Application of statistical functions to the numerical modelling of ceramic foam: From characterisation of CT-data via generation of the virtual microstructure to estimation of effective elastic properties

摘要

This paper illustrates a numerical methodology to quantify and recreate the microstructure of a ceramic foam using statistical functions and physical descriptors (together referred to as microstructure descriptors). The microstructure descriptors were employed to characterize a real foam material obtained from X-ray tomography (CT) scans. The statistical functions were further used to determine an appropriate size of a statistical volume element (SVE) within the foam sample to be further used in numerical determination of effective elastic properties. A ranking method was also developed to reduce the number of realizations of SVEs used in this calculation. Further, a novel reconstruction procedure was developed to synthesize artificial microstructure of the foam material that had the same microstructure descriptors as the real foam sample. Effective elastic properties of these artificial microstructures were determined as well. Comparison of these properties with experimental results showed that the statistical functions can be used to minimize the computational effort required for determining effective elastic properties of real microstructures. Further, the reconstruction methodology generates microstructure that matches the real microstructure not only in terms of its microstructural descriptors but also in terms of the effective elastic material properties.