Two-scale microstructure construction by statistical correlation functions

Abstract

In this research, a new procedure is presented for two-scale construction of three-dimensional microstructures. Based on two-point correlation functions and phases recovery algorithm the fine and coarse scale microstructures are constructed separately for arbitrary volume fractions. All required correlation functions are calculated using an exponentially decreasing sinusoidal function that makes all constructed microstructures to be bicontinuous for a wide range of volume faction. Using the Boolean subtraction of fine scale microstructure from the coarse scale one, the intended multiscale microstructure is constructed. Connectivity evaluation of constructed microstructure reveals that even for low volume fractions, the connectivity of different phase regions will be established throughout the three-dimensional volume element that is crucial if conduction of heat, ion, electron, etc. is required. Another important property of the constructed microstructure is that, due to the periodic assumption, the final sections of the volume element gradually become similar to the initial ones in three dimensions and as a result it is possible to use the volume element as a unit cell to construct an arbitrary large structure with complete continuity, smoothness and isotropy.