Background
Over the last 40 years, modern science has made great strides in computational analysis methodologies. The intense development of computer technology, combined with new numerical methods, has made it possible to create theoretical models that can be applied to everyday business.
The theory of Continuous Media Mechanics was consolidated by the studies of Trusdell, Eringen and other researchers. This led to significant advances in understanding the behavior of deformable and non-deformable solids and fluids.
Even considering different types of non-linearity, both physical and geometric, many engineering problems can be solved using numerical methods. However, the theory of Continuous Media Mechanics has its limitations. For example, when a fracture occurs in a particular component characterized by a material. What was once supposed to be continuous clearly ceases to be, compromising a premise of the theory.
Given this scenario, new methodologies linked to the experimental area and empiricism have been created, enabling more reliable studies, despite the complexity of the real scenario; among them the Discrete Element Method (DEM).
The emergence of the theoretical basis for the method is usually associated with an article by Cundall in 1971 on a large-scale computer model for the progressive movement of rock blocks [1]. As early as 1979, Cundall was directly recognized by the DEM application for his article "Discrete Numerical Model for Granular Assemblies" [2].
What is the Discrete Element Method?
The terminology Discrete Element Method ( DEM ) covers both computational methods that allow the analysis of displacements and rotations of discrete bodies, including fracture, and methods that automatically recognize new contacts as calculations and iterations are performed.
DEM can therefore be defined as a set of techniques suitable for simulating the dynamic behavior of a set of multiple rigid or deformable bodies that are subject to successive variations in contact conditions.
The Discrete Element Method is widely used in the numerical simulation of flows of granular materials with or without comminution.
Methods that use discrete elements can be differentiated according to the categorization of the particles, as in the case of undeformable bodies; or by the modeling approach, for example, the Lagrange Discrete theory.
The common process of solving a problem using the DEM starts by describing the individual movement of the particles in each increment of time. The displacement of the particles is given by Newton's general equation of motion and Euler's equation for rotations.
Applications of the Discrete Element Method
DEM is a very versatile method because it can deal with and introduce discontinuities in a very direct and intuitive way, unlike other methods. In addition, discrete methods offer convenient strategies for organizing the disorder in the microstructure of materials through statistical models.
Software that uses DEM can accurately simulate the behavior of granular materials of various shapes and sizes in equipment such as mills and transfer chutes, among others.
To make things clearer, here's an overview of the most common types of application:
1 - Multiphysics models: DEM can be used in conjunction and in an integrated manner with Computational Fluid Dynamics (CFD), Finite Element Method (FEM) and Lattice-Boltzmann Method (LBM) to simulate multiphase and multicomponent fluids. In this way, scenarios such as the behavior of a tractor structure (FEM) in a sandy environment (DEM) can be better studied.
Figure 1: DEM simulation predicting irregular particle loading and FEM applied to the blade structure - SOURCE: Kot Collection.
2 - Complex particle shapes: particles can be drawn in two or three dimensions for a more realistic representation. This representation can be extended to modeling fibers, which can be rigid or flexible.
Figura 2: Simulação DEM para um teste de compressão de palha, modeladas como fibras – FONTE: Rocky (todos os direitos reservados).
3 - Complex movements: can be easily specified. Free movements with 6 degrees of freedom can be specified in DEM software so that there are no dependencies on multibody dynamics software. In the example below, a complex case is simulated where the particles have different sizes and simultaneously a mechanism alternates the flow in the kick.
Figure 3: DEM simulation for a material flow in a chute directed by a deflector - SOURCE: Kot Collection.
4 - Breakage model: well-established models for simulating particle breakage are used, such as ABT10 and the Tavares model. For these cases, some studies try to avoid particle breakage and others aim to break the particles.
Figure 4: DEM simulation of a secondary crusher used to break up ore particles - SOURCE: Kot Collection.
5 - Energy spectrum: using statistical models, DEM is used to predict the probability of particles breaking up in a mixture of different materials (e.g. rock and steel). This result is obtained by taking into account the properties of the materials and the spectrum of collision energies.
Figura 5: Simulação DEM para diferentes materiais em um moinho industrial – FONTE: Acervo Kot.
6 - Wear model: it is possible to simulate wear on the surfaces of processing equipment using the Archard wear model in the area studied by tribology.
Figura 6: Simulação DEM para simulação de desgaste em uma moega – FONTE: Acervo Kot.
The Discrete Element Method has made great strides in the structural analysis of materials. However, just as the Continuous Media Theory presented impasses, the DEM also has its limitations. This raises the question: what further advances can be expected in the study of granular flows?
Companies can take advantage of the use and application of the Discrete Element Method in a wide variety of applications, as demonstrated in this article. Running software is just the tool for applying these methodologies. Analysis and case studies require professionals who not only master the theoretical basis, but also have extensive experience. They will be able to extrapolate analytical results, generating the best solution for each problem proposed.
Kot Engenharia can be your partner in applying this method with confidence in real and complex engineering scenarios.
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References:
[1] CUNDALL P. A. A Computer Model for Simulating Progressive, Large-scale Movement in Blocky Rock System. Disponível em: < https://ci.nii.ac.jp/naid/10018723276/>. Acesso em: 10 de Outubro de 2020.
[2] CUNDALL P. e Strack O. D. L. A discrete numerical model for granular assemblies. Disponível em: <https://www.icevirtuallibrary.com/doi/abs/10.1680/geot.1979.29.1.47>. Acesso em: 12 de Outubro de 2020.
[3] Rocky. ESSS. What is Discrete Element Method and how does it work? Disponível em: <rocky.esss.co/blog/what-is-discrete-element-method/>. Acesso em: 17 de Outubro de 2020.
