Skip to main content
Top

31-03-2017 | TECHNICAL ARTICLE

Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures

Authors: Ruoqian Liu, Yuksel C. Yabansu, Zijiang Yang, Alok N. Choudhary, Surya R. Kalidindi, Ankit Agrawal

Published in: Integrating Materials and Manufacturing Innovation

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The response of a composite material is the result of a complex interplay between the prevailing mechanics and the heterogenous structure at disparate spatial and temporal scales. Understanding and capturing the multiscale phenomena is critical for materials modeling and can be pursued both by physical simulation-based modeling as well as data-driven machine learning-based modeling. In this work, we build machine learning-based data models as surrogate models for approximating the microscale elastic response as a function of the material microstructure (also called the elastic localization linkage). In building these surrogate models, we particularly focus on understanding the role of contexts, as a link to the higher scale information that most evidently influences and determines the microscale response. As a result of context modeling, we find that machine learning systems with context awareness not only outperform previous best results, but also extend the parallelism of model training so as to maximize the computational efficiency.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Agrawal A, Choudhary A (2016) Perspective: materials informatics and big data: realization of the “fourth paradigm” of science in materials science. APL Mater 4(053208):1–10 Agrawal A, Choudhary A (2016) Perspective: materials informatics and big data: realization of the “fourth paradigm” of science in materials science. APL Mater 4(053208):1–10
2.
go back to reference Kalidindi S, Medford AJ, McDowell DL (2016) Vision for data and informatics in the future materials innovation ecosystem. JOM 68(8):2126–2137CrossRef Kalidindi S, Medford AJ, McDowell DL (2016) Vision for data and informatics in the future materials innovation ecosystem. JOM 68(8):2126–2137CrossRef
3.
go back to reference Panchal JH, Kalidindi S, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput-Aided Des 45(1):4–25CrossRef Panchal JH, Kalidindi S, McDowell DL (2013) Key computational modeling issues in integrated computational materials engineering. Comput-Aided Des 45(1):4–25CrossRef
4.
go back to reference Ward L, Agrawal A, Choudhary A, Wolverton C (2016) A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput Mater 2(16028) Ward L, Agrawal A, Choudhary A, Wolverton C (2016) A general-purpose machine learning framework for predicting properties of inorganic materials. npj Comput Mater 2(16028)
5.
go back to reference Deshpande P, Gautham B, Cecen A, Kalidindi S, Agrawal A, Choudhary A (2013) Application of statistical and machine learning techniques for correlating properties to composition and manufacturing processes of steels. In: 2nd World Congress on Integrated Computational Materials Engineering (ICME), pp 155–160 Deshpande P, Gautham B, Cecen A, Kalidindi S, Agrawal A, Choudhary A (2013) Application of statistical and machine learning techniques for correlating properties to composition and manufacturing processes of steels. In: 2nd World Congress on Integrated Computational Materials Engineering (ICME), pp 155–160
6.
go back to reference Meredig B, Agrawal A, Kirklin S, Saal JE, Doak J, Thompson A, Zhang K, Choudhary A, Wolverton C (2014) Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys Rev B 89(9):094104CrossRef Meredig B, Agrawal A, Kirklin S, Saal JE, Doak J, Thompson A, Zhang K, Choudhary A, Wolverton C (2014) Combinatorial screening for new materials in unconstrained composition space with machine learning. Phys Rev B 89(9):094104CrossRef
7.
go back to reference Liu R, Kumar A, Chen Z, Agrawal A, Sundararaghavan V, Choudhary A (2015) A predictive machine learning approach for microstructure optimization and materials design. Scient Rep 5 Liu R, Kumar A, Chen Z, Agrawal A, Sundararaghavan V, Choudhary A (2015) A predictive machine learning approach for microstructure optimization and materials design. Scient Rep 5
8.
