Abstract
Recent developments in the area of multiscale modeling of fiber-reinforced polymers are presented. The overall strategy takes advantage of the separation of length scales between different entities (ply, laminate, and component) found in composite structures. This allows us to carry out multiscale modeling by computing the properties of one entity (e.g., individual plies) at the relevant length scale, homogenizing the results into a constitutive model, and passing this information to the next length scale to determine the mechanical behavior of the larger entity (e.g., laminate). As a result, high-fidelity numerical simulations of the mechanical behavior of composite coupons and small components are nowadays feasible starting from the matrix, fiber, and interface properties and spatial distribution. Finally, the roadmap is outlined for extending the current strategy to include functional properties and processing into the simulation scheme.
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References
M. Elices, eds., Structural Biological Materials (New York: Elsevier Science Ltd., 2000).
A. Gautieri, S. Vesentini, A. Redaelli, and M.J. Buehler, Nano Lett. 11, 757 (2011).
K. Tai, M. Dao, S. Suresh, A. Palazoglu, and C. Ortiz, Nat. Mater. 6, 454 (2007).
H.D. Espinosa, A.L. Juster, F.J. Latourte, O.Y. Loh, D. Gregoire, and P.D. Zavattieri, Nat. Comm. 2 (2011).
M. Elices, G.V. Guinea, G.R. Plaza, C. Karatzas, C. Riekel, F. Agullo-Rueda, R. Daza, and J. Perez-Rigueiro, Macromolecules 44, 1166 (2011).
H.D. Espinosa, T. Filleter, and M. Naraghi, Adv. Mater. 24, 2805 (2012).
J. LLorca, C. González, J.M. Molina-Aldareguía, J. Segurado, R. Seltzer, F. Sket, M. Rodríguez, S. Sádaba, R. Muñoz, and L.P. Canal, Adv. Mater. 23, 5130 (2011).
L.P. Canal, C. González, J. Segurado, and J. Llorca, Comp. Sci. Technol. 72, 1223 (2012).
C. González and J. Llorca, Comp. Sci. Technol. 67, 2795 (2007).
B. Budiansky and N.A. Fleck, Appl. Mech. Rev. 47, S246 (1994).
F. Sket, R. Seltzer, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 72, 350 (2012).
B. Cox and Q. Yang, Science 314, 1102 (2006).
MIL-HDBK-17-1F, Composite Materials Handbook, Vol. 1—Polymer Matrix Composites, Guidelines for Characterization of Structural Materials, 2002.
M. Rodríguez, J.M. Molina-Aldareguía, C. González, and J. Llorca, Acta Mater. 60, 3953 (2012).
J.M. Molina-Aldareguía, M. Rodríguez, C. González, and J. Llorca, Philos. Mag. 91, 1293 (2011).
M. Rodriguez, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 72, 1924 (2012).
T.J. Vogler, S.-Y. Hsu, and S. Kyriakides, Int. J. Solids Struct. 37, 1765 (2000).
E. Totry, C. González, and J. Llorca, Comp. Sci. Technol. 68, 3128 (2008).
E. Totry, C. González, and J. Llorca, Comp. Sci. Technol. 68, 829 (2008).
L.P. Canal, J. Segurado, and J. Llorca, Int. J. Solids Struct. 46, 2265 (2009).
E. Totry, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 70, 970 (2010).
E. Totry, C. González, J. Llorca, and J. Molina-Aldareguía, Int. J. Fract. 158, 197 (2009).
T.J. Vaughan and C.T. McCarthy, Comp. Sci. Technol. 71, 388 (2011).
M. Romanowicz, Comput. Mater. Sci. 51, 7 (2012).
V. Smilauer, C.G. Hoover, Z.P. Bazant, F.C. Caner, A.M. Waas, and K.W. Shahwan, Eng. Fract. Mech. 78, 901 (2011).
P.P. Camanho and C.G. Dávila, Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials, NASA/TM-2002-211737, 2002.
J. Segurado and J. Llorca, Int. J. Solids Struct. 41, 2977 (2004).
ASTM, Test Method D6671-01 (West Conshohocken, PA: American Society for Testing and Materials, 2002).
A. Puck and H. Schürmann, Comp. Sci. Technol. 62, 1633 (2002).
C.G. Dávila, P.P. Camanho, and C.A. Rose, J. Comp. Mater. 39, 323 (2005).
S.T. Pinho, L. Iannucci, and P. Robinson, Composites A 37, 63 (2006).
