Keywords: multiscale computational method, transient dynamic, parametric study, domain decomposition, contact, friction.

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 appropriate and efficient computational method is of vital importance.

The aim of this work is to develop an efficient strategy for the parametric analysis of dynamic problems with multiple contacts. 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 an assembly into substructures and interfaces. Within each substructure, the problem is solved using the finite element method and an iterative scheme based on the multiscale LArge Time INcrement (LATIN) method [2]. The objective is to calculate a large number of design configurations [3], each of which corresponds to a set of values of all the variable parameters (friction coefficients, prestresses) introduced into the mechanical analysis. Here, using the capabilities of the multiscale LATIN method, instead of carrying out a full analysis for each design configuration, we propose to reuse the solution of a particular problem with one set of parameters in order to solve similar problems with other sets of parameters) [4]. The multiscale LATIN method is a mixed method which deals with both velocities and forces at the interfaces simultaneously and solves a homogenized macroscopic problem in order to accelerate the convergence of the numerical scheme.

First, we introduce the multiscale 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. Then, we address the details of the specific treatment of the interfaces which ensures continuity of loads and velocities. Finally, we illustrate the efficiency of the method through a parametric study of three-dimensional examples.

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

P. Ladevèze, O. Loiseau, D. Dureissex, "A micro-macro and parallel computational strategy for highly heterogeneous structures", Int J for Numerical Methods in Engineering, 52, 121-138, 2001. doi:10.1002/nme.274

3

K.S. Krishnamurthy, P. Mahajan, R.K. Mittal, "A parametric study of the impact response and damage of laminated cylindrical composite shells", Composites Science and Technology, 61, 1655-1669, 2001. doi:10.1016/S0266-3538(01)00015-X

4

P.A. Boucard, L. Champaney, "A suitable computational strategy for the parametric analysis of problems with multiple contact", Int J for Numerical Methods in Engineering, 57, 1259-1282, 2003. doi:10.1002/nme.724

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