A review of recent work on the discrete particle method at the University of Twente: an introduction to the open-source package MercuryDPM

In this paper we review some recent advances in DEM (DPM) modelling undertaken at the University of Twente. We introduce the new open-source package MercuryDPM that we have been developing over the last few years.\ud MercuryDPM is an object-oriented program with a simple C++ implementation and includes: support for moving and complex walls, such as polyhedra or screw-threads; state-of-the-art granular contact models; multi-species support; specialised classes, allowing the easy implementation of common geometries like chutes, hoppers, etc.; common handler interfaces for particles, walls and boundaries (so all type of objects are changed using the same interfaces); restarting; large self-test suite and numerous simple demos; and, visualisation support, both internal and using Visual Molecular Dynamics.\ud Additionally to these features, MercuryDPM has two major components that, to the best of our knowledge, cannot be found in other DPM packages. Firstly, it uses a novel advanced contact detection method that is able of dealing with multiple distinct granular components with sizes ranging over many orders of magnitude: the hierarchical grid. We explain how this algorithm works and demonstrate the speedup gained over the traditional linked cell approach. This algorithm has lower complexity for poly-dispersed ows which means for the first time large simulations with extremely wide size distributions are feasible.\ud Secondly, we present a novel way to extract continuum fields from discrete particle systems that is applicable to mixtures as well as boundaries and interfaces. The particle data is coarse grained in a way that is by construction compatible with the continuum equations of mass-, momentum-, and energy balance. Boundary interaction forces are taken into account in a self-consistent way and thus allow the construction of a continuous stress field even within one particle radius of the boundaries. The method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static and steady situations. This coarse-graining method is available from MercuryDPM either as a post-processing tool or it can be run in real time. In real-time mode, it not only reduces the data which has to be stored but also allows boundary conditions etc. to be updated depending on the current macroscopic state of the system, e.g. allowing the creation of a pressure-release wall.\ud Finally, we illustrate these tools and a selection of other features of MercuryDPM via various problems including size-driven segregation in chute flow, rotating drums, and screw-conveyer

Discrete element simulations and experiments: toward applications for cohesive powders

Granular materials are omnipresent in nature and widely used in various industries ranging from food and pharmaceutical to agriculture and mining – among others. It has been estimated that about 10% of the world’s energy consumption is used in the processing, storage and transport of granular materials. In this thesis, we couple experiments and particle simulations to bridge this gap and link the microscopic properties to the macroscopic response for frictionless, frictional and cohesive granular packings, with the final goal of industrial application. The procedure of studying frictionless, frictional and cohesive granular assemblies independent of each other allows to isolate the main features related to each effect and provides a gateway into the use of discrete element methods to model and predict more complex industrial applications.\ud For frictionless packings, we find that different deformation paths, namely isotropic/uniaxial over-compression or pure shear, slightly increase or reduce the jamming volume fraction below which the packing loses mechanical stability. This observation suggests a necessary generalization of the concept of the jamming volume fraction from a single value to a “wide range” of values as a consequence of the modifications induced in the microstructure, i.e. fabric, of the granular material in the deformation history. With this understanding, a constitutive model is calibrated using isotropic and deviatoric modes. We then predict both the stress and fabric evolution in the uniaxial mode. \ud By focusing on frictional assemblies, we find that uniaxial deformation activates microscopic phenomena not only in the active Cartesian directions, but also at intermediate orientations, with the tilt angle being dependent on friction, and different for stress and fabric. While a rank-2 tensor (representing a second order harmonic approximation) is sufficient to describe the evolution of the normal force directions, a sixth order harmonic approximation is necessary to describe the probability distributions of contacts, tangential forces and the mobilized friction.\ud As a further step, cohesion is introduced. From multi-stress level uniaxial experiments, by comparing two experimental setups and different cohesive materials, we report that while stress relaxation occurs at constant volume, the relative relaxation intensity decreases with increasing stress level. For longer relaxation, effects of previously experienced relaxation becomes visible at higher stress levels. A simple microscopic model is proposed to describe stress relaxation in cohesive powders, which accounts for the extremely slow force change via a response timescale and a dimensionless relaxation parameter.\ud In the final part of the thesis, we compare results from experiments and discrete element simulations of a cohesive powder in a simplified canister geometry to reproduce dosing (or dispensing) of powders by a turning coil in industrial applications. Since information is not easily accessible from physical tests, by scaling up the experimental particle size and calibrating material parameters like cohesive strength and interparticle friction, we obtain quantitative agreement between the mass per dose in simulations and experiments for different dosage times. The number of doses, for a given total filling mass is inversely proportional to dosage time and coil rotation speed, as expected, but increases with increasing number of coils. Using homogenization tools, we obtain the exact local velocity and density fields in our device

