A DEM—FEM two scale approach of the behaviour of granular materials

Abstract

We study the macroscopic behaviour of granular material, as a consequence of the interactions of individual grains at the micro scale. A two‐scale approach of computational homogenization is considered. On the micro‐level, we consider granular structures modelled using the Discrete Element Method (DEM). Grain interactions are modelled by normal and tangential contact laws with friction (Coulomb’s criterion). On the macro‐level, we use a Finite Element Formulation (FEM). The upscaling technique consists in using the response of the DEM model at each Gauss point of the FEM discretisation to derive numerically the constitutive response. In this process, a tangent operator is generated together with the stress increment corresponding to the strain increment in the Gauss point. In order to get more insight on the consistency of the resulting constitutive response, we compute the determinant of the acoustic tensor associated with the tangent operator. This quantity is known to be an indicator of a possible loss of uniqueness locally, at the macro scale, by strain localisation in shear band. Different numerical studies have been performed, as listed hereafter. We have considered different number of grains in the REV cell. Periodic boundary conditions have been compared with the ordinary wall conditions.