A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions
Abstract
1. Introduction
2. Creating Synthetic Clusters—Stage One
3. Reconstruction Using Entropic Descriptors—Stage Two
4. Results
4.1. Statistical Reconstruction of Silica Dispersed in Rubber Matrix
4.2. Statistical Reconstruction of Stones Dispersed in a Cement Paste
5. Discussion
6. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
Appendix A
References
- Torquato, S. Random Heterogeneous Materials: Microstructure and Macroscopic Properties; Springer: New York, NY, USA, 2002. [Google Scholar]
- Sahimi, M. Heterogeneous Materials I: Linear Transport and Optical Properties; Springer: New York, NY, USA, 2003. [Google Scholar]
- Sahimi, M. Heterogeneous Materials II: Nonlinear and Breakdown Properties and Atomistic Modeling; Springer: New York, NY, USA, 2003. [Google Scholar]
- Torquato, S. Microstructure optimization. In Handbook of Materials Modeling; Yip, S., Ed.; Springer: New York, NY, USA, 2005; pp. 2379–2396. [Google Scholar]
- Wang, M.; Pan, N. Predictions of effective physical properties of complex multiphase materials. Mater. Sci. Eng. R. Rep. 2008, 63, 1–30. [Google Scholar] [CrossRef]
- Sahimi, M. Flow and Transport in Porous Media and Fractured Rock: From Classical Methods to Modern Approaches, 2nd ed.; WILEY-VCH, Verlag GmbH & Co. KGaA: Weinheim, Germany, 2011. [Google Scholar]
- Li, D. Review of Structure Representation and Reconstruction. JOM 2014, 66, 444–454. [Google Scholar] [CrossRef]
- Bostanabad, R.; Zhang, Y.; Li, X.; Kearney, T.; Brinson, L.C.; Apley, D.W.; Liu, W.K.; Chen, W. Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques. Prog. Mater. Sci. 2018, 95, 1–41. [Google Scholar] [CrossRef]
- Roberts, A.P. Statistical reconstruction of three-dimensional porous media from two-dimensional images. Phys. Rev. E 1997, 56, 3203. [Google Scholar] [CrossRef]
- Yeong, C.L.Y.; Torquato, S. Reconstructing random media: II. Three-dimensional media from two-dimensional cuts. Phys. Rev. E 1998, 58, 224–233. [Google Scholar] [CrossRef]
- Tahmasebi, P.; Sahimi, M. Reconstruction of three-dimensional porous media using a single thin section. Phys. Rev. E 2012, 85, 066709. [Google Scholar] [CrossRef]
- Bodla, K.K.; Garimella, S.V.; Murthy, J.Y. 3D reconstruction and design of porous media from thin sections. Int. J. Heat Mass Transf. 2014, 73, 250–264. [Google Scholar] [CrossRef]
- Gao, M.L.; He, X.H.; Teng, Q.Z.; Zuo, C.; Chen, D.D. Reconstruction of 3D porous media from a single 2D image using three-step sampling. Phys. Rev. E 2015, 91, 013308. [Google Scholar] [CrossRef]
- Frączek, D.; Olchawa, W.; Piasecki, R.; Wiśniowski, R. Entropic descriptor based reconstruction of three-dimensional porous microstructures using a single cross-section. arXiv 2015, arXiv:1508.03857. [Google Scholar]
- Hasanabadi, A.; Baniassadi, M.; Abrinia, K.; Safdari, M.; Garmestani, H. 3D microstructural reconstruction of heterogeneous materials from 2D cross sections: A modified phase-recovery algorithm. Comput. Mater. Sci. 2016, 111, 107–115. [Google Scholar] [CrossRef]
- Feng, J.; Teng, Q.; He, X.; Qing, L.; Li, Y. Reconstruction of three-dimensional heterogeneous media from a single two-dimensional section via co-occurrence correlation function. Comput. Mater. Sci. 2018, 144, 181–192. [Google Scholar] [CrossRef]
- Torquato, S. Optimal Design of Heterogeneous Materials. Annu. Rev. Mater. Res. 2010, 40, 101–129. [Google Scholar] [CrossRef]
- Fullwood, D.; Niezgoda, S.; Adams, B.; Kalidindi, S. Microstructure sensitive design for performance optimization. Prog. Mater. Sci. 2010, 55, 477–562. [Google Scholar] [CrossRef]
- Gerrard, D.D.; Fullwood, D.T.; Halverson, D.M. Correlating structure topological metrics with bulk composite properties via neural network analysis. Comput. Mater. Sci. 2014, 91, 20–27. [Google Scholar] [CrossRef]
- Jiao, Y.; Stillinger, F.H.; Torquato, S. Modeling Heterogeneous Materials via Two-Point Correlation Functions. II. Algorithmic Details and Applications. Phys. Rev. E 2008, 77, 031135. [Google Scholar] [CrossRef] [PubMed]