go back to reference Liu R, Yabansu YC, Agrawal A, Kalidindi S, Choudhary A (2015) Machine learning approaches for elastic localization linkages in high-contrast composite materials. Integr Mater Manuf Innov 4(1):1–17CrossRef Liu R, Yabansu YC, Agrawal A, Kalidindi S, Choudhary A (2015) Machine learning approaches for elastic localization linkages in high-contrast composite materials. Integr Mater Manuf Innov 4(1):1–17CrossRef
9.
go back to reference Niezgoda SR, Yabansu YC, Kalidindi S (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59(16):6387–6400CrossRef Niezgoda SR, Yabansu YC, Kalidindi S (2011) Understanding and visualizing microstructure and microstructure variance as a stochastic process. Acta Mater 59(16):6387–6400CrossRef
10.
go back to reference Niezgoda SR, Kanjarla AK, Kalidindi S (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2(1): 1–27CrossRef Niezgoda SR, Kanjarla AK, Kalidindi S (2013) Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data. Integr Mater Manuf Innov 2(1): 1–27CrossRef
11.
go back to reference Gopalakrishnan K, Agrawal A, Ceylan H, Kim S, Choudhary A (2013) Knowledge discovery and data mining in pavement inverse analysis. Transport 28(1):1–10CrossRef Gopalakrishnan K, Agrawal A, Ceylan H, Kim S, Choudhary A (2013) Knowledge discovery and data mining in pavement inverse analysis. Transport 28(1):1–10CrossRef
12.
go back to reference Agrawal A, Deshpande PD, Cecen A, Basavarsu GP, Choudhary A, Kalidindi S (2014) Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters. Integr Mater Manuf Innov 3(1):1– 19CrossRef Agrawal A, Deshpande PD, Cecen A, Basavarsu GP, Choudhary A, Kalidindi S (2014) Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters. Integr Mater Manuf Innov 3(1):1– 19CrossRef
13.
go back to reference Yabansu YC, Patel DK, Kalidindi S (2014) Calibrated localization relationships for elastic response of polycrystalline aggregates. Acta Mater 81:151–160CrossRef Yabansu YC, Patel DK, Kalidindi S (2014) Calibrated localization relationships for elastic response of polycrystalline aggregates. Acta Mater 81:151–160CrossRef
14.
go back to reference Yabansu YC, Kalidindi S (2015) Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater 94:26–35CrossRef Yabansu YC, Kalidindi S (2015) Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals. Acta Mater 94:26–35CrossRef
15.
go back to reference Agrawal A, Meredig B, Wolverton C, Choudhary A (2016) A formation energy predictor for crystalline materials using ensemble data mining. In: Proceedings of IEEE International Conference on Data Mining (ICDM), pp 1276–1279 Agrawal A, Meredig B, Wolverton C, Choudhary A (2016) A formation energy predictor for crystalline materials using ensemble data mining. In: Proceedings of IEEE International Conference on Data Mining (ICDM), pp 1276–1279
16.
go back to reference Agrawal A, Choudhary A (2016) A fatigue strength predictor for steels using ensemble data mining. In: Proceedings of 25th ACM International Conference on Information and Knowledge Management (CIKM), pp 2497–2500 Agrawal A, Choudhary A (2016) A fatigue strength predictor for steels using ensemble data mining. In: Proceedings of 25th ACM International Conference on Information and Knowledge Management (CIKM), pp 2497–2500
17.
go back to reference Gagorik AG, Savoie B, Jackson N, Agrawal A, Choudhary A, Ratner MA, Schatz GC, Kohlstedt KL (2017) Improved scaling of molecular network calculations: the emergence of molecular domains. J Phys Chem Lett 8(2):415–421CrossRef Gagorik AG, Savoie B, Jackson N, Agrawal A, Choudhary A, Ratner MA, Schatz GC, Kohlstedt KL (2017) Improved scaling of molecular network calculations: the emergence of molecular domains. J Phys Chem Lett 8(2):415–421CrossRef
18.
go back to reference Fullwood DT, Niezgoda SR, Adams B, Kalidindi S (2010) Microstructure sensitive design for performance optimization. Progress Mater Sci 55(6):477–562CrossRef Fullwood DT, Niezgoda SR, Adams B, Kalidindi S (2010) Microstructure sensitive design for performance optimization. Progress Mater Sci 55(6):477–562CrossRef
19.
