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Multi Scale Random Sets: From Morphology to Effective Behaviour

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Progress in Industrial Mathematics at ECMI 2010

Part of the book series: Mathematics in Industry ((TECMI,volume 17))

Abstract

Complex microstructures in materials and in biology often involve multi-scale heterogeneous textures, that we model by random sets derived from Mathematical Morphology. Our approach starts from 2D or 3D images; a complete morphological characterization is performed, and used for the identification of a model of random structure. Simulations of realistic microstructures are introduced in a numerical solver to compute appropriate fields (electric, elastic, velocity, …) and to estimate the effective properties by numerical homogenization, accounting for scale dependent statistical fluctuations of the fields.

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Author information

Authors and Affiliations

  1. Centre de Morphologie Mathématique, Mathématiques et Systèmes, MINES ParisTech, 35, rue Saint-Honoré, F77300, Fontainebleau, France

    Dominique Jeulin

Authors
  1. Dominique Jeulin
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Correspondence to Dominique Jeulin .

Editor information

Editors and Affiliations

  1. Applied Math. and Numerical Analysis, University of Wuppertal, Gaußstr. 20, Wuppertal, 42119, Germany

    Michael Günther

  2. Applied Math. and Numerical Analysis, University of Wuppertal, Gaußstrasse 20, Wuppertal, 42119, Germany

    Andreas Bartel

  3. Corporate Research and Advance Engineeri, Robert Bosch GmbH, Robert-Bosch-Platz 1, Stuttgart, 70839, Germany

    Markus Brunk

  4. Applied Math. and Numerical Analysis, University of Wuppertal, Gaußstrasse 20, Wuppertal, 42119, Germany

    Sebastian Schöps

  5. Applied Math. and Numerical Analysis, University of Wuppertal, Gaußstrasse 20, Wuppertal, 42119, Germany

    Michael Striebel

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Jeulin, D. (2012). Multi Scale Random Sets: From Morphology to Effective Behaviour. In: Günther, M., Bartel, A., Brunk, M., Schöps, S., Striebel, M. (eds) Progress in Industrial Mathematics at ECMI 2010. Mathematics in Industry(), vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25100-9_45

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