Deformation modes of packings of frictionless polydisperse spheres

Dense granular materials are well known to demonstrate mechanical properties that are different from classical fluids or solids. An issue is the accurate prediction of mechanical properties of granular materials, which are controlled by the internal structure of the assembly of grains – where the internal structure itself depends on the history of the sample. In this work, the Discrete Element Method (DEM) approach is presented as a viable tool to investigate the behavior and dynamics of granular packings subjected to deformations. The results on uniaxial and deviatoric deformations are compared to earlier results on isotropic deformation. As main result, the evolution of pressure and coordination as a function of volume fraction are reported for both uniaxial and deviatoric deformation modes. Our findings compare astonishingly well with results for purely isotropic compression. The second stress response namely anisotropy, is present as the evolution of the deviatoric stress as a function of the deviatoric strain. Similar data can be measured from experiments with the true biaxial tester which is work-in-progress, and both deformation modes are especially simple to realize experimentally

Discrete Element Simulations and Experiments on the Deformation of Cohesive Powders in a Bi-Axial Box

We compare element test experiments and simulations on the deformation of frictional, cohesive particles in a bi-axial box. We show that computer simulations with the Discrete Element Method qualitatively reproduce a uniaxial compression element test in the true bi-axial tester. We highlight the effects of friction and polydispersity on our simulations and present the second stress response namely the deviatoric stress as a function of the deviatoric strain

Effects of polydispersity on the micro-macro behavior of granular assemblies under different deformation paths

The micromechanical and macromechanical behavior of idealized granular assemblies, made by linearly elastic, frictionless, polydisperse spheres, are studied in a periodic, triaxial box geometry, using the discrete element method. Emphasis is put on the effect of polydispersity under purely isotropic loading and unloading, deviatoric (volume conserving), and uniaxial compression paths. We show that scaled pressure, coordination number and fraction of rattlers behave in a very similar fashion as functions of volume fraction, irrespective of the deformation path applied. Interestingly, they show a systematic dependence on the deformation mode and polydispersity via the respective jamming volume fraction. This confirms that the concept of a single jamming point has to be rephrased to a range of variable jamming points, dependent on microstructure and history of the sample, making the jamming volume fraction a state-variable. This behavior is confirmed when a simplified constitutive model involving structural anisotropy is calibrated using the purely isotropic and deviatoric simulations. The basic model parameters are found to depend on the polydispersity of the sample through the different jamming volume fractions. The predictive power of the calibrated model is checked by comparison with an independent test, namely uniaxial compression. The important features of the uniaxial experiment are captured and a qualitative prediction for the evolution of stress and fabric is shown involving a “softening” regime in both stress and fabric – stronger for the latter – that was not prescribed into the model a priori

Element test experiments and simulations: From dry towards cohesive powders

Findings from experiments and particle simulations for dry and cohesive granular materials are presented with the goal to reach quantitative agreement between simulations and experiments. Results for the compressibility, tested with the FT4 Powder Rheometer are presented. The first simulation results involve the strain controlled uniaxial compression of frictionless polydisperse spheres in a biaxial box using a linear visco-elastic contact model. As main result, the evolution of pressure as a function of volume fraction is reported. Our anisotropic, uniaxial findings compare astonishingly well with results for purely isotropic compression. Concerning the second stress response, namely anisotropy, we present the evolution of the deviatoric stress as a function of the volume fraction, which cannot be measured with the FT4 experiment, but requires a bi-axial experiment

Evolution of the effective moduli for anisotropic granuar materials during pure shear

We analyze the behavior of a frictionless dense granular packing sheared at constant volume. Goal is to predict the evolution of the effective moduli along the loading path. Because of the structural anisotropy that develops in the system, volumetric and deviatoric stresses and strains are cross coupled via four distinct quantities, the classical bulk and shear moduli and two anisotropy moduli. Here, by means of numerical simulation, we apply small perturbations to various equilibrium states that previously experienced different pure shear strains and investigate the effect of the microstructure (2 nd rank fabric tensor) on the elastic bulk response. Besides the expected dependence of the bulk modulus on the isotropic fabric, we find that both the isotropic density of contacts and the (deviatoric) orientational anisotropy affect the anisotropy moduli. Interestingly, the shear modulus of the material depends also on the actual stress state, along with the (isotropic and anisotropic) contact configuration