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Multiscale modeling of microstructure–property relations

Published online by Cambridge University Press:  02 August 2016

M.G.D. Geers
Affiliation:
Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands; [email protected]
J. Yvonnet
Affiliation:
Université Paris-Est Marne-la-Vallée, France; [email protected]
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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.

Type
Research Article
Copyright
Copyright © Materials Research Society 2016 

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References

Phillips, R., Crystals, Defects, and Microstructures: Modeling across Scales (Cambridge University Press, Cambridge, 2001).Google Scholar
Taylor, G.I., J. Inst. Met. 62, 307 (1938).Google Scholar
Sachs, G., Z. Ver. Dtsch. Ing. 72, 734 (1928).Google Scholar
Eshelby, J.D., Proc. R. Soc. Lond. A 241, 376 (1957).Google Scholar
Hill, R., J. Mech. Phys. Solids 13, 89 (1965).CrossRefGoogle Scholar
Zaoui, A., J. Eng. Mech. 128, 808 (2002).Google Scholar
Kröner, E., Acta Metall. 9, 155 (1961).Google Scholar
Hutchinson, J.W., Proc. R. Soc. Lond. A 394, 87 (1976).Google Scholar
, W.E., Engquist, B., Lao, X.T., Ren, W.Q., Vanden-Eijnden, E., Commun. Comput. Phys. 2, 367 (2007).Google Scholar
, W.E., Principles of Multiscale Modeling (Cambridge University Press, Cambridge, 2011).Google Scholar
Fish, J., J. Nanopart. Res. 8, 577 (2006).Google Scholar
Fish, J., Multiscale Methods: Bridging the Scales in Science and Engineering (Oxford University Press, Oxford, 2009).CrossRefGoogle Scholar
Plews, J.A., Duarte, C.A., Int. J. Numer. Methods Eng. 102, 180 (2014).Google Scholar
Tadmor, E.B., Phillips, R., Ortiz, M., Philos. Mag. A73, 1529 (1996).CrossRefGoogle Scholar
Miehe, C., Bayreuther, C.G., Int. J. Numer. Methods Eng. 71, 1135 (2007).Google Scholar
Hughes, T.J.R., Feijoo, G.R., Mazzei, L., Quincy, J., Comput. Methods Appl. Mech. Eng. 166, 3 (1998).Google Scholar
Raabe, D., Computational Materials Science: The Simulation of Materials, Microstructures and Properties (Wiley-VCH, Weinheim, 1998).CrossRefGoogle Scholar
Liu, W.K., Karpov, E.G., Zhang, S., Park, H.S., Comput. Methods Appl. Mech. Eng. 193, 1529 (2004).Google Scholar
Agoras, P., Ponte Castañeda, P., Eur. J. Mech. A 30, 828 (2011).Google Scholar
Forest, S., Int. J. Solids Struct. 38, 4585 (2001).CrossRefGoogle Scholar
Ponte Castañeda, P., J. Mech. Phys. Solids 40, 1757 (1992).CrossRefGoogle Scholar
Fish, J., Fan, R., Int. J. Numer. Methods Eng. 76, 1044 (2008).Google Scholar
Feyel, F., Chaboche, J.-L., Comput. Methods Appl. Mech. Eng. 183, 309 (2000).Google Scholar
Zeman, J., de Geus, T.W.J., Vondrejc, J., Peerlings, R.H.J., Geers, M.G.D., Int. J. Numer. Methods Eng. (forthcoming).Google Scholar
Miehe, C., Schröder, J., Schotte, J., Comput. Methods Appl. Mech. Eng. 171, 387 (1999).Google Scholar
Kouznetsova, V.G., Brekelmans, W.A.M., Baaijens, F.P.T., Comput. Mech. 27, 37 (2001).CrossRefGoogle Scholar
