinuous) modeling technique that describes the material directly as an assembly of separate blocks or particles, e.g., as in the discrete element method (DEM). In the modified discrete element (MDEM) method, the effective forces between virtual particles are modified in all regions without failing elements so that they reproduce the discretization of linear FEM for linear elasticity. This provides an expression of the virtual forces in terms of general Hook's macro-parameters. Previously, MDEM has been formulated through an analogy with linear elements for FEM. We show the connection between MDEM and the virtual element method (VEM), which is a generalization of traditional FEM to polyhedral grids. Unlike standard FEM, which computes strain-states in reference space, MDEM and VEM compute stress-states directly in real space. This connection leads us to a new derivation of the MDEM method. Moreover, it gives the basis for coupling (M)DEM to domains with linear elasticity described by polyhedral grids, which makes it easier to apply realistic boundary conditions in hydraulic-fracturing simulations. This approach also makes it possible to combine fine-scale (M)DEM behavior near the fracturing region with linear elasticity on complex reservoir grids in the far-field region without regridding. To demonstrate simulation of hydraulic fracturing, the coupled (M)DEM-VEM method is implemented in the Matlab Reservoir Simulation Toolbox (MRST) and linked to an industry-standard reservoir simulator. Similar approaches have been presented previously using standard FEM, but due to the similarities in the approaches of VEM and MDEM, our work is a more uniform approach and extends previous work to general polyhedral grids for the non-fracturing domain.

A discrete element method (DEM) has widely been used to simulate asphalt mixture characteristics, and DEM models can consider the effect of aggregate gradation and interaction between particles. However, proper selection of model parameters is crucial to obtain convincing results from DEM‐based simulations. This paper presents a method to appropriately determine the mechanical parameters to be used in DEM‐based simulation of asphalt concrete mixture. Splitting test specimens are prepared by using asphalt mixture, and the splitting test results are compared with simulation results from two‐dimensional (2D) DEM and three‐dimensional (3D) DEM. Basing on the DEM results, the effects of contact model parameters on the simulation results are analyzed. The slope of the load‐displacement curve at the beginning stage is mainly affected by the stiffness parameters, and the peak load is mainly determined by using the value of the bond strength. The laboratory splitting test of AC‐20 and AC‐13 specimens were performed at different temperatures, namely, −10°C, 0°C, 10°C, and 20°C, and the load‐displacement relationships were plotted. According to the real load‐displacement curve’s slope at the beginning stage and peak load applied, the range of DEM bond model parameters is determined. On the basis of DEM results of the splitting test, the relationships between simulation load‐displacement curve’s characteristics and bond model parameters are fitted. The values of the parameters of the DEM contact bond model at different temperatures are obtained depending on the actual load‐displacement curve’s initial slope and peak load. Lastly the DEM and laboratory test results are compared, which illustrates that the parallel bond model can well simulate the behavior of asphalt mixture.

The discrete element method (DEM) is ideal for modeling many problems not accessible to traditional continuum-based methods such as finite difference and finite elements (Homer et al., 2001). DEM has the advantage of inherently capturing large non-affine deformations and the fluid--solid phase changes so commonly found in granular media. The DEM appears to derive much of its power from the kinematic freedom for the particles such that seemingly simplistic micro-scale models can replicate realistic macro-scale behavior. With the advent of large-scale computing, by which simulations of several million particles are possible, the DEM will become an important tool for geotechnical and industrial applications within the next 20 years. The advances in DEM have and will continue to mirror advances in computer hardware. Several advances in DEM technology will accompany the improvements in computer technology. The constitutive response of the DEM medium depends on micro-scale laws that define the contact mechanisms, particle size and shape, and particle distribution. The success of the method requires a correlation between the phenomenology of the DEM medium and the micro-scale laws. Most of these advances will be accomplished through numerical experiments, which at present are a popular tool for understanding granular media as a continuum. Is it reasonable to foresee a day when a continuum view is unnecessary? In this paper, this question is discussed from the standpoint of scale effects that infect all numerical approximations,

Numerical modeling methods, such as the discrete element method (DEM), are an increasingly popular alternative to traditional semi-empirical terramechanics techniques. While DEM has many advantages, including the ability to model more complex running gear and terrain profiles, it has not reached widespread popularity due to its high computation costs. In this study a surrogate DEM model (S-DEM) was developed to maintain the simulation accuracy and capabilities of DEM with reduced computation costs. This marks one of the first surrogate models developed for DEM, and the first known model developed for terramechanics. By storing wheel-soil interaction forces and soil velocities extracted from constant-velocity DEM simulations, S-DEM can quickly perform new dynamic wheel locomotion simulations. Using both DEM and S-DEM, wheel locomotion simulations were performed on flat and rough terrain. S-DEM was found to reproduce drawbar pull and driving torque well in both cases, though wheel sinkage errors were significant at times. Computation costs were reduced by three orders of magnitude in comparison to DEM, bringing the benefits of DEM modeling to vehicle design and control. The techniques used to develop S-DEM may be applicable to other common DEM applications, such as soil drilling, excavating, and plowing.

Laser-induced heating of dynamic particulate depositions in additive manufacturing

The Discrete element method (DEM) is a robust numerical tool for simulating crack propagation and wear in granular materials. However, the computational cost associated with DEM hinders its applicability to large domains. To address this limitation, we employ DEM to model regions experiencing crack propagation and wear, and utilize the finite element method (FEM) to model regions experiencing small deformation, thus reducing the computational burden. The two domains are linked using a FEM–DEM coupling, which considers an overlapping region where the deformation of the two domains is reconciled. We employ a “strong coupling” formulation, in which each DEM particle in the overlapping region is constrained to an equivalent position obtained by nodal interpolation in the finite element. While the coupling method has been proved capable of handling propagation of small-amplitude waves between domains, we examine in this paper its accuracy to efficiently model for material failure events. We investigate two cases of material failure in the DEM region: the first one involves mode I crack propagation, and the second one focuses on rough surfaces’ shearing leading to debris creation. For each, we consider several DEM domain sizes, representing different distances between the coupling region and the DEM undergoing inelasticity and fracture. The accuracy of the coupling approach is evaluated by comparing it with a pure DEM simulation, and the results demonstrate its effectiveness in accurately capturing the behavior of the pure DEM, regardless of the placement of the coupling region.

Understanding the rock creep behavior is necessary to determine the long-term strength and safety of several geotechnical designs. There are several formulations to study the rock creep; however, most of them do not properly capture the tertiary creep. To overcome such limitation, model improvements have been made and new creep models (e.g., creep models with an associated viscoplastic flow rule) have been proposed. As an alternative, the Rate Process Theory (RPT) has been recently used to study the soil/rock creep behavior. This article expands previous works by analyzing the applicability of the Discrete Element Method (DEM) with RPT implementation to simulate Rock Shear Creep (RSC). To do that, (i) 2D DEM direct shear creep tests under Constant Normal Load (CNL) conditions are used, (ii) DEM specimens are built by a combination of the Flat-Joint Contact Model (FJCM) and the Linear Model (LM), and (iii) the DEM + RPT approach is calibrated by using experimental tests from the literature. DEM results presented here illustrate the suitability of DEM–RPT methodology to reproduce all stages of RSC, including tertiary creep. The effect of the applied shear stress and normal stress on RCS is also analyzed. Finally, the most important novelties of this paper are: (1) the DEM–RPT methodology can be easily calibrated by using a laboratory direct shear creep test; (2) the calibrated DEM models are suitable to analyze the main aspects of RSC; and (3) DEM results qualitatively agree with the overall experimental trend published in the literature.

Chapter 3 - Coupled methods