A bridging scale method for granular materials with discrete particle assembly – Cosserat continuum modeling

Based on the bridging scale method (BSM) initially presented in nano mechanics [1] and [2], a new version of the BSM that couples discrete particle assembly modeling using the discrete element method (DEM) and Cosserat continuum modeling using the finite element method (FEM) at both micro–macro scale levels respectively is proposed for multiscale analysis of granular materials. The DEM is only applied to the limited localized regions for accurately simulating discontinuous failure phenomena in microscopic scale, meantime, the FEM that costs much less computational time and storage space covers the whole domain, with permitting to adopt different time step sizes for the time integration schemes in coarse and fine scales respectively. As a consequence, both computational accuracy and efficiency of the proposed BSM are greatly enhanced. With a bridging scale displacement (including translations and rotations) decomposition and based on the virtual work principle applied to the FEM nodes of the Cosserat continuum and the particle centers of the discrete particle assembly respectively, two decoupling sets of equations of motion of the combined coarse–fine scale system are formulated. The interfacial condition between the coarse and fine scale regions in the quasi-static and dynamic loading cases are presented and discussed. The non-reflecting boundary condition and its implementation, which is capable of effectively eliminating spurious reflected waves at the interfaces between the coarse and fine scale regions, are described in detail. The numerical results for 2D example problems demonstrate the applicability and advantages of the present BSM, and the performances of the non-reflecting boundary condition implemented to simulate dynamical responses in geo-structures composed of granular materials.

► We develop a bridge scale method for granular material.
► A discrete particle assembly – Cosserat continuum modeling is presented.
► The nonreflecting condition between coarse and fine scale regions is devised.