Terada, K., Kikuchi, N., Comput. Methods Appl. Mech. Eng. 190, 5247 (2001).CrossRefGoogle Scholar
Geers, M.G.D., Kouznetsova, V.G., Brekelmans, W.A.M., J. Comput. Appl. Math. 234, 2175 (2010).Google Scholar
Kouznetsova, V.G., Geers, M.G.D., Brekelmans, W.A.M., Comput. Methods Appl. Mech. Eng. 193, 5525 (2004).Google Scholar
Bosco, E., Kouznetsova, V.G., Geers, M.G.D., Int. J. Numer. Methods Eng. 102, 496 (2015).Google Scholar
Özdemir, I., Brekelmans, W.A.M., Geers, M.G.D., Int. J. Numer. Methods Eng. 73, 185 (2008).Google Scholar
Coenen, E.W.C., Kouznetsova, V.G., Geers, M.G.D., Int. J. Numer. Methods Eng. 83, 1180 (2010).CrossRefGoogle Scholar
Matouš, K., Kulkarni, M.G., Geubelle, P.H., J. Mech. Phys. Solids 56, 1511 (2008).Google Scholar
Temizer, I., Int. J. Numer. Methods Eng. 97, 582 (2014).Google Scholar
Pham, K., Kouznetsova, V.G., Geers, M.G.D., J. Mech. Phys. Solids 61, 2125 (2013).Google Scholar
Vossen, B.G., van der Sluis, O., Schreurs, P.J.G., Geers, M.G.D., Neggers, J., Hoefnagels, J.P.M., Mech. Mater. 88, 1 (2015).Google Scholar
Vossen, B.G., Schreurs, P.J.G., van der Sluis, O., Geers, M.G.D., J. Mech. Phys. Solids 66, 117 (2014).Google Scholar
Vossen, B.G., van der Sluis, O., Schreurs, P.J.G., Geers, M.G.D., Eng. Fract. Mech. (forthcoming).Google Scholar
Kooiman, M., Hütter, M., Geers, M.G.D., J. Stat. Mech. 2014, P04028 (2014).Google Scholar
Kooiman, M., Hütter, M., Geers, M.G.D., J. Stat. Mech. 2015, P06005 (2015).Google Scholar
Kooiman, M., Hütter, M., Geers, M.G.D., J. Mech. Phys. Solids 78, 186 (2015).Google Scholar
Kooiman, M., Hütter, M., Geers, M.G.D., J. Mech. Phys. Solids (forthcoming).Google Scholar
Öttinger, H.C., Beyond Equilibrium Thermodynamics (Wiley-VCH, Hoboken, NJ 2005).Google Scholar
van Beers, P.R.M., McShane, G.J., Kouznetsova, V.G., Geers, M.G.D., J. Mech. Phys. Solids 61, 2659 (2013).CrossRefGoogle Scholar
van Beers, P.R.M., Kouznetsova, V.G., Geers, M.G.D., Tschopp, M.A., McDowell, D.L., Acta Mater. 82, 513 (2015).Google Scholar
van Beers, P.R.M., Kouznetsova, V.G., Geers, M.G.D., Mech. Mater. 90, 69 (2015).Google Scholar
van Beers, P.R.M., Kouznetsova, V.G., Geers, M.G.D., J. Mech. Phys. Solids 83, 243 (2015).CrossRefGoogle Scholar
Ambos, A., Willot, F., Jeulin, D., Trumel, H., Int. J. Solids Struct. 60–61, 125 (2015).Google Scholar
Altendorf, H., Jeulin, D., Willot, F., Int. J. Solids Struct. 51, 3807 (2014).Google Scholar
Moulinec, H., Suquet, P., C. R. Acad. Sci. II 318, 1417 (1994).Google Scholar
Michel, J.C., Moulinec, H., Suquet, P., Comput. Methods Appl. Mech. Eng. 172, 109 (1999).Google Scholar
Moulinec, H., Suquet, P., Physica B 338, 58 (2003).Google Scholar
Escoda, J., Willot, F., Jeulin, D., Sanahuja, J., Toulemonde, C., Cement Concrete Res. 41, 542 (2011).Google Scholar
Lavergne, F., Sab, K., Sanahuja, J., Bornert, M., Toulemonde, C., Cement Concrete Res. 71, 14 (2015).Google Scholar
Chen, L., Chen, J., Lebensohn, R.A., Ji, Y.Z., Heo, T.W., Bhattacharyya, S., Chang, K., Mathaudhu, S., Liu, Z.K., Chen, L.-Q., Comput. Methods Appl. Mech. Eng. 285, 829 (2015).Google Scholar
