Improving pattern reconstruction using directional correlation functions

Gerke, Kirill M.; Karsanina, Marina V.; Vasilyev, Roman; Mallants, Dirk

doi:10.1209/0295-5075/106/66002

Cited by 83 publications

(35 citation statements)

References 36 publications

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“…Generating realizations of heterogeneous materials from limited morphological information is a topic of great interest [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Our procedure for reconstructing hyperuniform heterogeneous materials is developed within the Yeong-Torquato (YT) stochastic reconstruction framework [38], in which an initial random microstructure is evolved to minimize an energy function that measures the difference between the target correlation functions and the corresponding functions of the simulated microstructure.…”

Section: Generating Realizations Of Hyperuniform Materials Usingmentioning

confidence: 99%

Microstructure and mechanical properties of hyperuniform heterogeneous materials

Chen

et al. 2017

Phys. Rev. E

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A hyperuniform random heterogeneous material is one in which the local volume fraction fluctuations in an observation window decay faster than the reciprocal window volume as the window size increases. Recent studies show that this class of materials are endowed with superior physical properties such as large isotropic photonic band gaps and optimal transport properties. Here we employ a stochastic optimization procedure to systematically generate realizations of hyperuniform heterogeneous materials with controllable short-range order, which is partially quantified using the two-point correlation function S_{2}(r) associated with the phase of interest. Specifically, our procedure generalizes the widely used Yeong-Torquato reconstruction procedure by including an additional constraint for hyperuniformity, i.e., the volume integral of the autocovariance function χ(r)=S_{2}(r)-ϕ^{2} over the whole space is zero. In addition, we only require the reconstructed S_{2} to match the target function up to a certain cutoff distance γ, in order to give the system sufficient degrees of freedom to satisfy the hyperuniform condition. By systematically increasing the γ value for a given S_{2}, one can produce a spectrum of hyperuniform heterogeneous materials with varying degrees of partial short-range order compatible with the specified S_{2}. The mechanical performance including both elastic and brittle fracture behaviors of the generated hyperuniform materials is analyzed using a volume-compensated lattice-particle method. For the purpose of comparison, the corresponding nonhyperuniform materials with the same short-range order (i.e., with S_{2} constrained up to the same γ value) are also constructed and their mechanical performance is analyzed. Here we consider two specific S_{2} including the positive exponential decay function and the correlation function associated with an equilibrium hard-sphere system. For the constructed systems associated with these two specific functions, we find that although the hyperuniform materials are softer than their nonhyperuniform counterparts, the former generally possess a significantly higher brittle fracture strength than the latter. This superior mechanical behavior is attributed to the lower degree of stress concentration in the material resulting from the hyperuniform microstructure, which is crucial to crack initiation and propagation.

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Section: Generating Realizations Of Hyperuniform Materials Usingmentioning

confidence: 99%

Microstructure and mechanical properties of hyperuniform heterogeneous materials

Chen

et al. 2017

Phys. Rev. E

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“…Such approaches in calculating correlation functions cannot handle well anisotropic structures. Gerke et al [ 68 ] have proposed a new method to account for structure anisotropy by calculating directional correlation functions. In order to calculate the above cluster function, C 2 , the binary phase of interest is first marked into clusters using the Hoshen-Kopelman algorithm [ 72 ] and a set of boundary conditions [ 73 ].…”

Section: Methodsmentioning

confidence: 99%

“…In our preliminary study [ 67 ] we applied spatial correlation functions (with averaged two-point probability computed only in orthogonal directions) for soil reconstructions based on the original Yeong-Torquato method which considers isotropic heterogeneous materials. On the basis of our recent modifications to the Yeong-Torquato method, which involves computing directional correlation functions [ 68 ], we demonstrate it is now possible to characterize complex soils with direction-dependent or anisotropic structures. The current paper builds on our previous work and is a first-ever demonstration of the predictive capacity of the novel directional spatial correlation functions [ 67 – 68 ] for soil structure quantification and reconstruction.…”

Section: Introductionmentioning

confidence: 99%

“…On the basis of our recent modifications to the Yeong-Torquato method, which involves computing directional correlation functions [ 68 ], we demonstrate it is now possible to characterize complex soils with direction-dependent or anisotropic structures. The current paper builds on our previous work and is a first-ever demonstration of the predictive capacity of the novel directional spatial correlation functions [ 67 – 68 ] for soil structure quantification and reconstruction.…”

