Robust Inverse Homogenization of Elastic Microstructures

Marc Dambrine () and Salah Zerrouq
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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

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 1, No 7, 209-232

Abstract: 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.

Keywords: Scaffold structures; Inverse homogenization; Robust shape optimization; 49K20; 49Q10; 74Q05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02266-5

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