Discrete Element Method (DEM) consists in solving the equations of motion of a collection of rigid particles by accounting for their contact interactions [32, 137, 60, 29, 120]. Over the last 40 years, DEM has matured into a general-purpose tool for the simulation of industry-related particulate processes and for the investigation of the complex behavior of granular materials. With rising computational power and inclusion of realistic particle characteristics, both the accuracy and the computational efficiency of DEM simulations have continuously increased, but the level of expectations of DEM has considerably grown at the same time.
This report attempts to outline the horizons of granular modeling beyond the current practice of DEM. It is not meant to be a review of DEM and its recent numerous achievements or alternative methods to DEM, but to serve as an objective description of the issues and new resources that may lead to a paradigm shift in near future. The seminal report of P.W. Cleary for IFPRI, entitled “Review of DEM for Industrial Applications", in 2010 provides a clear and rich background of DEM together with the breadth of industrial applications that are possible with DEM [29]. Despite huge progress accomplished during the last decade, most themes and issues developed and exemplified in that report about discrete modeling and its applications are still relevant. The present report may be considered as a complement to that one, with the somewhat different goal of highlighting the shortcomings of the current practice of DEM and the novel trends that can allow us to identify the most promising future developments. Several examples of coupled DEM-CFD (Computational Fluid Dynamics) simulations are cited in this report, but the focus will be on the particles and their interactions in DEM.
In section 1, we discuss the role of DEM as an original approach for gaining knowledge on particulate systems alongside theory and experiment. We argue that DEM is an inherently bottom-up approach and the adequate definition of numerical material is as much important as the mathematical algorithm used for the prediction of cooperative dynamics. We also describe the three levels of DEM with increasing complexity of the numerical material and the scope of a data-driven approach with the potential power of providing tools to improve accuracy and efficiency. We underline the interpretive use of DEM in connection with theory and the origins of its general trustworthiness in connection with experiment.
In section 2, we highlight the role of contact interactions and their implementation in DEM. The focus will be on several ambiguities and shortcomings which need to be resolved, such as normal force positivity and memory of tangential displacements. We develop the difference between force laws and contact laws and the prospect of a shift from the hard-particle soft-contact approach to a soft particle hard-contact approach. We also consider different models of adhesion and recent models of elastoplastic contacts and discuss their applicability and consequences for granular dynamics. Finally, we focus on parametric randomness and more specifically polydisperse input parameters as a major ingredient of physics fidelity that has been so far ignored in DEM simulations.
Section 3 is devoted to the representation and implementation of particle shape with its variants as a key input of DEM. In particular, we discuss arbitrary particle shapes and their extraction from image data as a step towards data-driven DEM and the contact detection issues. We underline the role of shape polydispersity and discuss the issue of reducing particle shape to a small number of descriptors or through its effect in connection with dissipation.
In section 4 we describe different modeling strategies for particle breakage at the sub-particle and particle levels. The realism and efficiency of sub-particle methods are discussed, such as breakage criteria with regard to fracture mechanics, finite size effects, shapes of the generated fragments, and recently developed hybrid methods. We discuss how the higher physics-fidelity of sub-particle models can be combined with the computational efficiency of particle level models.
Section 5 is devoted to DEM models of soft particles, i.e. particles undergoing large deformations without breakage. We briefly present the surface deformation methods based on material points or nodes at the particle surface, and volume deformation methods based on continuum field description of the particle behavior.
In section 6 we discuss several computational issues. The important role of parallel computing, specially on General-Purpose GPUs, for the applicability of new models of high physics fidelity and for speedup of simulations is underlined. The limits of particle coarsening are discussed. We also recall new developments in original multiscale hybrid models and the benefits of concurrent use of discrete and continuum simulations of granular materials. Finally, we discuss the ways Machine Learning models can be used with DEM simulations and a data-driven approach allowing expensive calculations of contacts, forces and velocities in DEM algorithms to be replaced by a Machine Learning-enabled framework.
In section 7 we consider the issues of verification and validation and discuss the methods of uncertainty quantification as an asset to reinforce the reliability of DEM in application to real-world processes. We use examples of rigorous uncertainty quantification to illustrate the treatment of uncertainties related to the input data and model approximation. We also present the concept of validation metric for optimal use of experimental data for the evaluation of model form errors.
Finally, we present an outlook of future directions around and beyond DEM in section 8. Recent algorithmic developments are qualified according to their contributions to physics fidelity, data fidelity, computational efficiency, and game-changing nature. We discuss the developments beyond the hard-particle approximation and the scope of a data-driven DEM.