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  • Morphological models of heterogeneous materials

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    Stochastic geometry (external link) is a branch of modern mathematics, which is concerned with random geometric structures in the Euclidean space (external link), ranging from simple points or line segments to arbitrary closed sets. Typical problems of stochastic geometry arise in image processing and image reconstruction. Stochastic modeling and simulation of geometrical objects and statistica...
    Tags: random_setsstochastic_geometry
    Added by Martin on 2010-07-23 12:32


    Morphological models of heterogeneous materials Stochastic geometry (external link) is a branch of modern mathematics, which is concerned with random geometric structures in the Euclidean space (external link), ranging from simple points or line segments to arbitrary closed sets. Typical problems of stochastic geometry arise in image processing and image reconstruction. Stochastic modeling and simulation of geometrical objects and statistical analysis of the morphology of structures, e.g. shape and size of particles in composites, their surface, volume fractions, orientation etc. Here the geometrical material modeling of heterogeneous materials is considered. Besides composite materials, porous materials belong to the class of heterogeneous materials. Porous materials have the property that the elastic stiffness of one phase vanishes completely. The starting point of a stochastic material model are one or several 2D images (micro-sections) or a 3D image (computer tomograph) of the microstructure. After several image post-processing steps, the computation of stochastic parameters, which depend on the type of material, is performed. By using these computed parameters and specific assumptions, the structure of the material can simulated, i.e. realizations of the stochastic geometry can be computed in the computer. These realizations are representative volume elements (RVEs), which have the same statistical properties as a representative volume element of the real heterogeneous material. The benefit of such computed RVEs consists in the possibility to determine physical properties (e.g. flow resistivity, thermal, elastic, electromagnetic, and acoustic properties) of the heterogenous materials by using the corresponding properties of the single phases. Furthermore, the sensitivity of these physical properties with respect to the statistical parameters of the material can be analyzed without the necessity to produce any material variants.