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Original Articles

Statistics informed boundary conditions for statistically equivalent representative volume elements of clustered composite microstructures

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Pages 1205-1213 | Received 06 Mar 2017, Accepted 25 Mar 2017, Published online: 10 Nov 2017

References

  • S. Ghosh and D. Kubair, Exterior statistics based boundary conditions for representative volume elements of elastic composites, J. Mech. Phys. Solids, vol. 96, pp. 1–24, 2016.
  • M.P. Echlin, W.C. Lenthe, T.M. Pollock, Three-dimensional sampling of material structure for property modeling and design, Integ. Mater. Manuf. Innov., vol. 3, no. 21, pp. 1–14, 2014.
  • S. Swaminathan, S. Ghosh, and N. Pagano, Statistically equivalent representative volume elements for unidirectional composite microstructures: Part i-without damage, J. Comp. Mat., vol. 40, no. 7, pp. 583–604, 2006a.
  • S. Swaminathan, N. Pagano, and S. Ghosh, Statistically equivalent representative volume elements for unidirectional composite microstructures: Part ii-with interfacial debonding, J. Comp. Mat., vol. 40, no. 7, pp. 605–621, 2006b.
  • S. Ghosh, Micromechanical Analysis and Multi-Scale Modeling Using the Voronoi Cell Finite Element Method, CRC Press/Taylor & Francis, Boca Raton, FL, 2011.
  • R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, vol. 15, pp. 79–95, 1967.
  • R. Everett, Analysis and modeling of fiber clustering in composites using n-tuples, Scrip Metall. Mater., vol. 28, no. 6, pp. 663–668, 1993.
  • S. Torquato, Effective stiffness tensor of composite media-i. exact series expansions, J. Mech. Phys. Solids, vol. 45, no. 9, pp. 1421–1448, 1997.
  • J. Zeman and M. Sejnoha, From random microstructures to representative volume elements, Modell. Simul. Mat. Sci. Eng., vol. 15, no. 4, pp. S325–S335, 2007.
  • T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct., vol. 40, no. 13–14, pp. 3647–3679, 2003.
  • A. Al-Ostaz, A. Diwakar, and K. Alzebdeh, Statistical model for characterizing random microstructure of inclusion matrix composites, J. Mater. Sci., vol. 42, no. 16, pp. 7016–7030, 2007.
  • S.E. Wilding and D.T. Fullwood, Clustering metrics for two-phase composites, Comput. Mater. Sci., vol. 50, no. 7, pp. 2262–2272, 2011.
  • V. Romanov, S. Lomov, Y. Swolfs, S. Orlova, L. Gorbatikh, and I. Verpoest, Statistical analysis of real and simulated fibre arrangements in unidirectional composites, Comp. Sci. Tech., vol. 87, pp. 126–134, 2013.
  • B.A. Bednarcyk, J. Aboudi, and S.M. Arnold, Analysis of fiber clustering in composite materials using high-fidelity multiscale micromechanics, Int. J. Solids Struct., vol. 69–70, pp. 311–327, 2015.
  • X. Liu and V. Shapiro, Random heterogeneous materials via texture synthesis, Comput. Mater. Sci., vol. 99, pp. 177–189, 2015.
  • Y. Jiao, F. Stillinger, and S. Torquato, Modeling heterogeneous materials via two-point correlation functions: Basic principles, Phys. Rev. E, vol. 76, pp. 031110, 2007a.
  • Y. Jiao, F. Stillinger, and S. Torquato, A superior descriptor of random textures and its predictive capacity, Proc. Natl. Acad. Sci. USA, vol. 106, no. 42, pp. 17634–17639, 2007b.
  • A. Tewari, A. Gokhale, J. Spowart, and D. Miracle, Quantitative characterization of spatial clustering in three-dimensional microstructures using two-point correlation functions, Acta Mater., vol. 52, no. 2, pp. 307–319, 2004.
  • D. Fullwood, S. Niezgoda, and S. Kalidindi, Microstructure reconstructions from 2-point statistics using phase-recovery algorithms, Acta Materi., vol. 56, pp. 942–948, 2008.
  • S. Niezgoda, D. Fullwood, and S. Kalidindi, Delineation of the space of 2-point correlations in a composite material system, Acta Mat., vol. 56, pp. 5285–5292, 2008.
  • S. Niezgoda, D. Turner, D. Fullwood, and S. Kalidindi, Optimized structure based representative volume element sets reflecting the ensemble-averaged 2-point statistics, Acta Mat., vol. 58, pp. 4432–4445, 2010.
  • S. Hazanov and C. Huet, Order relationships for boundary conditions effect in heteogeneous bodies smaller than the representative volume, J. Mech. Phys. Solids, vol. 42, pp. 1995–2011, 1994.
  • T.I. Zohdi and P. Wriggers, An Introduction to Computational Micromechanics, Springer, Berlin, Germany, 2004.
  • M. Ostoja-Starzewski, Microstructural Randomness and Scaling in Mechanics of Materials, Chapman and Hall/CRC, Boca Raton, FL, 2007.
  • S. Torquato, Random Heterogeneous Materials; Microstructure and Macroscopic Properties, Springer-Verlag, New York, 2002.
  • T. Mura, Micromechanics of Defects in Solids, 2nd Edition. Kluwer Academic Publishers and Martinus Nijhoff, Leiden, Boston, 1987.
  • J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. R Soc. Lond., vol. A241, pp. 376–396, 1957.
  • X. Yin, A. To, C. McVeigh, and W. Liu, Statistical volume element method for predicting microstructure constitutive property relations, Comp. Meth. Appl. Mech. Eng., vol. 197, pp. 3516–3529, 2008.
  • D.L. McDowell, S. Ghosh, and S.R. Kalidindi, Representation and computational structure-property relations of random media, JOM, TMS, vol. 63, no. 3, pp. 45–51, 2011.

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