Finite element method–discrete element method bridging coupling for the modeling of gouge

We discuss the multiscale modeling of a granular material trapped between continuum elastic domains. The amorphous granular region, usually termed “gouge,” is under high confinement pressure, to represent the loading of faults at depth. We model the granularity of gouge using the discrete element method (DEM), while the elastic regions surrounding it are represented with two continuum domains modeled with the finite element method (FEM). We resort to a concurrent coupling of the discrete and continuum domains for a proper transmission of waves between the discrete and continuum domains. The confinement pressure results in the appearance of a new kind of ghost forces, which we address via two different overlapping coupling strategies. The first one is a generalization to granular materials of the bridging method, which was originally introduced to couple continuum domains to regular atomic lattices. This method imposes a strong formulation for the Lagrange constraints at the coupling interface. The second strategy considers a weak formulation. Different DEM samples sizes are tested in order to determine at which scale a convergence of the elastic properties is reached. This scale sets the minimal mesh element size in the DEM/FEM interface necessary to avoid undesirable effects due to an elastic properties mismatch. Then, the two DEM/FEM strategies are compared for a system initially at equilibrium. While the performance of both strategies is adequate, we show that the strong coupling is the most stable one as it generates the least spurious numerical noise. Finally, as a practical example for the strong coupling approach, we analyze the propagation of pressure and shear waves through the FEM/DEM interface and discuss dispersion as function of the incoming wave frequency.