A Bridging Scale Method for Multi-scale Analysis of Granular Materials

The bridging scale method (BSM) that couples the discrete particle assembly modeling with discrete element method (DEM) and the Cosserat continuum modeling with finite element method (FEM) in both fine and coarse scales respectively is proposed to study the mechanical behaviors in granular materials. The coarse scale domain, which is modeled with the Cosserat continuum and numerically simulated with the FEM, covers the whole medium concerned. While the fine scale one, which is modeled with the discrete particle assembly and numerically simulated with the DEM, is limited to a localized region, where the material microstructure and discontinuous deformation behaviors and their evolutions are needed to pay particular attentions. The interfacial condition between the two domains is presented and the scheme for its numerical implementation is proposed. By using a proper bridging scale projection operator, two decoupling sets of equations of motion of the combined coarse-fine scale system are allowed to solve with two separate solvers and to use distinct time step sizes, that will greatly enhance the computational efficiency of the BSM. The numerical results for a 2D example problem of the soil foundation illustrate the applicability and performance of the proposed method, and its advantages as compared with the FEM based on the Cosserat continuum modeling and the DEM based on the discrete particle assembly modeling.