Modeling as a Tool

Models for cellular materials are random tessellations, i. Filling systems of non-overlapping polytopes. A particularly flexible model are Laguerre tessellations.

Modelling of Microstructures: Foams

In many applications, it is important to understand how the micro structures influence physical properties of cellular materials as for instance permeability, acoustic or thermal insulation, stiffness. Models matching the geometric features of the micro structures are a powerful tool to investigate this link.

Laguerre Tessellations

Models for cellular materials are random tessellations, that is space-filling systems of non-overlapping polytopes. A particularly versatile model are Laguerre tessellations - a generalization of the well-known Voronoi tessellation allowing to control the cell sizes much better: Each generating point is assigned a weight that can be interpreted as a sphere radius. The cell volume distribution of a Laguerre tessellation generated by a system of non-overlapping spheres is closely related to the sphere volumes.

Original foam
© Photo ITWM

Original foam

Sphere packing
© Photo ITWM

Sphere packing

Model
© Photo ITWM

Model

The model is fit by minimizing a distance function between several characteristics of the model and the real microstructure where the latter are measured from 3D image data. Modelling combined with numerical simulation of materials properties enables optimization of the microstructure.

Original
© Photo ITWM

Original

Sphere packing
© Photo ITWM

Sphere packing

Model
© Photo ITWM

Model

Publications

  • I. Vecchio, C. Redenbach, K. Schladitz
    Angles in Laguerre Tessellation Models for Solid Foams
    Computational Materials Science, Volume 83, 15 February 2014, Pages 171-184, ISSN 0927-0256.
    Article.
     
  • C. Redenbach, O. Wirjadi, S. Rief, A. Wiegmann
    Modelling of Ceramic Foams for Filtration Simulation.
    Advanced Engineering Materials 13 (3), S. 171–177, 2011.

  • C. Redenbach
    Microstructure Models for Cellular Materials.
    Computational Materials Science 44 (4), S. 1397-1407, 2009.

 

Partner

Dr. Claudia Redenbach, Technische Universität Kaiserslautern, AG Statistik