Abstract
The unilaterality of non-penetration constraints, the velocity jumps which occur in case of collisions, the irregularity of the law of dry friction are 'nonsmooth' features of the dynamical systems in view. Numerical methods are presented, which face nonsmoothness without resorting to mollifying approximation procedures. A careful formulation of contact laws generates algorithms which, at every step of the time-discretization, are ready to face possible collisions on the same footing as permanent contacts. These algorithms prove efficient enough to treat on microcomputers or small workstations the dynamical motion of systems involving a few thousands of bodies. Granular materials are modelled as collections of spherical beads. The concerned numerical technique has recently permitted to discover a mechanism underlying the phenomenon of size-segregation in a granular material contained in a vertically shaken vessel. This mechanism, which connects segregation with the convection currents induced by boundary friction, has been exhibited independently by some experimentalists. The numerical assessment of boundary forces, presented here, throws some light on the generation of boundary currents.