A novel method for the 3D reconstruction of a microstructure from limited statistical information provided by 2D cross sections is developed. In the proposed approach, first full-set statistical information (two-point correlation functions) are extracted from 2D cross sections, and then an approximate 3D microstructure is realized based on them. The proposed method relies mainly on conditional probability theorem to establish explicit functional forms between two-point correlation functions extracted from 2D cross sections and full-set 3D statistics. For 3D realization, a novel phase-recovery algorithm is developed that captures prominent attributions of the microstructure. The salient feature of the proposed realization scheme is the ability to fully reconstruct 3D microstructures from statistical information provided by just one cross section for isotropic microstructures and two perpendicular cross sections for anisotropic ones. A number of illustrative examples are provided to demonstrate the accuracy and the versatility of the proposed scheme. The application of the method for the 3D realization of microstructure using an experimental dataset is demonstrated. Finally, the accuracy of the method in capturing and retaining essential features including volume fractions and characteristic attributions as well as the state of anisotropy and percolation of the phases is discussed.
The development of a predictive model for bone remodeling is becoming increasingly important for medical applications such as bone surgery or bone substitutes like prostheses. However, as bone remodeling is a complex multiphysics phenomenon and difficult to quantify experimentally, predictive numerical models remain, at best, phenomenologically driven. Patient dependency is often ignored as its influence is usually considered secondary, although it is known to play an important role over long periods of time. Another difficulty to study this patient dependency is the availability of experimental samples to carry out extensive analyses. Using our recently developed statistical reconstruction framework, a set of “bone like” microstructures with variety of distributions has been created to study pseudo “patient variabilities.” The method provides similar effective stiffness tensor, equivalent stresses, and strain energy distributions for the original and the statistically reconstructed samples. The main outcome of this study is the correlation of similar effective mechanical properties between samples when bone remodeling will depend on the local strain energy distribution as a function of each bone microstructure. It is expected that two different microstructures with equivalent bone volume fraction will lead to identical bone remodeling in a short period of time, whereas this needs to be proven for long term evolution. This work could be used to develop precise predictive numerical models while developing parametric studies on an infinite number of virtual samples and correlating patient dependency with more precise mechanobiological numerical models.
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).
A novel method for the optimization of the microstructure of a two-phase solid oxide fuel cell (SOFC) mixed ionic-electronic conductor (MIEC) cathode is presented. Two-point correlation functions (TPCFs) are used to manipulate the microstructure. At first, using an appropriate function, such as a decaying exponential multiplied by a sinusoidal function, initial full-set TPCFs are created. Based on the created TPCFs, a phase recovery algorithm is used, as a construction tool, to realize the three-dimensional (3D) porous microstructure of the SOFC. The reconstructed microstructures are evaluated based on the contribution of the geometrical attributes, such as tortuosity of the solid-phase and the active interfacial area, minimizing the cathode characteristic impedance. Shooting for a minimum solid-phase tortuosity and maximum active interfacial area of solid-and void-phase for a fixed volume fraction, a series of optimization simulations are carried out using two independent variables of autocovariance function as the design variables. Using this approach, it is possible to create very thick (or thin) pathways in the solid and void phases with small (or large) tortuosity and low (or high) interfacial area of the solid-void by applying various TPCF sets. By comparing the present results with some of the experimental ones reported in the literature, it is shown that the optimization process presented here can be used as a robust tool to design optimal microstructure with improved tortuosity and interfacial area for SOFCs and other similar bicontinuous applications.
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