Keywords: multiscale computational method, transient dynamics, domain decomposition, LATIN method, contact, friction, assembly.

Modeling and simulation have an important role in engineering and design departments and raise multiple problems, particularly in dynamics in the case of large assemblies with connections. These connections play a major role in the dimensioning process because they are subject to highly nonlinear local phenomena (contact and friction) which are even more important in fast transient dynamic problems and require very fine meshes in order to be represented correctly [1]. Therefore, the choice of an efficient computational method is of vital importance to simulate such problems within reasonable calculation time.

Among the methods usually used to deal with these problems in dynamics, one can quote the FETI method (often a qualified dual Schur method) applied to transient response simulations [2]. The dual substructuring method can be associated with multispace-multiscale methods: for example, in [3].

The aim of the paper is to build a specialized method to answer the problems previously described resulting from the fact that the non-linearities are localised at the connections. The applications concern elastic structural assemblies in dynamics with local nonlinearities, such as unilateral contact with friction. Our approach is based on a decomposition of the assembly into substructures and interfaces. An iterative scheme based on the multiscale LArge Time INcrement (LATIN) method [4] is used to solve the sub-structured problem. The multiscale LATIN method is a mixed method which deals with both velocities and forces at the interfaces simultaneously. Within each substructure, the problem is solved using the finite element method. This strategy has already been applied successfully to a variety of static problems. Here, the present work concerns the extension of the multiscale approach to dynamic problems. The multiscale approach consists in solving a homogenized macroscopic problem in order to accelerate the convergence of the iterative scheme.

First, we introduce the multiscale approach in the LATIN strategy for the dynamic case, focusing particularly on the construction of the "macroscopic" problem in space, which has a less conventional meaning in this case than in statics. This iterative computational strategy is also suitable for parallel computing on a PC cluster. It allows problems to be computed with a large number of degrees of freedom. This strategy was programmed in C++ in the framework of the finite element platform developed at the LMT Cachan. Librairies such as MPI and METIS are used for the parallelization of the strategy. We present the property of this parallel algorithm and illustrate its efficiency through three-dimensional examples among which some of them include several hundred contact interfaces.

1

J.O. Hallquist, G.L. Goudreau, D.J. Benson, "Sliding interfaces with contact-impact in large-scale lagrangien computations", Computer Methods in Applied Mechanics and Engineering, 51, 107-137, 1985. doi:10.1016/0045-7825(85)90030-1

2

C. Farhat, P.S. Chen, J. Mandel, "A scalable Lagrange multiplier based domain decomposition method for time-dependent problems", Int Jal for Numerical Methods in Engineering, 38, 3831-53, 1995. doi:10.1002/nme.1620382207

3

A. Gravouil, A. Combescure, "Multi-time-step and two-scale domain decomposition method for non-linear structural dynamics", Int Jal for Numerical Methods in Engineering, 58, 1545-69, 2003. doi:10.1002/nme.826

4

P. Ladevèze, D. Néron, P. Gosselet, "On a mixed and multiscale domain decomposition method", Computer Methods in Applied Mechanics and Engineering, 196, 8, 1526-40, 2007. doi:10.1016/j.cma.2006.05.014

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