ABSTRACT
This chapter is devoted to the fundamental concepts dealing with the quasi-static behavior of granular materials, in which inertia effect has little effect. Defining discrete mechanical quantities for such elements, we can formulate 3D discrete mechanics for granular assemblies, as in 2D. The heterogeneous characteristics of the grains and their configuration are very important in mechanical features of granular material and the homogenization theory is one of the most useful techniques. The ‘homogenization process’ is of great interest for materials whose behavior is essentially governed by the microstructure and its evolution. While the average field theory deals with field equations, the homogenization theory applies the singular perturbation analysis of the governing equation. Although the homogenization theory is based on the solid mathematical procedure of taking multi-scale perturbation for the displacement, it is possible to give a more physical interpretation.
