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Computational Homogenization of Architectured Materials

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Architectured Materials in Nature and Engineering

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

Abstract

Architectured materials involve geometrically engineered distributions of microstructural phases at a scale comparable to the scale of the component, thus calling for new models in order to determine the effective properties of materials. The present chapter aims at providing such models, in the case of mechanical properties. As a matter of fact, one engineering challenge is to predict the effective properties of such materials; computational homogenization using finite element analysis is a powerful tool to do so. Homogenized behavior of architectured materials can thus be used in large structural computations, hence enabling the dissemination of architectured materials in the industry. Furthermore, computational homogenization is the basis for computational topology optimization which will give rise to the next generation of architectured materials. This chapter covers the computational homogenization of periodic architectured materials in elasticity and plasticity, as well as the homogenization and representativity of random architectured materials.

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Notes

  1. 1.

    http://www.zset-software.com/.

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Authors and Affiliations

  1. Laboratoire PIMM, Arts et Métiers-ParisTech, CNRS, Cnam, 151 boulevard de l’Hôpital, 75013, Paris, France

    Justin Dirrenberger

  2. Centre des Matériaux, MINES-ParisTech, CNRS UMR 7633, BP 87, 91003, Evry cedex, France

    Samuel Forest

  3. Centre de Morphologie Mathématique, MINES-ParisTech, 35 rue St-Honoré, 77300, Fontainebleau, France

    Dominique Jeulin

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  1. Justin Dirrenberger
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  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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Dirrenberger, J., Forest, S., Jeulin, D. (2019). Computational Homogenization of Architectured Materials. 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_4

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