go back to reference Liu R, Agrawal A, Chen Z, Liao W-K, Choudhary A (2015) Pruned search: a machine learning based meta-heuristic approach for constrained continuous optimization. In: Proceedings of 8th IEEE International Conference on Contemporary Computing (IC3), pp 13–18 Liu R, Agrawal A, Chen Z, Liao W-K, Choudhary A (2015) Pruned search: a machine learning based meta-heuristic approach for constrained continuous optimization. In: Proceedings of 8th IEEE International Conference on Contemporary Computing (IC3), pp 13–18
20.
go back to reference Suh C, Rajan K (2009) Invited review: data mining and informatics for crystal chemistry: establishing measurement techniques for mapping structure–property relationships. Mater Sci Technol 25(4):466–471CrossRef Suh C, Rajan K (2009) Invited review: data mining and informatics for crystal chemistry: establishing measurement techniques for mapping structure–property relationships. Mater Sci Technol 25(4):466–471CrossRef
21.
22.
go back to reference Ward L, Liu R, Krishna A, Hegde V, Agrawal A, Choudhary A, Wolverton C (2016) Accurate models of formation enthalpy created using machine learning and voronoi tessellations. In: APS Meeting Abstracts Ward L, Liu R, Krishna A, Hegde V, Agrawal A, Choudhary A, Wolverton C (2016) Accurate models of formation enthalpy created using machine learning and voronoi tessellations. In: APS Meeting Abstracts
23.
go back to reference Choudhury A, Yabansu YC, Kalidindi S, Dennstedt A (2016) Quantification and classification of microstructures in ternary eutectic alloys using 2-point spatial correlations and principal component analyses. Acta Mater 110:131–141CrossRef Choudhury A, Yabansu YC, Kalidindi S, Dennstedt A (2016) Quantification and classification of microstructures in ternary eutectic alloys using 2-point spatial correlations and principal component analyses. Acta Mater 110:131–141CrossRef
24.
go back to reference Furmanchuk A, Agrawal A, Choudhary A (2016) Predictive analytics for crystalline materials: Bulk modulus. RSC Adv 6(97):95246–95251CrossRef Furmanchuk A, Agrawal A, Choudhary A (2016) Predictive analytics for crystalline materials: Bulk modulus. RSC Adv 6(97):95246–95251CrossRef
25.
go back to reference Steinmetz P, Yabansu YC, Hötzer J, Jainta M, Nestler B, Kalidindi S (2016) Analytics for microstructure datasets produced by phase-field simulations. Acta Mater 103:192–203CrossRef Steinmetz P, Yabansu YC, Hötzer J, Jainta M, Nestler B, Kalidindi S (2016) Analytics for microstructure datasets produced by phase-field simulations. Acta Mater 103:192–203CrossRef
26.
go back to reference Liu R, Ward L, Wolverton C, Agrawal A, Liao W-K, Choudhary A (2016) Deep learning for chemical compound stability prediction. In: Proceedings of ACM SIGKDD Workshop on Large-scale Deep Learning for Data Mining (DL-KDD), pp 1–7 Liu R, Ward L, Wolverton C, Agrawal A, Liao W-K, Choudhary A (2016) Deep learning for chemical compound stability prediction. In: Proceedings of ACM SIGKDD Workshop on Large-scale Deep Learning for Data Mining (DL-KDD), pp 1–7
27.
go back to reference Liu R, Agrawal A, Liao W-K, De Graef M, Choudhary A (2016) Materials discovery: understanding polycrystals from large-scale electron patterns. In: Proceedings of IEEE Big Data Workshop on Advances in Software and Hardware for Big Data to Knowledge Discovery (ASH), pp 2261–2269 Liu R, Agrawal A, Liao W-K, De Graef M, Choudhary A (2016) Materials discovery: understanding polycrystals from large-scale electron patterns. In: Proceedings of IEEE Big Data Workshop on Advances in Software and Hardware for Big Data to Knowledge Discovery (ASH), pp 2261–2269
28.
