It has been estimated that over 75% of raw materials that are processed in the industry are granular in nature. Prominent among them are minerals like coal, bauxite, iron ore, most food grains, sand, gravel and pharmaceutical powders and tablets. Many of the solids display difficult handling behaviours as they are not of uniform size, especially the minerals. This makes it challenging to design and operate the handling and processing plants. Modelling granular materials, solid and rocks has been a challenging engineering task for decades. Bulk material is governed by the micromechanics of individual particles that play a crucial role in determining the overall system behaviour. The mathematical equations that govern their flow are influenced by many parameters such as coefficient of restitution, coefficient of friction, particle size distribution, humidity, etc. Granular materials are characterized by hard inelastic contacts of their elementary constituents, friction, and negligible thermodynamic effects. Handling of such bulk material needs understanding of the Discrete Element Method (DEM). It is possible to improve and accelerate the design of handling systems once the engineering mathematics behind the dynamic processes of bulk material is understood properly, and DEM simulation is an indispensable tool today in the design and verification of transport and storage equipment.
DEM Explained
DEM is a numerical method based on Newton’s second law of motion ("the rate of change of momentum or acceleration of a body is directly proportional to the force applied for any object of constant mass") that considers the mutual interactions of discrete particles in contact and enables evaluations of mutual force interactions. DEM is based on molecular dynamics and was first proposed by Prof. Cundall and Otto D. L. Strack. One of the first uses of DEM was for the analysis of related problems in rock mechanics. DEM uses Contact Mechanics and Newton’s laws to determine the position of the particles in the system. The contact detection algorithms are used to check for contacts in the domain and calculate forces based on the amount of overlap between the colliding particles. The basic DEM model is solved using the linear visco-elasticity (a method mainly used for predicting the response of elastomer-like materials); other equations may be used for material flow that involves plastic deformations.
DEM and FEM (Finite Element Modelling)
While FEM deals with continuum problems, DEM deals with discontinuum problems. FEM involves a single or a coupled set of partial differential equations in order to mathematically model the observed phenomenon without giving detailed attention to the fundamental physical significance. FEM involves using mesh while DEM is a mesh-less approach; each particle is considered as an element. In more complex processes like rock milling or crushing, FEM models are not always suitable. In contrast to the continuum approach of FEM, the DEM approach works very well in bulk handling of material. DEM models every single particle as a distinct entity and represents granular material as an idealized assembly of particles. This makes the discrete approach very good for investigating phenomena occurring at the length scale of particle diameter and simulating the bulk behaviour of particles, as it deals with discontinuous, discrete matter. The coupling of the FEM with the DEM is an effective approach for problems where standard continuum finite elements are adequate to model a part of the analysis domain, whereas the use of only DEM is more adequate to treat other areas.
DEM can handle a wide range of materials constitutive behaviours, contact laws, and arbitrary geometries. Additionally, it allows the use of linear and non-linear laws, depending on the process that will be simulated. This permits the simulation of a problem in different scales, and even the modelling of the particles behaviour at its real size, involving the interaction of many particles in the system. DEM algorithm allows finite displacements and rotations of discrete bodies; including complete detachment and recognizes new interactions (contact) automatically as calculation progresses. Because it treats each particle as discrete (and not continuous), DEM requires high computational effort.
There are two types of DEM - explicit and implicit. Generally, explicit equations are simpler to solve than the implicit ones but they require a small time step to be utilized. Implicit integration methods enable larger time steps to be used. However a system of non-linear equations needs to be solved at each time step.
Advantages of using DEM include the ability to model the movement of individual particles, measurement of complete stress and strain tensors, time steps and the estimation of progressive failure.
Nowadays, the DEM is used in a wide range of engineering problems like fracture, rock crushing, excavation processes, rock mechanics, powder mechanics, granular materials or even in the pharmaceutical or chemical industry, for the transport of particles.
DEM Software
DEM is essentially a first principle physics technique based on Newton’s laws of motion and contact laws based on discrete particle physics. In this method, each particle of the bulk material is considered individually rather than collectively, and is represented through a representative shape and size that interacts with other particles and equipment geometry. In discrete element analysis, the system equilibrium is determined between particles in terms of mechanical, chemical, capillary, gravity, or other forces. Each particle is treated as a single element to assess interactions between particles. Such an approach allows for assemblies of thousands of particles and it is preferred for treating powder flow, container filling, and compaction and other situations involving particle arrays. As discussed above, DEM is an intensive computation process as it requires modelling of individual grains / particles as discrete elements rather than as a solid, continuous block. The better class of simulation software available today (like Altair EDEM™ for example) simulate any material and emulates its behaviour realistically, has intuitive and easy workflow, provides advanced analysis and visualization tools, and provides seamless CAE integration. This provides engineers with crucial insight into how those materials will interact with their equipment during a range of operation and process conditions. Such DEM software is used by leading companies in the heavy equipment, off-road, mining, steelmaking, and process manufacturing industries to understand and predict granular material behaviours, evaluate equipment performance, and optimize processes. As DEM software keeps advancing and computing power keeps on increasing, the demand for good DEM software should see a greater demand from industries that need bulk handling of material.