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Topological Optimization with Interfaces

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Architectured Materials in Nature and Engineering

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 282))

Abstract

Design of architectured materials and structures, whether in nature or in engineering, often relies on forms of optimization. In nature, controlling architecture or spatial heterogeneity is usually adaptive and incremental. Naturally occuring architectured materials exploit heterogeneity with typically graded interfaces, smoothly transitioning across properties and scales in the pursuit of performance and longevity. This chapter explores an engineering tool, topology optimization, that is at the frontier of designing architectured materials and structures. Topology optimization offers a mathematical framework to determine the most efficient material layout for prescribed constraints and loading conditions. In engineering, topology optimization is identifying designs with interfaces, materials, manufacturing methods, and functionalities unavailable to the natural world. The particular focus is on the variety of roles that interfaces may play in advancing architectured materials and structures with topology optimization.

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Notes

  1. 1.

    Plasma and other states of matter that occur under extreme conditions are not considered.

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Acknowledgements

This material is, in part, based upon work supported by the National Science Foundation under Grant No. 1538125.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA, 18015, USA

    N. Vermaak

  2. SIMaP, CNRS, Université Grenoble, 38000, Grenoble, France

    G. Michailidis, A. Faure, G. Parry, R. Estevez & Y. Bréchet

  3. Laboratoire J.L. Lions (UMR 7598), University Paris Diderot, Batiment Sophie Germain. 5 rue Thomas Mann, 75205, Paris, CEDEX 13, France

    F. Jouve

  4. CMAP, Ecole Polytechnique, 91128, Palaiseau, Cedex, France

    G. Allaire

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  1. N. Vermaak
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  2. G. Michailidis
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  4. G. Parry
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  6. F. Jouve
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  7. G. Allaire
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Corresponding author

Correspondence to N. Vermaak .

Editor information

Editors and Affiliations

  1. Department of Materials Science and Engineering, Monash University, Clayton, VIC, Australia

    Yuri Estrin

  2. SIMAP, Institut Polytechnique de Grenoble, Saint-Martin d’Hères, France

    Yves Bréchet

  3. Department of Chemistry and Physics of Materials, University of Salzburg, Salzburg, Austria

    John Dunlop

  4. Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, Potsdam, Germany

    Peter Fratzl

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Vermaak, N. et al. (2019). Topological Optimization with Interfaces. In: Estrin, Y., Bréchet, Y., Dunlop, J., Fratzl, P. (eds) Architectured Materials in Nature and Engineering. Springer Series in Materials Science, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-11942-3_6

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