Fem × dem multi-scale analysis of boundary value problems involving strain localization

Abstract

The paper presents a FEM × DEM multiscale modeling analysis of boundary value problems involving strain localization in cohesive granular materials. At the microscopic level, a discrete element method (DEM) is used to model the granular structure. At the macroscopic level, the numerical solution of the boundary value problem (BVP) is obtained via a finite element method (FEM) formulation. In order to bridge the gap between micro-and macro-scale, the concept of representative volume element (REV) is applied: the average REV stress and the consistent tangent operators are obtained in each macroscopic integration point as the results of DEM simulation. The numerical constitutive law is determined through the DEM modeling of the microstructure to take into account the discrete nature of granular materials. The computational homogenization method is described and illustrated in the case of a hollow cylinder made of cohesive-frictional granular material, submitted to different internal and external pressures. Strain localization is observed to occur at the macro scale in this simulation.