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Optimization of graded microstructured materials through a deformation mapping

The aim of this work is to present a new numerical method in order to optimize the shape of a microstructured multiphasic material, whose microstructure evolves on the macroscopic scale, so that a given cost functional associated to the material is minimized under some particular loading scenarii. Such a method should satisfy at least two requirements :

1) the reconstruction of a truly manufacturable material should be possible ;

2) the connectivity of at least one of the phases composing the material should be ensured.

The idea of our approach is to represent the structure of such a material as a macroscopic deformation, which is to be optimized upon, of a reference periodic microstructure. Such an optimization problem can be defined on the homogenized level, or not. Theoretical existence results associated with this approach will be presented, as well as numerical examples on 2-dimensional test cases. (Joint work with Claude Le Bris, Frédéric Legoll, Günter Leugering and Michael Stingl)


CMAP UMR 7641 École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex France, Tél: +33 1 69 33 46 23 Fax: +33 1 69 33 46 46