Coupling multibody system and granular dynamics application to a 2D benchmark

摘要

We present a benchmark to experimentally validate the method we have developed to simulate mechanical devices interacting with granular media. Consequently the method we develop is able to solve problems involving bilateral and unilateral constraints. The mechanical device is modelled with the multibody system approach and is described by the use of relative coordinates. With these coordinates, the bilateral constraints are mainly due to loop-closure conditions (or specific bilateral constraints such as imposed screw-joint motion). The bilateral constraints are solved thanks to the coordinate partitioning method. The problem of contact dynamics, which introduces the unilateral constraints, is solved by a non-linear Gauss-Seidel procedure applied in the contacts coordinates. The procedure accounts for the constrained motion of the mechanism because the coordinate partitioning is also applied to the mapping between the contacts coordinates and the generalized coordinates. Consequently the solution of the unilateral constraints problem is locally compatible with the set of bilateral constraints coming from the mechanical system. The proposed planar benchmark consists of a modified four-bar mechanism blending a set of disks contained in a vibrating box. The numerical results reveals the influence of the vibration frequency on the granular compactness and thus the mechanism motion.