Section: Introductionmentioning

confidence: 99%

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Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure

et al. 2015

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Structural features of porous materials such as soil define the majority of its physical properties, including water infiltration and redistribution, multi-phase flow (e.g. simultaneous water/air flow, or gas exchange between biologically active soil root zone and atmosphere) and solute transport. To characterize soil microstructure, conventional soil science uses such metrics as pore size and pore-size distributions and thin section-derived morphological indicators. However, these descriptors provide only limited amount of information about the complex arrangement of soil structure and have limited capability to reconstruct structural features or predict physical properties. We introduce three different spatial correlation functions as a comprehensive tool to characterize soil microstructure: 1) two-point probability functions, 2) linear functions, and 3) two-point cluster functions. This novel approach was tested on thin-sections (2.21×2.21 cm2) representing eight soils with different pore space configurations. The two-point probability and linear correlation functions were subsequently used as a part of simulated annealing optimization procedures to reconstruct soil structure. Comparison of original and reconstructed images was based on morphological characteristics, cluster correlation functions, total number of pores and pore-size distribution. Results showed excellent agreement for soils with isolated pores, but relatively poor correspondence for soils exhibiting dual-porosity features (i.e. superposition of pores and micro-cracks). Insufficient information content in the correlation function sets used for reconstruction may have contributed to the observed discrepancies. Improved reconstructions may be obtained by adding cluster and other correlation functions into reconstruction sets. Correlation functions and the associated stochastic reconstruction algorithms introduced here are universally applicable in soil science, such as for soil classification, pore-scale modelling of soil properties, soil degradation monitoring, and description of spatial dynamics of soil microbial activity.

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“…However, due to its stochastic nature, a large number of intermediate trial microstructures need to be generated and analyzed, which makes it computationally intensive. Several improved implementations of the Y-T procedure have been devised to improve efficiency [28][29][30][31][32], preserve isotropy [33][34][35] and handle anisotropic materials [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Dynamic reconstruction of heterogeneous materials and microstructure evolution

Chen

Jiao

2015

Phys. Rev. E

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Reconstructing heterogeneous materials from limited structural information has been a topic that attracts extensive research efforts and still poses many challenges. The Yeong-Torquato procedure is one of the most popular reconstruction techniques, in which the material reconstruction problem based on a set of spatial correlation functions is formulated as a constrained energy minimization (optimization) problem and solved using simulated annealing [Yeong and Torquato, Phys. Rev. E 57, 495 (1998)]. The standard two-point correlation function S2 has been widely used in reconstructions, but can also lead to large structural degeneracy for certain nearly percolating systems. To improve reconstruction accuracy and reduce structural degeneracy, one can successively incorporate additional morphological information (e.g., nonconventional or higher-order correlation functions), which amounts to reshaping the energy landscape to create a deep (local) energy minimum. In this paper, we present a dynamic reconstruction procedure that allows one to use a series of auxiliary S2 to achieve the same level of accuracy as those incorporating additional nonconventional correlation functions. In particular, instead of randomly sampling the microstructure space as in the simulated annealing scheme, our procedure utilizes a series of auxiliary microstructures that mimic a physical structural evolution process (e.g., grain growth). This amounts to constructing a series auxiliary energy landscapes that bias the convergence of the reconstruction to a favored (local) energy minimum. Moreover, our dynamic procedure can be naturally applied to reconstruct an actual microstructure evolution process. In contrast to commonly used evolution reconstruction approaches that separately generate individual static configurations, our procedure continuously evolves a single microstructure according to a time-dependent correlation function. The utility of our procedure is illustrated by successfully reconstructing nearly percolating hard-sphere packings and particle-reinforced composites as well as the coarsening process in a binary metallic alloy.

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Improving pattern reconstruction using directional correlation functions

Cited by 83 publications

References 36 publications

Microstructure and mechanical properties of hyperuniform heterogeneous materials

Microstructure and mechanical properties of hyperuniform heterogeneous materials

Universal Spatial Correlation Functions for Describing and Reconstructing Soil Microstructure

Dynamic reconstruction of heterogeneous materials and microstructure evolution

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