Concurrent multi-scale modeling of granular materials: Role of coarse-graining in FEM-DEM coupling

Abstract

The finite element method (FEM) and the discrete element method (DEM) are two commonly used techniques in modeling different types of materials. FEM is used for materials that behave like a continuous substance, while DEM is used for materials that can be seen as individual particles. Sometimes, it's necessary to combine these two methods to get a more accurate representation of the granular material's behavior. This is typically done by directly connecting the individual particles in DEM with the larger elements in FEM. A technique called coarse-graining (CG) is used to bridge the gap between these two methods. It takes the data from the individual particles and turns it into smooth, continuous fields that follow the laws of continuous materials. By choosing a specific scale, the coarse-grained fields are then mixed together and applied to the FEM model. In this research, we explore a new way of combining FEM and DEM, both for surfaces and volumes. When dealing with surfaces, we convert the discrete contact forces between particles and surfaces into a smooth, continuous traction field that is then applied to the FEM model. For volumes, we enhance the homogenization process with additional functions to connect the discrete particles, their coarse-grained fields, and the finite element formulation. This new approach offers better accuracy and symmetry in surface coupling, reducing the energy produced during the combination of FEM and DEM, and for volume coupling, it significantly decreases numerical dissipation, especially when the load applied contains high-frequency components. This technique has the potential to be expanded beyond the current examples. It could be applied to different types of materials and governing equations, allowing for more advanced multi-scale and multi-physical modeling methods.