Bridging the micro and macro for granular media: A computational multi-scale paradigm

We present a hierarchical multi-scale framework to model geotechnical problems relevant to granular media. The framework employs a rigorous hierarchical coupling between the Finite Element Method (FEM) and the Discrete Element Method (DEM). The FEM is used to discretise the macroscopic geometric domain of a boundary value problem into a FEM mesh. A DEM assembly with memory of its loading history is embedded at each Gauss integration point of the mesh to receive the global deformation from the FEM as input boundary conditions and is solved for the incremental stress-strain relation at the specific material point to advance the FEM computation. The hierarchical framework helps to avoid the phenomenological nature of conventional continuum approaches of constitutive modelling and meanwhile retains the computational efficiency of the FEM in solving large-scale Boundary Value Problems (BVPs). By virtue of its hierarchical structure, the predictive power of the proposed method can be further unleashed with proper implementation of parallel computing techniques. By corroborating the rich information obtained from the particle level with the macroscopically observed responses, the framework helps to shed light on a cross-scale understanding of granular media. We demonstrate the predictive capability of the proposed framework by simulations of shear localisations in monotonic biaxial compression and cavity inflation in a thick-walled cylinder, as well as liquefaction and cyclic mobility in cyclic simple shear tests. © 2015 Taylor & Francis Group