Resolution of Different Length Scales by an Efficient Combination of the Finite Element Method and the Discrete Element Method

Abstract

The objective of this paper is to resolve different length scales in structure analysis using an interface coupling the discrete element method (DEM) with the finite element method (FEM). This approach distinguishes itself from other methods in so far that no overlapping domains between finite and discrete elements exist. Both domains are separated in the physical space and the numerical simulation domain. The proposed approach is relevant to almost all engineering applications that deal with granular matter such as storage in hoppers, transport on conveyor belts or the displacement of granular material as in mixers or the excavation of the soil. For these applications an engineering device such as mixer blades or cutting tools are in contact with granular matter. Contacts with individual particles generate contact forces that act on both the engineering device and the granular material. The latter experiences a displacement of individual particles whereby the engineering structure responds with deformation and stresses. In order to predict and optimise both the behaviour and motion of granular material and the structures in contact, numerical simulation tools are increasingly employed. Simulations are popular especially because experiments are often expensive, time-consuming and sometimes even dangerous. The continuous increase in computing power is now enabling researchers to implement numerical methods that do not focus on the granular assembly as an entity, but rather deduce its global characteristics from observing the individual behaviour of each grain. An interaction between granular media and a structure relies on a transfer of forces between them. Granular media consists of an ensemble of particles of which a number of particles may be in contact with a surface e.g. walls as surfaces of solid structures. The contact is resolved similar to inter-particle contacts by a representative overlap. It defines the position of impact as well as the force acting on the particle at this position. The same force, however, in the opposite direction defines a mechanical load for the structure. In order to determine the effect of forces on the solid structure, it is discretised using finite elements. The impact of the force is transferred to the nodes