Towards a weakly intrusive space-time multi-scale strategy for the prediction of delamination under impact.
Résumé
Composite laminated materials are increasingly employed in aeronautics but can be prone to extensive delamination when submitted to impact loads such as from bird strikes. For most practical purposes, current analysis tools allow to determine whether a given structure can sustain given impact loads while appropriate safety margins are considered. In order to improve a given design, further insight needs to be gained into the complex interactions associated with impact on composites. The need to be able to perform virtual delamination testing, that is to be able to predict the extension of damage under impact, becomes essential to engineering workflows. In that case the use of a meso-scale modeling scheme for laminates, where individual modeling of the plies and interfaces are introduced, seems desirable. However, the computational cost associated with such modeling schemes for large structures would be prohibitively high for the engineering practice, as the precise study of the damage and failure response requires the consideration of phenomena encompassing multiple spatial scales and temporal scales. In order to construct an efficient numerical scheme, the basic idea is that while a rather detailed mesoscale model could be used to simulate delamination where needed, the rest of the structure could be described by a less detailed more economical macroscale model. The paper will first discuss in broad terms the possibility to adapt a commercial software package (such as Abaqus) to deal as efficiently as possible with such a multi-scale scheme. Estimates of potential advantages of multi-scale strategies compared to monolithic solutions for industrial applications are also given. In order to efficiently follow the delamination front propagation, the classical Domain Decomposition would have to be coupled with a re-meshing technique, which is costly and complex to implement. The paper will present the basis of a proposed less intrusive approach, called the Substitution method. The method is designed in such a way that is possible to make use of an unchanged coarse macro model for the whole structure and to couple it with an evolutive meso-scale analysis where needed. The computational price to pay is that the method is "locally" iterative. Two versions of the Substitution method have been developed, based on two different formulations on how to couple the macro and meso models. A weakly intrusive version of the method developed in has first been obtained. It leads to satisfying results but with a level of dissipated energy difficult to control. Therefore a second formulation based on has been developed which avoids the precedent drawback. First simple applications of this method in the case of the propagation of delamination under impact should be presented during the conference.