Since its origins in the 1970s, the Discrete Element Modeling (DEM) technique has emerged as one of the dominant particle-based numerical techniques for the modelling of a wide range of scientific and engineering problems involving particle/particulate systems. In its classic form, DEM represents individual disjoint physical particles as rigid elements which interact only along their interfaces. DEM has been able to provide powerful predictive tools that can be applied to many complex physical processes in the areas of powder flow, container filling and compaction and fluidised beds. However, there are still significant computational challenges that must be addressed before industrial scale applications can be effectively simulated. This multi-part paper focuses on the development of a theoretical framework for establishing a comprehensive set of scaling conditions, under which a scaled discrete element model can exactly reproduce the mechanical behaviour of a physical system. It is shown that this can be achieved by directly dealing with the governing equations of general particle systems, and by using three basic physical quantities and their corresponding scale factors, which can be freely chosen.

The main advantages of DEM compared to continuum based methods are its ability to handle a large number of particles, the fact that the topology of the particles is defined at run time, and that the interaction between the particles can be influenced by varying contact forces and friction laws. These properties are crucial for modelling the behaviour of real-world granular materials. The DEM algorithm allows for finite displacements and rotations of the particles and, unlike Continuum Mechanics, detects and recognises new interactions as the calculation progresses. This makes it suitable for simulating both dynamic and static granular flows.

It is also possible to use a variety of different material constitutive models, and a multitude of different interaction laws, including both linear and non-linear. This makes the DEM approach very flexible and adaptable to specific physical problems. Furthermore, it is possible to incorporate a range of additional simulation modules into a single DEM software package such as Heat Transfer, Chemical Reaction, and Coupling to CFD and FEM, which can significantly expand the scope and applicability of the method.

As such, despite its relatively simple underlying structure, the discrete element method is an extremely powerful tool that is used across a broad spectrum of industry. From pharmaceuticals to civil engineering, the application of this versatile technique is widespread. As the world becomes increasingly technologically advanced, it is vital that we are able to keep pace with its demands, and this will require us to continue to develop our simulation tools. Discrete Element Modeling is one of these essential tools, and its continued evolution and improvements are key to this process.

Ultimately, a full understanding of the fundamental behaviour of granular materials will enable us to create a more sustainable world. Discrete Element Modeling offers the possibility of accurately simulating this important area of science and technology, helping us to meet the needs of our ever-growing society.