- Piasecki, R. Statistical mechanics characterization of spatio-compositional inhomogeneity. Phys. A Stat. Mech. Appl. 2009, 388, 4229–4240. [Google Scholar] [CrossRef]
- Sundararaghavan, V.; Zabaras, N. Classification and reconstruction of three-dimensional microstructures using support vector machines. Comput. Mater. Sci. 2005, 32, 223–239. [Google Scholar] [CrossRef]
- Patelli, E.; Schuëller, G. On optimization techniques to reconstruct microstructures of random heterogeneous media. Comput. Mater. Sci. 2009, 45, 536–549. [Google Scholar] [CrossRef]
- Piasecki, R. Microstructure reconstruction using entropic descriptors. Proc. R. Soc. A Math. Phys. Eng. Sci. 2011, 467, 806–820. [Google Scholar] [CrossRef]
- Olchawa, W.; Piasecki, R.; Wiśniowski, R.; Frączek, D. Low-cost approximate reconstructing of heterogeneous microstructures. Comput. Mater. Sci. 2016, 123, 26–30. [Google Scholar] [CrossRef]
- Frączek, D.; Piasecki, R.; Olchawa, W.; Wiśniowski, R. Controlling spatial inhomogeneity in prototypical multiphase microstructures. arXiv 2017, arXiv:1706.06880. [Google Scholar]
- Piasecki, R.; Olchawa, W.; Frączek, D.; Wiśniowski, R. Statistical Reconstruction of Microstructures Using Entropic Descriptors. Transp. Porous Media 2018, 125, 105–125. [Google Scholar] [CrossRef]
- Xu, H.; Dikin, D.A.; Burkhart, C.; Chen, W. Descriptor-based methodology for statistical characterization and 3D reconstruction of microstructural materials. Comput. Mater. Sci. 2014, 85, 206–216. [Google Scholar] [CrossRef]
- Baniassadi, M.; Garmestani, H.; Li, D.S.; Ahzi, S.; Khaleel, M.; Sun, X. Three-phase solid oxide fuel cell anode microstructure realization using two-point correlation functions. Acta Mater. 2011, 59, 30–43. [Google Scholar] [CrossRef]
- Mariethoz, G.; Lefebvre, S. Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research. Comput. Geosci. 2014, 66, 66–80. [Google Scholar] [CrossRef]
- Ding, K.; Teng, Q.; Wang, Z.; He, X.; Feng, J. Improved multipoint statistics method for reconstructing three-dimensional porous media from a two-dimensional image via porosity matching. Phys. Rev. E 2018, 97, 063304. [Google Scholar] [CrossRef]
- Liu, X.; Shapiro, V. Random heterogeneous materials via texture synthesis. Comput. Mater. Sci. 2015, 99, 177–189. [Google Scholar] [CrossRef]
- Tahmasebi, P.; Sahimi, M. Reconstruction of nonstationary disordered materials and media: Watershed transform and cross-correlation function. Phys. Rev. E 2015, 91, 032401. [Google Scholar] [CrossRef]
- Bostanabad, R.; Bui, A.T.; Xie, W.; Apley, D.W.; Chen, W. Stochastic microstructure characterization and reconstruction via supervised learning. Acta Mater. 2016, 103, 89–102. [Google Scholar] [CrossRef]
- Bostanabad, R.; Chen, W.; Apley, D.W. Characterization and reconstruction of 3D stochastic microstructures via supervised learning. J. Microsc. 2016, 264, 282–297. [Google Scholar] [CrossRef]
- Cang, R.; Li, H.; Yao, H.; Jiao, Y.; Ren, Y. Improving direct physical properties prediction of heterogeneous materials from imaging data via convolutional neural network and a morphology-aware generative model. Comput. Mater. Sci. 2018, 150, 212–221. [Google Scholar] [CrossRef]
- Li, X.; Zhang, Y.; Zhao, H.; Burkhart, C.; Brinson, L.C.; Chen, W. A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions. Sci. Rep. 2018, 8, 13461. [Google Scholar] [CrossRef] [PubMed]
- Kamrava, S.; Tahmasebi, P.; Sahimi, M. Linking Morphology of Porous Media to Their Macroscopic Permeability by Deep Learning. Transp. Porous Media 2020, 131, 427–448. [Google Scholar] [CrossRef]
- Yang, M.; Nagarajan, A.; Liang, B.; Soghrati, S. New algorithms for virtual reconstruction of heterogeneous microstructures. Comput. Methods Appl. Mech. Eng. 2018, 338, 275–298. [Google Scholar] [CrossRef]
- Gao, M.; Li, X.; Xu, Y.; Wu, T.; Wang, J. Reconstruction of three-dimensional anisotropic media based on analysis of morphological completeness. Comput. Mater. Sci. 2019, 167, 123–135. [Google Scholar] [CrossRef]
