A Two-Scale Model of Granular Materials

A concurrent two-scale and two-method approach for modeling the mechanical behavior of dry frictional non-cohesive granular materials is presented. In domains of large eventually discontinuous deformation the material is modeled on the grain scale using a three-dimensional discrete element method. In the remaining domain the material is considered continuous and modeled by the finite element method using an elasto–plastic constitutive equation whose parameters are fit to the particle model via a homogenization scheme. The discrete and finite element models are coupled at the interface by the Arlequin method. An overlapping domain is introduced where the overall virtual work is interpolated between both models and compatibility is assured by kinematic constraints. For this purpose the discrete particle displacements are split into a fine and coarse scale part and equality of the coarse scale part and the continuum solution is enforced through the penalty method.