A.S. Kaddour, M.J. Hinton, and P.D. Soden, Comp. Sci. Technol. 64, 449 (2004).
P.P. Camanho, P. Maimí, and C.G. Dávila, Comp. Sci. Technol. 67, 2715 (2007).
S.T. Pinho, P. Robinson, and L. Iannucci, Comp. Sci. Technol. 66, 2069 (2006).
S.R. Hallet and M.R. Wisnom, J. Comp. Mater. 40, 1229 (2006).
W.G. Jiang, S.R. Hallet, and M.R. Wisnom, Int. J. Numer. Methods Eng. 69, 1982 (2007).
S.R. Hallet, W.G. Jiang, B. Khan, and M.R. Wisnom, Comp. Sci. Technol. 68, 80 (2008).
C. Bouver, B. Castanié, M. Bizeul, and J.-J. Barrau, Int. J. Solids Struct. 46, 2809 (2009).
E.V. Iarve, M.R. Gurvich, D.H. Mollenhauer, C.A. Rose, and C.G. Dávila, Int. J. Numer. Methods Eng. 88, 749 (2011).
X.J. Fang, Q.D. Yang, B.N. Cox, and Z.Q. Zhou, Int. J. Numer. Methods Eng. 88, 841 (2011).
P. Ladevèze and G. Lubineau, Comp. Sci. Technol. 61, 2149 (2001).
P. Maimí, P.P. Camanho, J.A. Mayugo, and C.G. Dávila, Mech. Mater. 39, 897 (2007).
P. Maimí, P.P. Camanho, J.A. Mayugo, and C.G. Dávila, Mech. Mater. 39, 909 (2007).
C.S. Lopes, P.P. Camanho, Z. Gürdal, and B.F. Tatting, Int. J. Solids Struct. 44, 8493 (2007).
E. Arévalo, C. González, F. Gálvez, and J. LLorca, Proc. 23rd Int. Symp. Ballistics, ed. F. González and V. Sánchez-Gá lvez (Madrid, Spain: Universidad Politecnica de Madrid, 2007), pp. 1123–1132.
C.S. Lopes, P.P. Camanho, Z. Gürdal, P. Maimí, and E.V. González, Comp. Sci. Technol. 69, 937 (2009).
E.V. González, P. Maimí, P.P. Camanho, C.S. Lopes, and N. Blanco, Comp. Sci. Technol. 71, 805 (2011).
C.S. Lopes, O. Seresta, Z. Gürdal, P.P. Camanho, and B. Thuis, Comp. Sci. Technol. 69, 926 (2009).
T.A. Sebaey, E.V. González, C.S. Lopes, N. Blanco, and J. Costa, Comp. Struct. 95, 569 (2013).
National Research Council of the U.S. National Academies, Integrated Computational Materials Engineering (Washington, DC: The National Academy Press, 2008).
National Science and Technology Council, Materials Genome Initiative for Global Competitiveness (Washington, DC: The National Academy Press, 2011).
J. LLorca and C. González, 1st World Congress on Integrated Computational Materials Engineering (Warrendale, PA: TMS, 2011), pp. 121–127.
Q.H. Zeng, A.B. Yu, and G.Q. Lu, Prog. Pol. Sci. 33, 191 (2008).
S. Lopatnikov, P. Simacek, J. Gillespie Jr., and S.G. Advani, Model. Simul. Mater. Sci. Eng. 12, S191 (2004).
F. Trochu, E. Ruiz, V. Achim, and S. Soukane, Composites A 37, 890 (2006).
S.G. Advani, Int. J. Mater. Form. 2, 39 (2009).
Acknowledgements
This investigation was supported by the Ministerio de Ciencia e Innovación of Spain through grant MAT2009-14396, by the Comunidad de Madrid through the program ESTRUMAT (S2009/MAT-1585), by the research project DEFCOM (Era-Net MATERA, EU, 6th FP), and by the European Community’s Seventh Framework Programme FP7/2007-2013 under Grant agreement 213371 (MAAXIMUS, www.maaximus.eu). In addition, the authors want to acknowledge the support of Airbus, Astrium, Abengoa Research, Gamesa, Aernnova, Aciturri, and Airbus Military through various industrial projects.
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LLorca, J., González, C., Molina-Aldareguía, J.M. et al. Multiscale Modeling of Composites: Toward Virtual Testing … and Beyond. JOM 65, 215–225 (2013). https://doi.org/10.1007/s11837-012-0509-8
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DOI: https://doi.org/10.1007/s11837-012-0509-8