Polish Academy of Sciences
Department of Information and Computational Science
DEM simulations
The discrete element method (DEM) is a wide family of numerical methods for discrete and discontinuous modelling of materials and systems which can be represented by a large collection of particles (discrete elements) interacting with one another by contact or by long range forces. Being a relatively new numerical method, the DEM has become a powerful tool for predicting the behaviour of various particulate and non-particulate materials such as soils, powders, rocks, concrete, ceramics and even metals.
The motion of the discrete element is described by the Newton-Euler rigid body dynamics equations which are integrated in time using explicit or implicit schemes. The disadvantage of the explicit integration scheme is its conditional numerical stability imposing the limitation on the time step. Despite this drawback the explicit integration is most often used because of simple and easy implementation, high computational efficiency of the solution for a single step and lack of problems with convergence required in implicit schemes.
Discrete elements can be of an arbitrary shape, however, spherical particles are often a preferable choice because of the simplicity of the formulation and the computational efficiency of contact detection algorithms for spherical objects.
The contact algorithm plays an essential role in the discrete element method. The contact forces control the motion of individual discrete elements and govern the macroscopic behaviour of the particle assembly. Two different approaches to contact treatment in the DEM can be identified, the so-called soft-contact approach and the hard-contact concept. The soft-contact approach employs regularization of the contact constraints, while the hard contact approach uses the methods of nonsmooth analysis to solve the problem with unilateral contact constraints. In the hard-contact approach it is assumed that the collision time is negligible and the change of the particle momentum due to a collision is determined.
In the soft-contact approach the contact time is longer than the integration time step which allows us to follow the evolution of the contact interaction. Various models of contact interaction can be defined. Contact models may take into account different deformation mechanisms and physical phenomena involved in contact such as elasticity, viscosity, damping, plasticity, friction, cohesion/adhesion and others. Cohesive bonds can be broken under loading which allows to model initiation and propagation of fractures. Easy treatment of fractures is one of the most important advantages of the DEM.
The present lecture will present theoretical background of the DEM, a broad spectrum of applications, strengths and weaknesses of the method, largest challenges present and future trends in this field. The lecture will be focused at the discrete element method based on the soft-contact approach. Various contact models will be reviewed. Modelling capabilities of the DEM will be assessed. Selection of a suitable contact models and model parameters yielding desired material behaviour is a key issue in the DEM and it still a serious challenge. The contact model can be viewed upon as a micromechanical material model. Micro-macro relationships in the DEM will be discussed. Enhancement of modelling capabilities by taking into account deformability of the particles will be demonstrated. Coupling of the DEM with other numerical methods and possibility of the use of the DEM in multiscale modelling framework will be presented. Multiphysics DEM applications will be reviewed. DEM modelling of thermal, magnetic or electric and various coupled multiphysics problems will be addressed.
The lecture will be illustrated with numerical results of various engineering problems including granular flows, rock mechanics, powder metallurgy, fluid-particle flows and others.
Biography to be confirmed.
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