SERVE-Boundary Conditions
327
20. M. Pinz, G. Weber, W. Lenthe, M. Uchic, T.M. Pollock, S. Ghosh, Microstructure and property
based statistically equivalent RVEs for intragranular γ − γ microstructures of Ni-based
superalloys. Acta Mater. 157(15), 245–258 (2018)
21. A. Bagri, G. Weber, J.-C. Stinville, W. Lenthe, T. Pollock, C. Woodward, S. Ghosh,
Microstructure and property-based statistically equivalent representative volume elements for
polycrystalline Ni-based superalloys containing annealing twins. Metall. Mater. Trans. A
49(11), 5727–5744 (2018)
22. X. Tu, A. Shahba, J. Shen, S. Ghosh, Microstructure and property based statistically equivalent
RVEs for polycrystalline-polyphase aluminum alloys. Int. J. Plast. 115, 268–292 (2019)
23. T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin, Determination of the size of the
representative volume element for random composites: statistical and numerical approach. Int.
J. Solids Struct. 40(13–14), 3647–3679 (2003)
24. P. Trovalusci, M. Ostoja-Starsewski, M.L. De Bellis, A. Murrali, Scale-dependent homogenization of random composites as micropolar continua. Eur. J. Mech. A Solids 49, 396–407
(2015)
25. E. Recciaa, M.L. De Bellis, P. Trovalusci, R. Masiani, Sensitivity to material contrast in
homogenization of random particle composites as micropolar continua. Compos. Part B 136,
39–45 (2018)
26. R. Pyrz, Correlation of microstructure variability and local stress-field in 2-phase materials.
Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 177(1–2), 253–259 (1994)
27. S. Torquato, Effective stiffness tensor of composite media-I. exact series expansions. J. Mech.
Phys. Solids 45(9), 1421–1448 (1997)
28. S.E. Wilding, D.T. Fullwood, Clustering metrics for two-phase composites. Comput. Mater.
Sci. 50(7), 2262–2272 (2011)
29. E.-Y. Guo, N. Chawla, T. Jing, S. Torquato, Y. Jiao, Accurate modeling and reconstruction of
three-dimensional percolating filamentary microstructures from two-dimensional micrographs
via dilation-erosion method. Mater. Charact. 89, 33–42 (2014)
30. Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76, 031110 (2007)
31. Y. Jiao, F.H. Stillinger, S. Torquato, A superior descriptor of random textures and its predictive
capacity. Proc. Nat. Acad. Sci. USA 106(42), 17634–17639 (2007)
32. A Tewari, A.M Gokhale, J.E Spowart, D.B Miracle, Quantitative characterization of spatial
clustering in three-dimensional microstructures using two-point correlation functions. Acta
Mater. 52(2), 307–319 (2004)
33. D.T. Fullwood, S.R. Niezgoda, S.R. Kalidindi, Microstructure reconstructions from 2-point
statistics using phase-recovery algorithms. Acta Mater. 56, 942–948 (2008)
34. S.R. Niezgoda, D.T. Fullwood, S.R. Kalidindi, Delineation of the space of 2-point correlations
in a composite material system. Acta Mater. 56(18), 5285–5292 (2008)
35. D.V. Kubair, S. Ghosh, Exterior statistics based boundary conditions for establishing statistically equivalent representative volume elements of statistically nonhomogeneous elastic
microstructures. Int. J. Solids Struct. 112, 106–121 (2017)
36. T.I. Zohdi, P. Wriggers, An introduction to Computational Micromechanics (Springer-Verlag
Berlin, Heidelberg, 2004). https://doi.org/10.1007/978-3-540-32360-0
37. M. Ostoja-Starzewski, Microstructural Randomness and Scaling in Mechanics of Materials
(Chapman and Hall/CRC, Boca Raton, 2007)
38. S. Ghosh, D.V. Kubair, Exterior statistics based boundary conditions for representative volume
elements of elastic composites. J. Mech. Phys. Solids 96, 1–24 (2016)
39. D. V. Kubair, M. Pinz, K. Kollins, C. Przybyla, S. Ghosh, Role of exterior statistics-based
boundary conditions for property-based statistically equivalent RVEs of polydispersed elastic
composites. J. Comput. Mech. 52(21), 2919–2928 (2018)
40. S. Torquato, Random Heterogeneous Materials; Microstructure and Macroscopic Properties
(Springer, New York, 2002)
41. T. Mura, Micromechanics of Defects in Solids, 2nd edn. (Kluwer Academic Publishers and
Martinus Nijhoff, Dordrecht, 1987)
327
20. M. Pinz, G. Weber, W. Lenthe, M. Uchic, T.M. Pollock, S. Ghosh, Microstructure and property
based statistically equivalent RVEs for intragranular γ − γ microstructures of Ni-based
superalloys. Acta Mater. 157(15), 245–258 (2018)
21. A. Bagri, G. Weber, J.-C. Stinville, W. Lenthe, T. Pollock, C. Woodward, S. Ghosh,
Microstructure and property-based statistically equivalent representative volume elements for
polycrystalline Ni-based superalloys containing annealing twins. Metall. Mater. Trans. A
49(11), 5727–5744 (2018)
22. X. Tu, A. Shahba, J. Shen, S. Ghosh, Microstructure and property based statistically equivalent
RVEs for polycrystalline-polyphase aluminum alloys. Int. J. Plast. 115, 268–292 (2019)
23. T. Kanit, S. Forest, I. Galliet, V. Mounoury, D. Jeulin, Determination of the size of the
representative volume element for random composites: statistical and numerical approach. Int.
