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Multiscale modeling of microstructure–property relations

  • Microstructure Informatics in Process–Structure–Property Relations
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Abstract

The recent decades have seen significant progress in linking the mechanical performance of materials to their underlying microstructure. This article presents an overview of some of these achievements, trends, and challenges. Attention is given to methods initially developed for micromechanics and their gradual evolution toward powerful multiscale methods. Various methods have been proposed for bridging scales in mechanics of materials, all aiming for efficiency and accuracy. Computational homogenization is one of these powerful approaches, now used systematically for the assessment of structure–property relations. Novel solution methods and model reduction techniques provide tools to speed up the structure–property analysis, whereby large-scale computations have been made possible. Truly fast analyses of microstructures may be expected in the near future.

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References

  1. R. Phillips, Crystals, Defects, and Microstructures: Modeling across Scales (Cambridge University Press, Cambridge, 2001).

    Google Scholar 

  2. G.I. Taylor, J. Inst. Met. 62, 307 (1938).

    Google Scholar 

  3. G. Sachs, Z. Ver. Dtsch. Ing. 72, 734 (1928).

  4. J.D. Eshelby, Proc. R. Soc. Lond. A 241, 376 (1957).

  5. R. Hill, J. Mech. Phys. Solids 13, 89 (1965).

  6. A. Zaoui, J. Eng. Mech. 128, 808 (2002).

  7. E. Kröner, Acta Metall. 9, 155 (1961).

  8. J.W. Hutchinson, Proc. R. Soc. Lond. A 394, 87 (1976).

  9. W.E., B. Engquist, X.T. Lao, W.Q. Ren, E. Vanden-Eijnden, Commun. Comput. Phys. 2, 367 (2007).

  10. W.E., Principles of Multiscale Modeling (Cambridge University Press, Cambridge, 2011).

  11. J. Fish, J. Nanopart. Res. 8, 577 (2006).

  12. J. Fish, Multiscale Methods: Bridging the Scales in Science and Engineering (Oxford University Press, Oxford, 2009).

  13. J.A. Plews, C.A. Duarte, Int. J. Numer. Methods Eng. 102, 180 (2014).

  14. E.B. Tadmor, R. Phillips, M. Ortiz, Philos. Mag. A73, 1529 (1996).

  15. C. Miehe, C.G. Bayreuther, Int. J. Numer. Methods Eng. 71, 1135 (2007).

  16. T.J.R. Hughes, G.R. Feijoo, L. Mazzei, J. Quincy, Comput. Methods Appl. Mech. Eng. 166, 3 (1998).

  17. D. Raabe, Computational Materials Science: The Simulation of Materials, Microstructures and Properties (Wiley-VCH, Weinheim, 1998).

