Keywords: implementation of computational procedures, composite materials and structures, micro-mechanics models, domain decomposition, partitioning.

For many years, the use of composites in aeronautics seems to be of great interest. Even if today some essential structures are developed in composites, the characterization procedures of such materials and structures consists in a large number of tests. It shows how important it is to have a real confidence in models to reduce the cost of developments. A computational micromodel is established in order to simulate the damage mechanisms at any point of a laminated structure [1,2,3]. This rather simple model couples two approaches : the micromechanics which mainly studies the morphology of the degradation [4,5] and the mesomechanics which takes into account the degradation thanks to the damage continuum mechanics [6]. Therefore discrete mechanisms at the ply's scale such as transverse cracks and local delamination are introduced according to the "finite fracture mechanics". These degradations develop through a discrete model by the breaking of "minimum cracking surfaces" whose dimensions are chosen from energetical considerations. The surfaces break according to an energy release rate criterion which takes into account experimental observations such as the difference between initiation and propagation for small and thick plies. Continuum damage at the ply's scale (such as fiber matrix decohesions) are associated to diffuse damage. It is described through the continuum damage mechanics by introducing damage variable into the ply. The micromodel is then hybrid.

Unfortunately, to make the simulation robust, one has to introduce a large number of minimum cracking surfaces. This leads to prohibitive calculation costs if one uses current industrial codes. Improvements are made in order to couple this micromodel with a multiscale strategy based on homogenization in space [7].

A keypoint of this strategy is the splitting of the structure into sub-structures and interfaces. In this approach, minimum cracking surfaces coincide with some interfaces. Sub-structures (called cells) are made of an orthotropic damageable material to describe the continuous mechanisms. The interfaces have their own behaviour, they are perfect interfaces when no degradation occurs or interfaces with contact and friction when the criterion of failure is reached. The computation is then robust thanks to this discrete part of the model and avoids problems due to localization. To get as many degradations as possible, several dozen millions of cells are required and lead to problems with more than a billion degrees of freedom even for localized zones. Two scales (a macro and a micro) are introduced to improve the convergence of the iterative strategy and reduce the calculation cost from a factor 10 to 100.

The size of the problem is still important. Two improvements are then necessary. A third scale is used in order to approximate the global macro problem and reach reasonable costs. Then, to limit the number of calculations, micro problems are solved on some particular cells and the solution is rebuilt for the other cells by an interpolation. An particular attention is also taken for the implementation of the criterion for interfaces in the strategy. Several approaches have been tested to develop a simple computational criterion with a reduced calculation cost using both analytical expressions and localized problems.

We carried out basic simulations on cross-ply laminates with material properties representative of carbon-epoxy composites. These samples were assumed to be initially subjected to thermal loading due to the process, then to pure mechanical loading in tension. It seems that the computational model is capable of reproducing main basic features of classical experimental results. Extensions to complex geometry such as plate with holes show how performant the strategy is.

1

P. Ladevèze, "Multiscale computational damage modelling of laminate composites", in T. Sadowski, ed., Multiscale modelling of damage and fracture processes in composite materials, Springer-Verlag, 2005.

2

G. Lubineau, P. Ladevèze, D. Violeau, "Durability of CFRP laminates under thermomechanical loading: A micro-meso damage model", 66(7-8), 983-992, 2006. doi:10.1016/j.compscitech.2005.07.031

3

P. Ladevèze, G. Lubineau, D. Violeau, "A computational damage micromodel of laminated composites", 137(1-4), 139-150, 2006. doi:10.1007/s10704-005-3077-x

4

J. Nairn, "Matrix microcracking in composites, in Taljera-Manson, ed., Polymer Matrix Composites, Comprehensive Composite Materials", Ch.13, 403-432, Elsevier Science, 2000.

5

J. Berthelot, "Transverse cracking and delamination in cross-ply glass-fiber and carbon-fiber reinforced plastic laminates: Static and fatigue loading", Applied Mechanics Reviews, 56(1), 111-147, 2003. doi:10.1115/1.1519557

6

P. Ladevèze, E. LeDantec, "Damage modeling of the elementary ply for laminated composites", 43(3), 257-267, 1992. doi:10.1016/0266-3538(92)90097-M

7

P. Ladevèze, A. Nouy, "On a multiscale computational strategy with time and space homogenization for structural mechanics", 192, 3061-3088, 2003. doi:10.1016/S0045-7825(03)00341-4

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