Keywords: finite element, fracture mechanics.

A large number of problems in the field of solid mechanics deal with heterogeneous structures. Many of these problems can be dealt with successfully through a homogenization approach. However, there are several cases where the homogenization theory cannot be used. In these cases, one of the ways to solve numerically these problems is through an approach where the different constituents of the structure are modelled explicitly. This approach was not possible several years ago - partly because of the lack of computational power and memory requirements. It has now become possible to use such an approach to analyse multi-material forming processes as well as carry out structural analysis of multi-material structures. This paper describes the work we have carried out during these last years on these topics, by showing some results on various cases of application.

We first provide a short overview of the mechanical model and of the numerical techniques used. A global overview of mechanical models and numerical techniques for material processing simulations is provided in [1].

Finite element modelling of multimaterials structures first requires specific meshing techniques. We provide here some details on the mesher we have set up in order to carry out the meshing stage. Moreover, modelling of forming processes needs to take into account large deformations; since we use a reactualised Lagrangian method, we have to use a specific remeshing technique, which keeps track of interfaces between the constituents. We shall provide some details about this specific point.

We shall then present a first case dealing with the modelling of a fracture mechanics test for adhesively bonded joints. This case is detailed in [2]. It is an interesting case because it exhibits two aspects quite specific of multimaterial problems: meshing problems, as well as ill-conditioned systems.

We then introduce two cases dealing with large deformation for multimaterial systems. The first one is centred on the modelling of a consolidation process for multimaterial layers; more information on this case is provided in [4]. The second case deals with an assembling process - a self-piercing riveting process; [5] provides further details on this case. The large deformations involved in these two cases shows the need for an efficient remeshing technique.

In the last section, we deal with fracture mechanics and crack propagation modelling in multimaterial structures. We show some results on the numerical modelling of crack propagation in multimaterial structures. The basic strategy for carrying out this task is detailed in [6,7]. The crack propagation technique is based on the multi-material meshing/remeshing tool introduced previously. We wish in the longer term to investigate and predict relation between the forming process and the final mechanical properties of manufactured parts. The work carried out here is a first step in the setting up of a global optimization approach through numerical modelling of the forming process down to structural analysis for multimaterial structures. The same numerical tool has been in fact used to model all these cases.

1

J.-L. Chenot, F. Bay "An overview of Numerical Modeling Techniques", Journal of Materials Processing Technology, 1998. doi:10.1016/S0924-0136(98)00205-2

2

F. Bay, P.O. Bouchard, E. Darque-Ceretti, E. Felder, S. Scotto-Sheriff "Numerical and Experimental Analysis of a Fracture Mechanics Test of Adhesive Bonded Joints", Journal of Adhesion Science and Technology, 1999. doi:10.1163/156856199X00758

3

Y. Chastel, C. Magny, F. Bay "An elastic-viscoplastic finite element model for multimaterials: formulation and experimental validation", Engineering Computations, Vol. 15, No 1, pp. 139-150, 1998. doi:10.1108/02644409810200730

4

P.O. Bouchard, F. Bay, Y. Chastel, I.Tovena "Crack Propagation Modelling Using an Advanced Remeshing Technique", Computer Methods in Applied Mechanics and Engineering, 189, pp. 723-742, 2000. doi:10.1016/S0045-7825(99)00324-2

5

P.O. Bouchard, P. Lasne, "Numerical modeling of riveted joint structures - From riveting process modeling down to structural analysis", Esaform Conference, Trondheim, April 2004.

6

P.O. Bouchard, F. Bay, Y. Chastel, "Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria", Computer Methods in Applied Mechanics and Engineering, vol. 192, pp 3887-3908, 2003. doi:10.1016/S0045-7825(03)00391-8

7

P.O. Bouchard, F. Bay, "Computation of the Strain Energy Release Rate using the Gtheta method", Association Brésilienne de Métallurgie (ABM) 58 Annual Congress, Rio de Janeiro (Brazil) July 2003.

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