  18. W.K. Liu, E.G. Karpov, S. Zhang, H.S. Park, Comput. Methods Appl. Mech. Eng. 193, 1529 (2004).

  19. P. Agoras, P. Ponte Castañeda, Eur. J. Mech. A 30, 828 (2011).

  20. S. Forest, Int. J. Solids Struct. 38, 4585 (2001).

  21. P. Ponte Castañeda, J. Mech. Phys. Solids 40, 1757 (1992).

  22. J. Fish, R. Fan, Int. J. Numer. Methods Eng. 76, 1044 (2008).

  23. F. Feyel, J.-L. Chaboche, Comput. Methods Appl. Mech. Eng. 183, 309 (2000).

  24. J. Zeman, T.W.J. de Geus, J. Vondrejc, R.H.J. Peerlings, M.G.D. Geers, Int. J. Numer. Methods Eng. (forthcoming).

  25. C. Miehe, J. Schröder, J. Schotte, Comput. Methods Appl. Mech. Eng. 171, 387 (1999).

  26. V.G. Kouznetsova, W.A.M. Brekelmans, F.P.T. Baaijens, Comput. Mech. 27, 37 (2001).

  27. K. Terada, N. Kikuchi, Comput. Methods Appl. Mech. Eng. 190, 5247 (2001).

  28. M.G.D. Geers, V.G. Kouznetsova, W.A.M. Brekelmans, J. Comput. Appl. Math. 234, 2175 (2010).

  29. V.G. Kouznetsova, M.G.D. Geers, W.A.M. Brekelmans, Comput. Methods Appl. Mech. Eng. 193, 5525 (2004).

  30. E. Bosco, V.G. Kouznetsova, M.G.D. Geers, Int. J. Numer. Methods Eng. 102, 496 (2015).

  31. I. Özdemir, W.A.M. Brekelmans, M.G.D. Geers, Int. J. Numer. Methods Eng. 73, 185 (2008).

  32. E.W.C. Coenen, V.G. Kouznetsova, M.G.D. Geers, Int. J. Numer. Methods Eng. 83, 1180 (2010).

  33. K. Matouš, M.G. Kulkarni, P.H. Geubelle, J. Mech. Phys. Solids 56, 1511 (2008).

  34. I. Temizer, Int. J. Numer. Methods Eng. 97, 582 (2014).

  35. K. Pham, V.G. Kouznetsova, M.G.D. Geers, J. Mech. Phys. Solids 61, 2125 (2013).

  36. B.G. Vossen, O. van der Sluis, P.J.G. Schreurs, M.G.D. Geers, J. Neggers, J.P.M. Hoefnagels, Mech. Mater. 88, 1 (2015).

  37. B.G. Vossen, P.J.G. Schreurs, O. van der Sluis, M.G.D. Geers, J. Mech. Phys. Solids 66, 117 (2014).

  38. B.G. Vossen, O. van der Sluis, P.J.G. Schreurs, M.G.D. Geers, Eng. Fract. Mech. (forthcoming).

  39. M. Kooiman, M. Hütter, M.G.D. Geers, J. Stat. Mech. 2014, P04028 (2014).

  40. M. Kooiman, M. Hütter, M.G.D. Geers, J. Stat. Mech. 2015, P06005 (2015).

  41. M. Kooiman, M. Hütter, M.G.D. Geers, J. Mech. Phys. Solids 78, 186 (2015).

  42. M. Kooiman, M. Hütter, M.G.D. Geers, J. Mech. Phys. Solids (forthcoming).

  43. H.C. Öttinger, Beyond Equilibrium Thermodynamics (Wiley-VCH, Hoboken, NJ 2005).

  44. P.R.M. van Beers, G.J. McShane, V.G. Kouznetsova, M.G.D. Geers, J. Mech. Phys. Solids 61, 2659 (2013).

  45. P.R.M. van Beers, V.G. Kouznetsova, M.G.D. Geers, M.A. Tschopp, D.L. McDowell, Acta Mater. 82, 513 (2015).

  46. P.R.M. van Beers, V.G. Kouznetsova, M.G.D. Geers, Mech. Mater. 90, 69 (2015).

  47. P.R.M. van Beers, V.G. Kouznetsova, M.G.D. Geers, J. Mech. Phys. Solids 83, 243 (2015).

  48. A. Ambos, F. Willot, D. Jeulin, H. Trumel, Int. J. Solids Struct. 60–61, 125 (2015).

  49. H. Altendorf, D. Jeulin, F. Willot, Int. J. Solids Struct. 51, 3807 (2014).

  50. H. Moulinec, P. Suquet, C. R. Acad. Sci. II 318, 1417 (1994).

  51. J.C. Michel, H. Moulinec, P. Suquet, Comput. Methods Appl. Mech. Eng. 172, 109 (1999).

  52. H. Moulinec, P. Suquet, Physica B 338, 58 (2003).

  53. J. Escoda, F. Willot, D. Jeulin, J. Sanahuja, C. Toulemonde, Cement Concrete Res. 41, 542 (2011).

  54. F. Lavergne, K. Sab, J. Sanahuja, M. Bornert, C. Toulemonde, Cement Concrete Res. 71, 14 (2015).

  55. L. Chen, J. Chen, R.A. Lebensohn, Y.Z. Ji, T.W. Heo, S. Bhattacharyya, K. Chang, S. Mathaudhu, Z.K. Liu, L.-Q. Chen, Comput. Methods Appl. Mech. Eng. 285, 829 (2015).

  56. J. Yvonnet, Int. J. Numer. Methods Eng. 92, 178 (2012).

  57. C.F. Dunant, B. Bary, A.B. Giorla, C. Péniguel, J. Sanahuja, C. Toulemonde, A.B. Tran, F. Willot, J. Yvonnet, Adv. Eng. Softw. 58, 1 (2013).

