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Robust Inverse Homogenization of Elastic Microstructures

Author

Listed:
  • Marc Dambrine

    (Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP)

  • Salah Zerrouq

    (Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP)

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.

Suggested Citation

  • Marc Dambrine & Salah Zerrouq, 2023. "Robust Inverse Homogenization of Elastic Microstructures," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 209-232, October.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:1:d:10.1007_s10957-023-02266-5
    DOI: 10.1007/s10957-023-02266-5
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