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.
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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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DOI: https://doi.org/10.1007/978-3-319-10064-7_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10063-0
Online ISBN: 978-3-319-10064-7
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