Keywords: impact, damage mesomodel, fracture prediction, computation, domain decomposition, dynamics.

In a previous work done at LMT Cachan in collaboration with CE Gramat, a modeling of a 3D C/C composite at the mesoscale (scale of the matrix blocks, yarns sections, interfaces) including damage, sliding and compaction has been proposed and identified (see [1,2]). These non-linearities have to be taken into account to represent correctly the mesodynamics of the material. Moreover, in order to represent accurately the geometry of the mesoconstituents (see figure 1a for characteristic lengths), we need at least 10,000 DOFs per mm.

Thus, the 3D calculation of the shock behaviour of this material at such a scale leads to computations of very large size and highly non-linear. The approach deals with a domain decomposition strategy in order to :

• decrease the numerical cost of an analysis and make it parallel
• have a specific treatment of the interface

We extend a mixed domain decomposition method used in dynamics for the cases where the non-linearities were concentrated at the interface (see [3]) to the case where both the interfaces and the substructures have a non-linear behaviour. The method is based on three main ideas:

• Decomposition into substructures and interfaces
  In the case of a 3D C/C, a natural decomposition consists in choosing the mesoconstituents as the substructures. Thus, the numerical interfaces are the interfaces between the different mesoconstituents, which play a very important role in the behavior of the material. Doing so, we see a strong relation between mesomodeling and mesocomputing.
• Splitting of the difficulties
  The second step consists in splitting the difficulties into two groups. The first group of solutions ( ) is composed of the solutions of the dynamic equilibrium in each substructure defined over the whole time interval .

  The second group of solutions ( ) is composed of solutions verifying the constitutive relation on each interface and in each mesostructure over the whole time interval .

  The solution of the problem ( ) is the only solution which satisfies the requirements of both groups (equilibrium and constitutive relations).

• Iterative resolution: the Latin method
  The idea is then to find alternatively a solution in and in following search directions (see [3] for details).

The result of a parallel 3D computation with linear substructures and contact interfaces is shown in figure 1b.

1

O. Allix, M. Dommanget, M. Gratton, P.L. Héreil, "A multi-scale approach for the response of a 3D Carbon/Carbon Composite under shock loading", Composite Science and Technology, 61, 409-415, 2001. doi:10.1016/S0266-3538(00)00111-1

2

P.L. Héreil, O. Allix, M. Gratton, "Shock behavior of 3D carbon/carbon composite", J. de Physique IV, Colloque C3, 7, 529-534, 1997. doi:10.1051/jp4:1997391

3

P. Ladevèze, H. Lemoussu, P.A. Boucard, "A modular approach to 3D impact computation with frictional contact", Computers & Structures, 78, 45-52, 2000. doi:10.1016/S0045-7949(00)00094-8

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