Formulation and numerical implementation of micro-scale boundary   conditions for particle aggregates
  The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM), consistent with a micro-macro homogenization scheme formulated in the transition from a continuous to a discrete setting. The three classical types of boundary conditions (displacement, periodic and displacement) are implemented with a servo-control method. Two types of algorithms are developed, which consider or not an initial prediction for the displacement field of the particles. Additionally, to simulate in a more realistic manner the effect of macroscopic deformation on the micro-structure, a mixed type of boundary conditions is introduced, i.e. a combination of classical boundary conditions. The effectiveness of the algorithms is tested on a series of DEM simulations. The influence of the micro-structural morphology and of the size of the micro-structure on the overall response is finally investigated. 
J. Liu, E. Bosco, A.S.J. Suiker
cond-mat.soft