go back to reference Yabansu YC, Steinmetz P, Hötzer J, Kalidindi S, Nestler B (2017) Extraction of reduced-order process-structure linkages from phase-field simulations. Acta Mater 124(1):182–194CrossRef Yabansu YC, Steinmetz P, Hötzer J, Kalidindi S, Nestler B (2017) Extraction of reduced-order process-structure linkages from phase-field simulations. Acta Mater 124(1):182–194CrossRef
29.
go back to reference LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444CrossRef LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444CrossRef
30.
go back to reference Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi S (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254CrossRef Gupta A, Cecen A, Goyal S, Singh AK, Kalidindi S (2015) Structure–property linkages using a data science approach: application to a non-metallic inclusion/steel composite system. Acta Mater 91:239–254CrossRef
31.
go back to reference Nguyen S, Tran-Le A, Vu M, To Q, Douzane O, Langlet T (2016) Modeling thermal conductivity of hemp insulation material: a multi-scale homogenization approach. Build Environ 107:127–134CrossRef Nguyen S, Tran-Le A, Vu M, To Q, Douzane O, Langlet T (2016) Modeling thermal conductivity of hemp insulation material: a multi-scale homogenization approach. Build Environ 107:127–134CrossRef
32.
go back to reference Zhou X-Y, Gosling P, Pearce C, Ullah Z (2016) Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties. Comput Methods Appl Mech Eng 300:84–105CrossRef Zhou X-Y, Gosling P, Pearce C, Ullah Z (2016) Perturbation-based stochastic multi-scale computational homogenization method for the determination of the effective properties of composite materials with random properties. Comput Methods Appl Mech Eng 300:84–105CrossRef
33.
go back to reference Cruzado A, Gan B, Jiménez M, Barba D, Ostolaza K, Linaza A, Molina-Aldareguia J, Llorca J, Segurado J (2015) Multiscale modeling of the mechanical behavior of in718 superalloy based on micropillar compression and computational homogenization. Acta Mater 98:242–253CrossRef Cruzado A, Gan B, Jiménez M, Barba D, Ostolaza K, Linaza A, Molina-Aldareguia J, Llorca J, Segurado J (2015) Multiscale modeling of the mechanical behavior of in718 superalloy based on micropillar compression and computational homogenization. Acta Mater 98:242–253CrossRef
34.
go back to reference Fast T, Kalidindi S (2011) Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 59(11):4595–4605CrossRef Fast T, Kalidindi S (2011) Formulation and calibration of higher-order elastic localization relationships using the MKS approach. Acta Mater 59(11):4595–4605CrossRef
35.
go back to reference Landi G, Niezgoda SR, Kalidindi S (2010) Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel dft-based knowledge systems. Acta Mater 58(7):2716–2725CrossRef Landi G, Niezgoda SR, Kalidindi S (2010) Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel dft-based knowledge systems. Acta Mater 58(7):2716–2725CrossRef
36.
go back to reference Landi G, Kalidindi S (2010) Thermo-elastic localization relationships for multi-phase composites. Comput, Mater, Contin 16(3):273–293 Landi G, Kalidindi S (2010) Thermo-elastic localization relationships for multi-phase composites. Comput, Mater, Contin 16(3):273–293
37.
go back to reference Guo N, Zhao J (2016) 3d multiscale modeling of strain localization in granular media. Computers and Geotechnics Guo N, Zhao J (2016) 3d multiscale modeling of strain localization in granular media. Computers and Geotechnics
38.
go back to reference Seko A, Maekawa T, Tsuda K, Tanaka I (2014) Machine learning with systematic density-functional theory calculations: application to melting temperatures of single-and binary-component solids. Phys Rev B 89 (5):054303CrossRef Seko A, Maekawa T, Tsuda K, Tanaka I (2014) Machine learning with systematic density-functional theory calculations: application to melting temperatures of single-and binary-component solids. Phys Rev B 89 (5):054303CrossRef
39.