Yvonnet, J., Int. J. Numer. Methods Eng. 92, 178 (2012).Google Scholar
Dunant, C.F., Bary, B., Giorla, A.B., Péniguel, C., Sanahuja, J., Toulemonde, C., Tran, A.B., Willot, F., Yvonnet, J., Adv. Eng. Softw. 58, 1 (2013).Google Scholar
Moës, N., Cloirec, M., Cartraud, P., Remacle, J.F., Comput. Methods Appl. Mech. Eng. 192, 3163 (2003).Google Scholar
Tran, A.B., Yvonnet, J., He, Q.-C., Toulemonde, C., Sanahuja, J., Int. J. Numer. Methods Eng. 85, 1436 (2011).Google Scholar
Toulemonde, C., Masson, R., Gharib, J.E., C. R. Mec. 336, 275 (2008).Google Scholar
Nguyen, V.P., Stroeven, M., Sluys, L.J., Comput. Methods Appl. Mech. Eng. 201–204, 139 (2012).Google Scholar
Ladevèze, P., Loiseau, O., Dureisseix, D., Int. J. Numer. Methods Eng. 52, 121 (2001).Google Scholar
Fritzen, F., Hodapp, M., Leuschner, M., Comput. Methods Appl. Mech. Eng. 278, 186 (2014).Google Scholar
Mosby, M., Matouš, K., Extreme Mech. Lett. 6, 68 (2016).Google Scholar
Yvonnet, J., He, Q.-C., J. Comput. Phys. 223, 341 (2007).Google Scholar
Lumley, J.L., in Atmospheric Turbulence and Radio Wave Propagation, Yaglom, A.M., Tataski, V.I., Eds. (Nauka, Moscow, 1967), p. 166.Google Scholar
Hernández, J.A., Oliver, J., Huespe, A.E., Caicedo, M.A., Cante, J.C., Comput. Methods Appl. Mech. Eng. 276, 149 (2014).Google Scholar
Wen, B., Zabaras, N., Comput. Mater. Sci. 63, 269 (2012).Google Scholar
Sparks, P., Oskay, C., Int. J. Multiscale Comput. Eng. 11, 185 (2013).CrossRefGoogle Scholar
El Halabi, F., González, D., Chico, A., Doblaré, M., Comput. Methods Appl. Mech. Eng. 257, 183 (2013).Google Scholar
Chinesta, F., Ammar, A., Cueto, E., Arch. Comput. Methods Eng. 17, 327 (2010).Google Scholar
Dvorak, G.J., Proc. R. Soc. Lond. A 437, 311 (1992).Google Scholar
Michel, J.C., Suquet, P., Int. J. Solids Struct. 40, 6937 (2003).Google Scholar
Roussette, S., Michel, J.C., Suquet, P., Compos. Sci. Technol. 69, 22 (2009).Google Scholar
Fritzen, F., Sepe, S.V., Comput. Struct. 157, 114 (2015).Google Scholar
Yvonnet, J., Gonzalez, D., He, Q.-C., Comput. Methods Appl. Mech. Eng. 198, 2723 (2009).Google Scholar
Terada, K., Kato, J., Hirayama, N., Inugai, T., Yamamoto, K., Comput. Mech. 52, 1199 (2013).Google Scholar
Temizer, I., Zohdi, T.I., Comput. Mech. 40, 281 (2007).Google Scholar
Temizer, I., Wriggers, P., Comput. Methods Appl. Mech. Eng. 196, 3409 (2007).Google Scholar
Klusemann, B., Ortiz, M., Int. J. Numer. Methods Eng. (forthcoming).Google Scholar
Yvonnet, J., Monteiro, E., He, Q.-C., Int. J. Multiscale Comput. Eng. 11, 201 (2013).Google Scholar
Clement, A., Soize, C., Yvonnet, J., Int. J. Numer. Methods Eng. 91, 799 (2012).Google Scholar
Clement, A., Soize, C., Yvonnet, J., Comput. Methods Appl. Mech. Eng. 254, 61 (2013).Google Scholar
Le, B.A., Yvonnet, J., He, Q.-C., Int. J. Numer. Methods Eng. 104, 1061 (2015).Google Scholar
Guilleminot, J., Soize, C., Multiscale Model. Simul. 11, 840 (2013).Google Scholar
Zhou, X.-Y., Gosling, P.D., Pearce, C.J., Kaczmarczyk, Ł., Ullah, Z., Int. J. Solids Struct. 80, 368 (2016).Google Scholar