Geodesic
Using correlation functions to model material’s structure with desired physical properties
Matematičeskoe modelirovanie, Tome 27 (2015) no. 4, pp. 50-63.

Voir la notice de l'article provenant de la source Math-Net.Ru

To solve numerous fundamental and applied problems across different scientific disciplines and industrial applications it is crucial to design materials with desired structural and physicochemical properties. One of the methods to quantify microstructure of a porous material is by means of correlation functions. Using so-called simulated annealing stochastic optimization method one can use correlation functions to construct/reconstruct of different structures. In this study we use analytical correlation functions with three parameters to construct 60 different structures of hypothetical porous materials. Using finite-difference solution of Stokes equation effective permeability values are obtained for each constructed 3D structure. Based on the results we show that it is possible to design a porous material with desired physical (permeability) and structural (characteristic pore size) properties.
Keywords: material design, porous media, alloys, permeability, effective property, pore-scale modeling. 
@article{MM_2015_27_4_a3,
     author = {M. V. Karsanina and K. M. Gerke and R. V. Vasilyev and D. V. Korost},
     title = {Using correlation functions to model material{\textquoteright}s structure with desired physical properties},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {50--63},
     publisher = {mathdoc},
     volume = {27},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_4_a3/}
}
TY  - JOUR
AU  - M. V. Karsanina
AU  - K. M. Gerke
AU  - R. V. Vasilyev
AU  - D. V. Korost
TI  - Using correlation functions to model material’s structure with desired physical properties
JO  - Matematičeskoe modelirovanie
PY  - 2015
SP  - 50
EP  - 63
VL  - 27
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2015_27_4_a3/
LA  - ru
ID  - MM_2015_27_4_a3
ER  - 
%0 Journal Article
%A M. V. Karsanina
%A K. M. Gerke
%A R. V. Vasilyev
%A D. V. Korost
%T Using correlation functions to model material’s structure with desired physical properties
%J Matematičeskoe modelirovanie
%D 2015
%P 50-63
%V 27
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2015_27_4_a3/
%G ru
%F MM_2015_27_4_a3
M. V. Karsanina; K. M. Gerke; R. V. Vasilyev; D. V. Korost. Using correlation functions to model material’s structure with desired physical properties. Matematičeskoe modelirovanie, Tome 27 (2015) no. 4, pp. 50-63. http://geodesic.mathdoc.fr/item/MM_2015_27_4_a3/

[1] S. Torquato, “Optimal design of heterogeneous materials”, Annual Review of Materials Research, 40 (2010), 101–129 | DOI

[2] T. Ohji, M. Fukushima, “Macro-porous ceramics: processing and properties”, International Materials Reviews, 57:2 (2012), 115–131 | DOI

[3] A. C. Jones, C. H. Arns, D. W. Hutmacher, B. K. Milthorpe, A. P. Sheppard, M. A. Knackstedt, “The correlation of pore morphology, interconnectivity and physical properties of 3D ceramic scaffolds with bone ingrowth”, Biomaterials, 30 (2009), 1440–1451 | DOI

[4] M. Sejnoha, J. Zeman, “Micromechanical modeling of imperfect textile composites”, International Journal of Engineering Science, 46:6 (2008), 513–526 | DOI

[5] K. N. Grew, W. K. S. Chiu, “A review of modeling and simulation techniques across the length scales for the solid oxide fuel cell”, Journal of Power Sources, 199 (2012), 1–13 | DOI

[6] D. V. Korost, G. A. Kalmykov, V. O. Iapaskurt, M. K. Ivanov, “Primenenie kompiuternoi mikrotomografii dlia izucheniia stroeniia terrigennykh kollektorov”, Geologiia nefti i gaza, 2010, no. 2, 36–42 | MR

[7] D. V. Korost, K. M. Gerke, SPE Russian Oil and Gas Exploration and Production Technical Conference and Exhibition, SPE Technical Paper 162023-MS (16–18 October 2012, Moscow, Russia) | DOI

[8] K. M. Gerke, R. V. Vasilyev, D. V. Korost, M. V. Karsanina, N. Balushkina, R. Khamidullin, G. A. Kalmykov, D. Mallants, SPE Unconventional Resources Conference and Exhibition, SPE 167058 Technical paper (11–13 November 2013, Brisbane, Australia)

[9] K. M. Gerke, E. B. Skvortsova, D. V. Korost, “Tomograficheskii metod issledovaniya porovogo prostranstva pochv: sostoyanie problemy i izuchenie nekotorykh pochv Rossii”, Pochvovedenie, 2012, no. 7, 781–791

[10] S. Torquato, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer Verlag, New York, 2002, 701 pp. | MR | Zbl

[11] V. I. Osipov, V. N. Sokolov, N. A. Rumiantseva, Mikrostruktura glinistykh porod, Nedra, M., 1989, 211 pp.