go back to reference Bhadeshia H, Dimitriu R, Forsik S, Pak J, Ryu J (2009) Performance of neural networks in materials science. Mater Sci Technol 25(4):504–510CrossRef Bhadeshia H, Dimitriu R, Forsik S, Pak J, Ryu J (2009) Performance of neural networks in materials science. Mater Sci Technol 25(4):504–510CrossRef
40.
go back to reference Curtarolo S, Morgan D, Persson K, Rodgers J, Ceder G (2003) Predicting crystal structures with data mining of quantum calculations. Phys Rev Lett 91(13):135503CrossRef Curtarolo S, Morgan D, Persson K, Rodgers J, Ceder G (2003) Predicting crystal structures with data mining of quantum calculations. Phys Rev Lett 91(13):135503CrossRef
41.
go back to reference Fischer CC, Tibbetts KJ, Morgan D, Ceder G (2006) Predicting crystal structure by merging data mining with quantum mechanics. Nat Mater 5(8):641–646CrossRef Fischer CC, Tibbetts KJ, Morgan D, Ceder G (2006) Predicting crystal structure by merging data mining with quantum mechanics. Nat Mater 5(8):641–646CrossRef
42.
go back to reference Da Silva BC, Basso EW, Bazzan AL, Engel PM (2006) Dealing with non-stationary environments using context detection Proceedings of the 23rd International Conference on Machine Learning. ACM, pp 217–224 Da Silva BC, Basso EW, Bazzan AL, Engel PM (2006) Dealing with non-stationary environments using context detection Proceedings of the 23rd International Conference on Machine Learning. ACM, pp 217–224
43.
go back to reference Kalidindi S, Niezgoda SR, Landi G, Vachhani S, Fast T (2010) A novel framework for building materials knowledge systems. Comput, Mater, Contin 17(2):103–125 Kalidindi S, Niezgoda SR, Landi G, Vachhani S, Fast T (2010) A novel framework for building materials knowledge systems. Comput, Mater, Contin 17(2):103–125
44.
go back to reference Fast T, Niezgoda SR, Kalidindi S (2011) A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models. Acta Mater 59(2):699–707CrossRef Fast T, Niezgoda SR, Kalidindi S (2011) A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models. Acta Mater 59(2):699–707CrossRef
45.
go back to reference Kröner E (1986) Statistical modelling. Springer, Netherlands, pp 229–291 Kröner E (1986) Statistical modelling. Springer, Netherlands, pp 229–291
46.
go back to reference Kröner E (1977) Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 25(2):137–155CrossRef Kröner E (1977) Bounds for effective elastic moduli of disordered materials. J Mech Phys Solids 25(2):137–155CrossRef
47.
go back to reference Fullwood DT, Niezgoda SR, Kalidindi S (2008) Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater 56(5):942–948CrossRef Fullwood DT, Niezgoda SR, Kalidindi S (2008) Microstructure reconstructions from 2-point statistics using phase-recovery algorithms. Acta Mater 56(5):942–948CrossRef
48.
go back to reference Hibbitt Karlsson Sorensen (2001) ABAQUS/standard User’s Manual, vol 1. Hibbitt, Karlsson & Sorensen, Providence, RI Hibbitt Karlsson Sorensen (2001) ABAQUS/standard User’s Manual, vol 1. Hibbitt, Karlsson & Sorensen, Providence, RI
49.
go back to reference Kalidindi S, Landi G, Fullwood DT (2008) Spectral representation of higher-order localization relationships for elastic behavior of polycrystalline cubic materials. Acta Mater 56(15):3843–3853CrossRef Kalidindi S, Landi G, Fullwood DT (2008) Spectral representation of higher-order localization relationships for elastic behavior of polycrystalline cubic materials. Acta Mater 56(15):3843–3853CrossRef
50.
go back to reference Al-Harbi HF, Landi G, Kalidindi S (2012) Multi-scale modeling of the elastic response of a structural component made from a composite material using the materials knowledge system. Modell Simul Mater Sci Eng 20 (5):055001CrossRef Al-Harbi HF, Landi G, Kalidindi S (2012) Multi-scale modeling of the elastic response of a structural component made from a composite material using the materials knowledge system. Modell Simul Mater Sci Eng 20 (5):055001CrossRef
51.
