DEM-FEM Multiscale Analysis of Geomaterials Boundary Value Problems

Besides long-standing works on experimental characterisation of geomaterials in laboratory tests computational geomechanics has been the subject of theoretical and numerical works for a long while.
Recently, multi-scale analysis using a numerical approach of the homogenisation of the microstructural behaviour of materials to derive the constitutive response at the macro scale has become a new trend in numerical modelling. DEM takes part of this multi-scale analysis as a microscale configuration for each one of the integration points of a macroscale FEM scheme. Compared with analytical constitutive law models, this approach allows us to take into account in a natural way the inherent anisotropy and rheology of the material and at the same time to perform real-size macroscale problems which would be impossible with pure DEM code. The counterpart of this approach is linked to the computational cost, nevertheless, while in a analytical law model the critical part of the computation is the solver of the global stiffness matrix, in the DEM-FEM approach the critical part is the integration of the microstructure, which can be efficiently optimized using parallel computing paradigms, this possibility makes the DEM-FEM code a promising candidate for continuum mechanics multiscale modelling.
An implementation of the FEM-DEM method in the FEM code Lagamine (ULg) is presented, and representative results are discussed, including aspects related to strain localisation in this context.