[12] K. M. Gerke, M. V. Karsanina, E. B. Skvortsova, “Opisanie i rekonstruktsiya stroeniya porovogo prostranstva pochvy s pomoschyu korrelyatsionnykh funktsii”, Pochvovedenie, 2012, no. 9, 962–973

[13] N. Vivet, S. Chupin, E. Estrade, T. Piquero, P. L. Pommier, D. Rochais, E. Bruneton, “3D microstructural characterization of a solid oxide fuel cell anode reconstructed by focused ion beam tomography”, Journal of Power Sources, 196 (2011), 7541–7549 | DOI

[14] L. Talon, D. Bauer, N. Gland, S. Youssef, H. Auradou, I. Ginzburg, “Assessment of the two relaxation time Lattice-Boltzmann scheme to simulate Stokes flow in porous media”, Water Resources Research, 48 (2012), W04526 | DOI

[15] P. H. Valvatne, M. J. Blunt, “Predictive pore-scale modeling of two phase flow in mixed wet media”, Water Resources Research, 40 (2004), W07406 | DOI

[16] P. M. Adler, C. G. Jacquin, J.-F. Throvert, “The formation factor of reconstructed porous media”, Water Resources Research, 28 (1992), 1571–1576 | DOI

[17] D. Makarinska, B. Gurevich, R. Ciz, C. H. Arns, M. A. Knackstedt, “Finite element modeling of the effective elastic properties of partially saturated rocks”, Computer and Geosciences, 34 (2008), 647–657 | DOI

[18] J. A. Quiblier, “A new three-dimensional modeling technique for studying porous media”, Journal of Colloid and Interface Science, 98 (1984), 84–102 | DOI

[19] H. Okabe, M. J. Blunt, “Pore space reconstruction of vuggy carbonates using microtomography and multiple-point statistic”, Water Resour. Res., 43 (2007), 0043–1397 | DOI

[20] P. E. Øren, S. Bakke, “Process based reconstruction of sandstones and prediction of transport properties”, Transport in Porous Media, 46 (2002), 311–314 | DOI

[21] C. L. Y. Yeong, S. Torquato, “Reconstructing random media”, Phys. Rev. E, 57 (1998), 495–506 | DOI | MR

[22] C. L. Y. Yeong, S. Torquato, “Reconstructing random media. II: Three dimensional media from two dimensional cuts”, Phys. Rev. E, 58 (1998), 224–233 | DOI | MR

[23] P. Čapek, V. Hejtmánek, J. Kolafa, I. Brabec, “Transport properties of stochastically reconstructed porous media with improved pore connectivity”, Transp. Porous. Med., 88 (2011), 87–106 | DOI | MR

[24] Y. Jiao, F. H. Stillinger, S. Torquato, “Modeling heterogeneous materials via two-point correlation functions: Basic principles”, Phys. Rev. E, 76 (2007), 031110 | DOI | MR

[25] S. Torquato, “Random heterogeneous media: Microstructure and improved bounds on effective properties”, Appl. Mech. Rev., 44 (1991), 37–76 | DOI | MR

[26] Y. Jiao, F. H. Stillinger, S. Torquato, “A superior descriptor of random textures and its predictive capacity”, Proceedings of National Academy of Science, 106 (2009), 17634 | DOI

[27] Y. Jiao, F. H. Stillinger, S. Torquato, “Geometrical ambiguity of pair statistics. II: Heterogeneous media”, Phys. Rev. E, 82 (2010), 011106 | DOI | MR

[28] Y. Jiao, F. H. Stillinger, S. Torquato, “Modeling heterogeneous materials via two-point correlation functions. II: Algorithmic details and applications”, Phys. Rev. E, 77 (2008), 031135 | DOI | MR

[29] C. Manwart, R. Hilfer, “Reconstruction of random media using Monte-Carlo methods”, Phys. Rev. E, 59 (1999), 5596–5599 | DOI

[30] K. M. Gerke, M. V. Karsanina, R. V. Vasilyev, D. Mallants, “Improving pattern reconstruction using directional correlation functions”, Europhysics Letters, 106 (2014), 66002 | DOI