The Application of Spectral Analysis in the Numerical Homogenization of Non-Periodic Structures

摘要

Homogenization methods are applied to calculate effective material properties and material models of structured materials considering the microstructural effects. These numerical homogenization methods are based on different physical and mathematical assumptions. One method is the homogenization for periodic structures adapted from the asymptotic expansion theory. A methodology was developed to make the application of the homogenization for periodic structures possible for non-periodic structured materials. The focus of this article is on the application of spectral analysis on microstructure models of non-periodic materials. The spectral analysis is adapted for the investigation of the distribution of microstructural defects like pores, cracks and micro cracks. Furthermore, an algorithm based on the spectral analysis of the structures is presented to estimate partial porosities for the implementation in a periodic model of the structure. The algorithm was investigated in the calculation of effective material properties of plasma sprayed ceramic thermal barrier coatings and in the investigation of open porous metal foams.