This paper presents ways for modeling the unilateral contact with friction between solids in order to simulate a collection of polyhedrons during evolution. In a first stage 2D problems of polygon collections are explored, then the friction conditions are easy to take into account by several available equivalent modeling. In a second stage 3D problems of polyhedron collections are considered. The aim of this paper is to propose efficient algorithm to solve the 3D numerical problems in granular material simulations.

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