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

The combination of the discrete element method and the finite element method is shown to be a suitable technique to resolve different length scales within almost all engineering problems dealing with granular assemblies, which are also in contact with a deformable body of an engineering device. The extended discrete element method (XDEM) describes the motion and forces of each individual grain within the granular assembly. Hence, the XDEM as a discrete approach accounts for each grain individually rather than describing the granular assembly as a continuous entity. On the other hand, the finite element method predicts accurately the deformations and the responding stress of the engineering device. Thus, this part of the simulation domain is efficiently approximated by a continuum approach.

The two domains share an interface which enables the employment of contact models fitting the particular behaviour of the contact problem between each grain and the surface of the device. At the interface impact forces develop which then propagate into the different length scales. Thus, the combined discrete and continuum approach now enables the tracking of both responses by the appropriate resolution. Each grain of the assembly in contact with the solid body generates a contact force and experiences a repulsive force which it reacts on individually. The contact forces sum up on the interface and cause the solid body to deform. This results in stresses which again the assembly recognise as a repulsive response.

The coupling method utilises quite naturally the advantages of both the continuum and the discrete approach and thereby compensating the shortages of each method. The coupling method not only resolves the different scales it further contributes to the efficiency of the computations. The method employs a fast contact detection algorithm, which spares valuable computation time by a fast separation of the important pairs of particles and surface element for the contact force prediction.

The discrete element method - finite element method (DEM-FEM) simulation technique is introduced with two engineering application of entirely different fields. However, both applications inherit similar physical problems of different length scales. In both cases individual particles are in contact with a widely used engineering device that is in contact with the granular material. Thus, the DEM-FEM coupling is shown to resolve the different scale responses within each domain separately.