Efficient three‐phase reconstruction of heterogeneous material from 2D cross‐sections via phase‐recovery algorithm

Abstract

Digital reconstruction of a complex heterogeneous media from the limited statistical information, mostly provided by different imaging techniques, is the key to the successful computational analysis of this important class of materials. In this study, a novel approach is presented for three-dimensional (3D) reconstruction of a three-phase microstructure from its statistical information provided by two-dimensional (2D) cross-sections. In this three-step method, first two-point correlation functions (TPCFs) are extracted from the cross-section(s) using a spectral method suitable for the three-phase media. In the next step, 3D TPCFs are approximated for all vectors in a representative volume element (RVE). Finally, the 3D microstructure is realized from the full-set TPCFs obtained in the previous step, using a modified phase-recovery algorithm. The method is generally applicable to any complex three-phase media, here illustrated for an SOFC anode microstructure. The capabilities and shortcomings of the method are then investigated by performing a qualitative comparison between example cross-sections obtained computationally and their experimental equivalents. Finally, it is shown that the method almost conserves key microstructural properties of the media including tortuosity, percolation and three-phase boundary length (TPBL).

Influence of bone microstructure distribution on developed mechanical energy for bone remodeling using a statistical reconstruction method

“…An improvement of this method was recently proposed by Hasanabadi et al [54,55] on a new approximation for the calculation of the TPCFs for a 3D RVE. We assume that the TPCF of an identical vector in a given RVE in two parallel planes are approximately equal.…”

“…As shown in Figure 1, an arbitrary vector r in space can be decomposed into r z and r xy . If the TPCFs of two planes, xy and yz are known, the full set of TPCF for 3D RVE can be approximated [55] based on…”

“…Following our previous works [54,55], several bone microstructures were generated with identical effective stiffness tensor to evaluate the effect of the geometrical distribution of bone microstructure on local energy. This enabled to study many different scenarios (different virtual samples), using the full spectrum of two-point correlation function (TPCF) for eigen microstructure, without the need of extracting real bone samples.…”

A Generalized and Modular Framework for Digital Generation of Composite Microstructures

“…This is because, with a small set of statistics, the number of potential solutions is quite large. The complete set of two-point spatial correlations has been targeted in some recent microstructure generation efforts [27,38]. Since these approaches employ optimization strategies, they implicitly assume that there is an underlying absolute target to be matched.…”

“…In other words, similar to the case of texture synthesis, these methods target the reference strongly, and only weakly target the population from which the reference was sampled. Furthermore, most phase recovery approaches [27,38] can be applied only when the complete set of two-point spatial correlations are available.…”