go back to reference Panait L, Luke S (2005) Cooperative multi-agent learning: the state of the art. Auton Agent Multi-Agent Syst 11(3):387–434CrossRef Panait L, Luke S (2005) Cooperative multi-agent learning: the state of the art. Auton Agent Multi-Agent Syst 11(3):387–434CrossRef
53.
go back to reference Garmestani H, Lin S, Adams B, Ahzi S (2001) Statistical continuum theory for large plastic deformation of polycrystalline materials. J Mech Phys Solids 49(3):589–607CrossRef Garmestani H, Lin S, Adams B, Ahzi S (2001) Statistical continuum theory for large plastic deformation of polycrystalline materials. J Mech Phys Solids 49(3):589–607CrossRef
54.
go back to reference Saheli G, Garmestani H, Adams B (2004) Microstructure design of a two phase composite using two-point correlation functions. J Comput-aided Mater Des 11(2-3):103–115CrossRef Saheli G, Garmestani H, Adams B (2004) Microstructure design of a two phase composite using two-point correlation functions. J Comput-aided Mater Des 11(2-3):103–115CrossRef
55.
go back to reference Fullwood DT, Adams B, Kalidindi S (2008) A strong contrast homogenization formulation for multi-phase anisotropic materials. J Mech Phys Solids 56(6):2287–2297CrossRef Fullwood DT, Adams B, Kalidindi S (2008) A strong contrast homogenization formulation for multi-phase anisotropic materials. J Mech Phys Solids 56(6):2287–2297CrossRef
56.
go back to reference Adams B, Canova GR, Molinari A (1989) A statistical formulation of viscoplastic behavior in heterogeneous polycrystals. Textures Microstruct 11:57–71CrossRef Adams B, Canova GR, Molinari A (1989) A statistical formulation of viscoplastic behavior in heterogeneous polycrystals. Textures Microstruct 11:57–71CrossRef
57.
go back to reference MacQueen J (1967) Some methods for classification and analysis of multivariate observations Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol 1, CA, USA, pp 281–297 MacQueen J (1967) Some methods for classification and analysis of multivariate observations Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol 1, CA, USA, pp 281–297
58.
go back to reference Torquato S (2002) Statistical description of microstructures. Ann Rev Mater Res 32(1):77–111CrossRef Torquato S (2002) Statistical description of microstructures. Ann Rev Mater Res 32(1):77–111CrossRef
59.
go back to reference Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties, vol 16. Springer, New YorkCrossRef Torquato S (2002) Random heterogeneous materials: microstructure and macroscopic properties, vol 16. Springer, New YorkCrossRef
60.
go back to reference Liu Y, Greene MS, Chen W, Dikin DA, Liu WK (2013) Computational microstructure characterization and reconstruction for stochastic multiscale material design. Comput-Aided Des 45(1):65–76CrossRef Liu Y, Greene MS, Chen W, Dikin DA, Liu WK (2013) Computational microstructure characterization and reconstruction for stochastic multiscale material design. Comput-Aided Des 45(1):65–76CrossRef
61.
go back to reference Øren P-E, Bakke S (2002) Process based reconstruction of sandstones and prediction of transport properties. Transp Porous Media 46(2-3):311–343CrossRef Øren P-E, Bakke S (2002) Process based reconstruction of sandstones and prediction of transport properties. Transp Porous Media 46(2-3):311–343CrossRef
Metadata
Title
Context Aware Machine Learning Approaches for Modeling Elastic Localization in Three-Dimensional Composite Microstructures
Authors
Ruoqian Liu
Yuksel C. Yabansu
Zijiang Yang
Alok N. Choudhary
Surya R. Kalidindi
Ankit Agrawal
Publication date
31-03-2017
Publisher
Springer International Publishing
Published in
Integrating Materials and Manufacturing Innovation
Print ISSN: 2193-9764
Electronic ISSN: 2193-9772
DOI
https://doi.org/10.1007/s40192-017-0094-3

Premium Partners