A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions

The main goal of our research is to develop an effective method with a wide range of applications for the statistical reconstruction of heterogeneous microstructures with compact inclusions of any shape, such as highly irregular grains. The devised approach uses multi-scale extended entropic descriptors (ED) that quantify the degree of spatial non-uniformity of configurations of finite-sized objects. This technique is an innovative development of previously elaborated entropy methods for statistical reconstruction. Here, we discuss the two-dimensional case, but this method can be generalized into three dimensions. At the first stage, the developed procedure creates a set of black synthetic clusters that serve as surrogate inclusions. The clusters have the same individual areas and interfaces as their target counterparts, but random shapes. Then, from a given number of easy-to-generate synthetic cluster configurations, we choose the one with the lowest value of the cost function defined by us using extended ED. At the second stage, we make a significant change in the standard technique of simulated annealing (SA). Instead of swapping pixels of different phases, we randomly move each of the selected synthetic clusters. To demonstrate the accuracy of the method, we reconstruct and analyze two-phase microstructures with irregular inclusions of silica in rubber matrix as well as stones in cement paste. The results show that the two-stage reconstruction (TSR) method provides convincing realizations for these complex microstructures. The advantages of TSR include the ease of obtaining synthetic microstructures, very low computational costs, and satisfactory mapping in the statistical context of inclusion shapes. Finally, its simplicity should greatly facilitate independent applications.

[1]  Xiaohai He,et al.  Reconstruction of multiphase microstructure based on statistical descriptors , 2014 .

[2]  Wei Chen,et al.  Stochastic microstructure characterization and reconstruction via supervised learning , 2016 .

[3]  M. Sahimi,et al.  Cross-correlation function for accurate reconstruction of heterogeneous media. , 2013, Physical Review Letters.

[4]  Hangil You,et al.  Computationally fast morphological descriptor-based microstructure reconstruction algorithms for particulate composites , 2019, Composites Science and Technology.

[5]  Karthik K. Bodla,et al.  3D reconstruction and design of porous media from thin sections , 2014 .

[6]  Anthony Roberts.  Statistical reconstruction of three-dimensional porous media from two-dimensional images , 1997 .

[7]  Qizhi Teng,et al.  Improved multipoint statistics method for reconstructing three-dimensional porous media from a two-dimensional image via porosity matching. , 2018, Physical review. E.

[8]  Xingchen Liu,et al.  Random heterogeneous materials via texture synthesis , 2015 .

[9]  Tao Wu,et al.  Reconstruction of three-dimensional anisotropic media based on analysis of morphological completeness , 2019, Computational Materials Science.

[10]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[11]  Ryszard Piasecki.  Detecting self-similarity in surface microstructures , 2000 .

[12]  F. Stillinger,et al.  Modeling heterogeneous materials via two-point correlation functions: basic principles. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  F. Stillinger,et al.  Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Salvatore Torquato,et al.  Generating random media from limited microstructural information via stochastic optimization , 1999 .

[15]  Muhammad Sahimi,et al.  Linking Morphology of Porous Media to Their Macroscopic Permeability by Deep Learning , 2020, Transport in Porous Media.

[16]  Pejman Tahmasebi,et al.  Reconstruction of three-dimensional porous media using a single thin section. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Wing Kam Liu,et al.  Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques , 2018, Progress in Materials Science.

[18]  XiaoHai He,et al.  Reconstruction of three-dimensional porous media from a single two-dimensional image using three-step sampling. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  David T. Fullwood,et al.  Correlating structure topological metrics with bulk composite properties via neural network analysis , 2014 .

[20]  Pejman Tahmasebi,et al.  Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Wei Chen,et al.  Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials , 2014 .

[22]  Eugene D. Skouras,et al.  Advanced Laguerre Tessellation for the Reconstruction of Ceramic Foams and Prediction of Transport Properties , 2019, Materials.

[23]  Nicholas Zabaras,et al.  Classification and reconstruction of three-dimensional microstructures using support vector machines , 2005 .

[24]  R. Piasecki.  A versatile entropic measure of grey level inhomogeneity , 2009 .

[25]  Karen Abrinia,et al.  3D microstructural reconstruction of heterogeneous materials from 2D cross sections: A modified phase-recovery algorithm , 2016 .

