Comparison and Coupling of Algorithms for Collisions, Contact and Friction in Rigid Multi-body Simulations

Numerous works in Computational Mechanics are dedicated to the simulation of multi-body systems with contact and friction. The case of dense multi-contact assemblies is one of the more complex one: the problem have often a large number of unknowns and the non uniqueness of solutions is usual. Moreover this problem becomes harder when the Coulomb’s friction or more complex laws are introduced. In this context, fast and robust solvers are required to carry out relevant mechanical studies. In a general way, these performances can be improved if the special structure of the problem can be exploited. For multi-body systems with contact and friction, the sparse block structured matrices involved in the time-discretised problem is one such structure. Our work is embedded in the Non Smooth Contact Dynamics framework introduced by J.J. Moreau. The method is based on a time-stepping integrator without explicit event-handling procedure and an unilateral contact/impact formulation associated with the Coulomb’s friction. In this paper, different iterative algorithms such as Gauss–Seidel, projected conjugate gradient and direct ones such as Lemke’s method and Quadratic Program solvers are compared. The efficiency of the methods is compared in terms of complexity, convergence criterion and of CPU time. Methods are illustrated with the simulation of granular assemblies. All of these 3D frictional contact simulations are performed with ConF&TiS and the SICONOS/Numerics library.