SPECTRAL METHODS IN THE STATISTICAL DESCRIPTION AND DESIGN OF MICROSTRUCTURE

摘要

Various tools are useful in the design of materials from texture and related higher order structure statistics. This paper presents recent results in two key areas - homogenization methods linking the material structure to its properties, and reconstruction techniques that produce material realizations from the statistics.Homogenization techniques that are based upon material statistics captured by correlation functions have been available for several decades. With recent increases in computational power, and with the added efficiencies of spectral methods, attention has returned to these methods as viable inputs to multiscale models. One such method that involves a more complex integration scheme than the typical Kroner-type approach, is the strong contrast formulation pioneered by Brown, and more recently developed by Torquato. In this paper we utilize spectral techniques to apply the strong contrast formulation to the computationally demanding case of polycrystalline materials, and discuss the potential benefits to material design.Another important capability in the statistical modeling, analysis and design of materials involves the reconstruction of statistical data in order to recover detailed realizations that can be used in deterministic models. Popular reconstruction techniques such as simulated annealing take large amounts of computational power and time to create relatively small realizations. Recent work, based upon image analysis methods, has resulted in dramatic increases in speed. These advances in reconstruction capabilities are presented and some of the issues inherent in the approach are discussed as they relate to material design.