Stochastic Geometry Models

Geometric Modelling of Micro- and Nanostructures

  • Fitting of stochastic geometric models
  • Reconstruction of materials
  • Virtual material design and simulation of materials properties

Based on 3D and 2D images, macroscopic homogeneous materials, which are heterogeneous on a microscopic scale, are modelled. Therefore a suitable model is chosen. By 3D image analysis, geometric features like porosity and surface density can be determined. The model parameters are computed from these features. In simulated realizations of the model, other material features, e.g. permeability and acoustical absorption, can be calculated.


Using a Model

  • is the only chance if 3D images are not available
  • enables calculations in a variety of realizations. Hence, it is possible to allow for the areal variety of the material
  • makes virtual experiments possible: testing the influences of minimal changes of the geometry without really creating the material

The basis are model from stochastic geometry like Boolean model, line processes and mosaics. The macroscopic homogeneity is accorded to using stationary models. This means that it is not important from which area of the material the probe was taken.

Examples for Modelling of Microstructures