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Random Tessellations and their Application to the Modelling of Cellular Materials

Part of the Lecture Notes in Mathematics book series (LNM,volume 2120)

Abstract

This chapter introduces various tessellation models and discusses their application as models for cellular materials. First, the notion of a random tessellation, the most well-known model types (Voronoi and Laguerre tessellations, hyperplane tessellations, STIT tessellations), and their basic geometric characteristics are introduced. Assuming that a cellular material is a realisation of a suitable random tessellation model, these characteristics can be estimated from 3D images of the material. It is explained how estimates are obtained and how these characteristics can be used to fit tessellation models to the observed structure. All analysis and modelling steps are illustrated using the example of an open cell aluminium foam.

Keywords

  • Cellular Material
  • Aluminium Foam
  • Voronoi Tessellation
  • Intrinsic Volume
  • Random Tessellation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Claudia Redenbach .

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© 2015 Springer International Publishing Switzerland

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Redenbach, C., Liebscher, A. (2015). Random Tessellations and their Application to the Modelling of Cellular Materials. In: Schmidt, V. (eds) Stochastic Geometry, Spatial Statistics and Random Fields. Lecture Notes in Mathematics, vol 2120. Springer, Cham. https://doi.org/10.1007/978-3-319-10064-7_3

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