J. Solids Struct. 40(13–14), 3647–3679 (2003)
24. P. Trovalusci, M. Ostoja-Starsewski, M.L. De Bellis, A. Murrali, Scale-dependent homogenization of random composites as micropolar continua. Eur. J. Mech. A Solids 49, 396–407
(2015)
25. E. Recciaa, M.L. De Bellis, P. Trovalusci, R. Masiani, Sensitivity to material contrast in
homogenization of random particle composites as micropolar continua. Compos. Part B 136,
39–45 (2018)
26. R. Pyrz, Correlation of microstructure variability and local stress-field in 2-phase materials.
Mater. Sci. Eng. A-Struct. Mater. Prop. Microstruct. Process. 177(1–2), 253–259 (1994)
27. S. Torquato, Effective stiffness tensor of composite media-I. exact series expansions. J. Mech.
Phys. Solids 45(9), 1421–1448 (1997)
28. S.E. Wilding, D.T. Fullwood, Clustering metrics for two-phase composites. Comput. Mater.
Sci. 50(7), 2262–2272 (2011)
29. E.-Y. Guo, N. Chawla, T. Jing, S. Torquato, Y. Jiao, Accurate modeling and reconstruction of
three-dimensional percolating filamentary microstructures from two-dimensional micrographs
via dilation-erosion method. Mater. Charact. 89, 33–42 (2014)
30. Y. Jiao, F.H. Stillinger, S. Torquato, Modeling heterogeneous materials via two-point correlation functions: basic principles. Phys. Rev. E 76, 031110 (2007)
31. Y. Jiao, F.H. Stillinger, S. Torquato, A superior descriptor of random textures and its predictive
capacity. Proc. Nat. Acad. Sci. USA 106(42), 17634–17639 (2007)
32. A Tewari, A.M Gokhale, J.E Spowart, D.B Miracle, Quantitative characterization of spatial
clustering in three-dimensional microstructures using two-point correlation functions. Acta
Mater. 52(2), 307–319 (2004)
33. D.T. Fullwood, S.R. Niezgoda, S.R. Kalidindi, Microstructure reconstructions from 2-point
statistics using phase-recovery algorithms. Acta Mater. 56, 942–948 (2008)
34. S.R. Niezgoda, D.T. Fullwood, S.R. Kalidindi, Delineation of the space of 2-point correlations
in a composite material system. Acta Mater. 56(18), 5285–5292 (2008)
35. D.V. Kubair, S. Ghosh, Exterior statistics based boundary conditions for establishing statistically equivalent representative volume elements of statistically nonhomogeneous elastic
microstructures. Int. J. Solids Struct. 112, 106–121 (2017)
36. T.I. Zohdi, P. Wriggers, An introduction to Computational Micromechanics (Springer-Verlag
Berlin, Heidelberg, 2004). https://doi.org/10.1007/978-3-540-32360-0
37. M. Ostoja-Starzewski, Microstructural Randomness and Scaling in Mechanics of Materials
(Chapman and Hall/CRC, Boca Raton, 2007)
38. S. Ghosh, D.V. Kubair, Exterior statistics based boundary conditions for representative volume
elements of elastic composites. J. Mech. Phys. Solids 96, 1–24 (2016)
39. D. V. Kubair, M. Pinz, K. Kollins, C. Przybyla, S. Ghosh, Role of exterior statistics-based
boundary conditions for property-based statistically equivalent RVEs of polydispersed elastic
composites. J. Comput. Mech. 52(21), 2919–2928 (2018)
40. S. Torquato, Random Heterogeneous Materials; Microstructure and Macroscopic Properties
(Springer, New York, 2002)
41. T. Mura, Micromechanics of Defects in Solids, 2nd edn. (Kluwer Academic Publishers and
Martinus Nijhoff, Dordrecht, 1987)