- Tahmasebi, P. Accurate modeling and evaluation of microstructures in complex materials. Phys. Rev. E 2018, 97, 023307. [Google Scholar] [CrossRef]
- Stiapis, C.S.; Skouras, E.D.; Burganos, V.N. Advanced Laguerre Tessellation for the Reconstruction of Ceramic Foams and Prediction of Transport Properties. Materials 2019, 12, 1137. [Google Scholar] [CrossRef]
- Stiapis, C.S.; Skouras, E.D.; Burganos, V.N. Three-Dimensional Digital Reconstruction of Ti2AlC Ceramic Foams Produced by the Gelcast Method. Materials 2019, 12, 4085. [Google Scholar] [CrossRef]
- Yeong, C.L.Y.; Torquato, S. Reconstructing random media. Phys. Rev. E 1998, 57, 495–506. [Google Scholar] [CrossRef]
- Cule, D.; Torquato, S. Generating random media from limited microstructural information via stochastic optimization. J. Appl. Phys. 1999, 86, 3428–3437. [Google Scholar] [CrossRef][Green Version]
- Chen, D.; He, X.; Teng, Q.; Xu, Z.; Li, Z. Reconstruction of multiphase microstructure based on statistical descriptors. Phys. A Stat. Mech. Appl. 2014, 415, 240–250. [Google Scholar] [CrossRef]
- Jiao, Y.; Stillinger, F.H.; Torquato, S. A Superior Descriptor of Random Textures and Its Predictive Capacity. Proc. Natl. Acad. Sci. USA 2009, 106, 17634–17639. [Google Scholar] [CrossRef] [PubMed]
- Piasecki, R. Entropic measure of spatial disorder for systems of finite-sized objects. Phys. A Stat. Mech. Appl. 2000, 277, 157–173. [Google Scholar] [CrossRef][Green Version]
- Piasecki, R.; Martin, M.T.; Plastino, A. Inhomogeneity and complexity measures for spatial patterns. Phys. A Stat. Mech. Appl. 2002, 307, 157–171. [Google Scholar] [CrossRef][Green Version]
- Piasecki, R.; Plastino, A. Entropic descriptor of a complex behavior. Phys. A Stat. Mech. Appl. 2010, 389, 397–407. [Google Scholar] [CrossRef]
- Piasecki, R.; Olchawa, W. Speeding up of microstructure reconstruction: I. Application to labyrinth patterns. Model. Simul. Mater. Sci. Eng. 2012, 20, 055003. [Google Scholar] [CrossRef]
- Olchawa, W.; Piasecki, R. Speeding up of microstructure reconstruction: II. Application to patterns of poly-dispersed islands. Comput. Mater. Sci. 2015, 98, 390–398. [Google Scholar] [CrossRef]
- Cinacchi, G.; Torquato, S. Hard convex lens-shaped particles: Characterization of dense disordered packings. Phys. Rev. E 2019, 100, 062902. [Google Scholar] [CrossRef]
- Frączek, D.; Piasecki, R. Decomposable multiphase entropic descriptor. Phys. A Stat. Mech. Appl. 2014, 399, 75–81. [Google Scholar] [CrossRef][Green Version]
- Piasecki, R. Versatile entropic measure of grey level inhomogeneity. Phys. A Stat. Mech. Appl. 2009, 388, 2403–2429. [Google Scholar] [CrossRef][Green Version]
- Tahmasebi, P.; Sahimi, M. Cross-Correlation Function for Accurate Reconstruction of Heterogeneous Media. Phys. Rev. Lett. 2013, 110, 078002. [Google Scholar] [CrossRef] [PubMed]
- You, H.; Kim, Y.; Yun, G.J. Computationally fast morphological descriptor-based microstructure reconstruction algorithms for particulate composites. Compos. Sci. Technol. 2019, 182, 107746. [Google Scholar] [CrossRef]
Actions | f1(New) < f1(Old) | f2(New) < f2(Old) | Q > Qmax |
---|---|---|---|
accept attempt and set Q ← 0 | 1 | 1 | * |
1 | 0 | 1 | |
reject attempt and increase Q ← Q + 1 | 1 | 0 | 0 |
0 | * | * |
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Piasecki, R.; Olchawa, W.; Frączek, D.; Bartecka, A. A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions. Materials 2020, 13, 2748. https://doi.org/10.3390/ma13122748
Piasecki R, Olchawa W, Frączek D, Bartecka A. A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions. Materials. 2020; 13(12):2748. https://doi.org/10.3390/ma13122748
Chicago/Turabian StylePiasecki, Ryszard, Wiesław Olchawa, Daniel Frączek, and Agnieszka Bartecka. 2020. "A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions" Materials 13, no. 12: 2748. https://doi.org/10.3390/ma13122748
APA StylePiasecki, R., Olchawa, W., Frączek, D., & Bartecka, A. (2020). A Two-Stage Reconstruction of Microstructures with Arbitrarily Shaped Inclusions. Materials, 13(12), 2748. https://doi.org/10.3390/ma13122748