Résumé
Numerous works in computational mechanics are dedicated to multi-body systems [1], [2]. This leads to the use of various methods to simulate the static or dynamic evolution of complex systems. The case of dense multi-contact assemblies is one of the more complex one: the problem have often a large number of unknown and have a infinity of solution due to the definition of the matrix of the system. Moreover this problem become harder when friction or more complex laws are introduced in the system. Thus we need fast and robust solvers to perform mechanical studies. These performances can be increased when the special problem structure is considered (sparse matrices, block structured problem).
Our work is based on the Non Smooth Contact Dynamic framework introduced by Moreau [3]. The method uses a time-stepping integrator without explicit event-handling procedure and an unilateral contact impact formulation associated to Coulomb’s friction. In this paper we use and compare different iterative algorithms such as Gauss-Seidel, projected conjugate gradient and direct ones as Lemke and Quadratic programming solvers [4]. The efficiency of the methods is compared in terms of complexity, convergence criterion and of CPU time.
To illustrate the results, we focus on granular assemblies. 3D frictional contact simulations are performed with ConF&TiS and the Numerics library of the siconos project.