In this work, we present a numerical framework for the modelling of friction and wear of rough surfaces. This framework is based on the Discrete Element Method (DEM), and aims to mimic the inner microstructure of polycrystalline materials. For this purpose, a sample generation program has been developed, into which each grain of this microstructure is represented by a rigid 3D Voronoi cell. A typical sample generated by this program represents a body composed of a degradable and a non-degradable parts, both of which presenting several well-controlled features: size and geometry of the grains (controlled by the positions of the seeding points of the Voronoi tessellation), roughness of the surface and of the underlying substrate (controlled by the means of the frequency content and possible anisotropy of this roughness), and periodic or planar lateral boundaries. These features enable the modelling of a large number of contact situations with a great flexibility. After presenting in details the algorithmic routines developed for this sample generation, we detail some examples of generated samples and we provide insight of their implementation in the implicit discrete code LMGC90. An Illustrative simulation is then performed to demonstrate the ability of this framework to model diverse situations of friction and wear, by representing accurately the creation and the rheology of third bodies. (C) 2015 Elsevier Ltd. All rights reserved.