[26]  D. Fraczek,et al.  Decomposable multiphase entropic descriptor , 2013, 1309.1782.

[27]  R. Piasecki,et al.  Low-cost approximate reconstructing of heterogeneous microstructures , 2016 .

[28]  Edoardo Patelli,et al.  On optimization techniques to reconstruct microstructures of random heterogeneous media , 2009 .

[29]  S. Torquato,et al.  Reconstructing random media , 1998 .

[30]  R. Piasecki,et al.  Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands , 2014, 1406.0037.

[31]  David T. Fullwood,et al.  Microstructure Sensitive Design for Performance Optimization , 2012 .

[32]  R. Piasecki,et al.  Speeding up of microstructure reconstruction: I. Application to labyrinth patterns , 2011, 1109.3819.

[33]  F. Stillinger,et al.  A superior descriptor of random textures and its predictive capacity , 2009, Proceedings of the National Academy of Sciences.

[34]  N. Pan,et al.  Predictions of effective physical properties of complex multiphase materials , 2008 .

[35]  W Chen,et al.  Characterization and reconstruction of 3D stochastic microstructures via supervised learning , 2016, Journal of microscopy.

[36]  Wei Chen,et al.  A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions , 2018, Scientific Reports.

[37]  R. Piasecki,et al.  Inhomogeneity and complexity measures for spatial patterns , 2002 .

[38]  Ming Yang,et al.  New algorithms for virtual reconstruction of heterogeneous microstructures , 2018, Computer Methods in Applied Mechanics and Engineering.

[39]  Ryszard Piasecki,et al.  Statistical Reconstruction of Microstructures Using Entropic Descriptors , 2017, Transport in Porous Media.

[40]  Ryszard Piasecki.  Entropic measure of spatial disorder for systems of finite-sized objects , 2000 .

[41]  Eugene D. Skouras,et al.  Three-Dimensional Digital Reconstruction of Ti2AlC Ceramic Foams Produced by the Gelcast Method , 2019, Materials.

[42]  Dongsheng Li,et al.  Review of Structure Representation and Reconstruction on Mesoscale and Microscale , 2014 .

[43]  Ryszard Piasecki.  Statistical mechanics characterization of spatio-compositional inhomogeneity , 2009 .

[44]  Yi Ren,et al.  Improving direct physical properties prediction of heterogeneous materials from imaging data via convolutional neural network and a morphology-aware generative model , 2017, Computational Materials Science.

[45]  J. Kärger,et al.  Flow and Transport in Porous Media and Fractured Rock , 1996 .

[46]  Muhammad Sahimi,et al.  Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches , 1995 .

[47]  S. Torquato,et al.  Reconstructing random media. II. Three-dimensional media from two-dimensional cuts , 1998 .

[48]  Entropic descriptor based reconstruction of three-dimensional porous microstructures using a single cross-section , 2015, 1508.03857.

[49]  Salvatore Torquato,et al.  Optimal Design of Heterogeneous Materials , 2010 .

[50]  Pejman Tahmasebi,et al.  Accurate modeling and evaluation of microstructures in complex materials. , 2018, Physical review. E.

[51]  Bin Wen,et al.  Computing mechanical response variability of polycrystalline microstructures through dimensionality reduction techniques , 2010 .

[52]  Controlling Spatial Inhomogeneity in Prototypical Multiphase Microstructures , 2017, 1706.06880.

[53]  R. Piasecki,et al.  Entropic descriptor of a complex behaviour , 2010 .

[54]  Xin Sun,et al.  Three-phase solid oxide fuel cell anode microstructure realization using two-point correlation functions , 2011 .

[55]  MariethozGregoire,et al.  Bridges between multiple-point geostatistics and texture synthesis , 2014 .

[56]  Yang Li,et al.  Reconstruction of three-dimensional heterogeneous media from a single two-dimensional section via co-occurrence correlation function , 2018 .

[57]  Sylvain Lefebvre,et al.  Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research , 2014, Comput. Geosci..

[59]  M. Sahimi.  Nonlinear and breakdown properties and atomistic modeling , 2003 .

[60]  R. Piasecki,et al.  Microstructure reconstruction using entropic descriptors , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.