  58. N. Moës, M. Cloirec, P. Cartraud, J.F. Remacle, Comput. Methods Appl. Mech. Eng. 192, 3163 (2003).

  59. A.B. Tran, J. Yvonnet, Q.-C. He, C. Toulemonde, J. Sanahuja, Int. J. Numer. Methods Eng. 85, 1436 (2011).

  60. C. Toulemonde, R. Masson, J.E. Gharib, C. R. Mec. 336, 275 (2008).

  61. V.P. Nguyen, M. Stroeven, L.J. Sluys, Comput. Methods Appl. Mech. Eng. 201–204, 139 (2012).

  62. P. Ladevèze, O. Loiseau, D. Dureisseix, Int. J. Numer. Methods Eng. 52, 121 (2001).

  63. F. Fritzen, M. Hodapp, M. Leuschner, Comput. Methods Appl. Mech. Eng. 278, 186 (2014).

  64. M. Mosby, K. Matouš, Extreme Mech. Lett. 6, 68 (2016).

  65. J. Yvonnet, Q.-C. He, J. Comput. Phys. 223, 341 (2007).

  66. J.L. Lumley, in Atmospheric Turbulence and Radio Wave Propagation, A.M. Yaglom, V.I. Tataski, Eds. (Nauka, Moscow, 1967), p. 166.

  67. J.A. Hernández, J. Oliver, A.E. Huespe, M.A. Caicedo, J.C. Cante, Comput. Methods Appl. Mech. Eng. 276, 149 (2014).

  68. B. Wen, N. Zabaras, Comput. Mater. Sci. 63, 269 (2012).

  69. P. Sparks, C. Oskay, Int. J. Multiscale Comput. Eng. 11, 185 (2013).

  70. F. El Halabi, D. González, A. Chico, M. Doblaré, Comput. Methods Appl. Mech. Eng. 257, 183 (2013).

  71. F. Chinesta, A. Ammar, E. Cueto, Arch. Comput. Methods Eng. 17, 327 (2010).

  72. G.J. Dvorak, Proc. R. Soc. Lond. A 437, 311 (1992).

  73. J.C. Michel, P. Suquet, Int. J. Solids Struct. 40, 6937 (2003).

  74. S. Roussette, J.C. Michel, P. Suquet, Compos. Sci. Technol. 69, 22 (2009).

  75. F. Fritzen, S.V. Sepe, Comput. Struct. 157, 114 (2015).

  76. J. Yvonnet, D. Gonzalez, Q.-C. He, Comput. Methods Appl. Mech. Eng. 198, 2723 (2009).

  77. K. Terada, J. Kato, N. Hirayama, T. Inugai, K. Yamamoto, Comput. Mech. 52, 1199 (2013).

  78. I. Temizer, T.I. Zohdi, Comput. Mech. 40, 281 (2007).

  79. I. Temizer, P. Wriggers, Comput. Methods Appl. Mech. Eng. 196, 3409 (2007).

  80. B. Klusemann, M. Ortiz, Int. J. Numer. Methods Eng. (forthcoming).

  81. J. Yvonnet, E. Monteiro, Q.-C. He, Int. J. Multiscale Comput. Eng. 11, 201 (2013).

  82. A. Clement, C. Soize, J. Yvonnet, Int. J. Numer. Methods Eng. 91, 799 (2012).

  83. A. Clement, C. Soize, J. Yvonnet, Comput. Methods Appl. Mech. Eng. 254, 61 (2013).

  84. B.A. Le, J. Yvonnet, Q.-C. He, Int. J. Numer. Methods Eng. 104, 1061 (2015).

  85. J. Guilleminot, C. Soize, Multiscale Model. Simul. 11, 840 (2013).

    Google Scholar 

  86. X.-Y. Zhou, P.D. Gosling, C.J. Pearce, Ł. Kaczmarczyk, Z. Ullah, Int. J. Solids Struct. 80, 368 (2016).

    Google Scholar 

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Acknowledgments

M.G. and J.Y. gratefully acknowledge all of the co-authors of their papers cited in this overview, in particular, V. Kouznetsova, M. Hütter, R. Peerlings, O. van der Sluis, P. Schreurs, M. Kooiman, B. Vossen, P. van Beers, and T. de Geus.

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Geers, M.G.D., Yvonnet, J. Multiscale modeling of microstructure–property relations. MRS Bulletin 41, 610–616 (2016). https://doi.org/10.1557/mrs.2016.165

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  • DOI: https://doi.org/10.1557/mrs.2016.165

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