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Robust Inverse Homogenization of Elastic Microstructures

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Abstract

This paper combines shape optimization and homogenization techniques in searching for the optimal design of microstructures in elastic scaffolds. The development of materials with specific properties is of practical interest, for example, for medical applications or for the development of lightweight structures in aeronautics. In particular, the optimal design of microstructures leads to fundamental questions for elastic porous media: how to calculate a microstructure leading to a target effective Hooke tensor. We propose a robust approach to find a design that is as insensitive as possible to domain variations. Our strategy is based on the shape derivative for the problem of achieving a prescribed effective tensor. We demonstrate the applicability and feasibility of our approach through numerical experiments.

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Authors and Affiliations

  1. Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau, France

    Marc Dambrine & Salah Zerrouq

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  1. Marc Dambrine
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  2. Salah Zerrouq
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Correspondence to Marc Dambrine.

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Communicated by Siva Nadarajah.

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Dambrine, M., Zerrouq, S. Robust Inverse Homogenization of Elastic Microstructures. J Optim Theory Appl 199, 209–232 (2023). https://doi.org/10.1007/s10957-023-02266-5

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