Skip to main content

Multiscale Modeling of Composites: Toward Virtual Testing … and Beyond

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.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. M. Elices, eds., Structural Biological Materials (New York: Elsevier Science Ltd., 2000).

    Google Scholar 

  2. A. Gautieri, S. Vesentini, A. Redaelli, and M.J. Buehler, Nano Lett. 11, 757 (2011).

    Article  Google Scholar 

  3. K. Tai, M. Dao, S. Suresh, A. Palazoglu, and C. Ortiz, Nat. Mater. 6, 454 (2007).

    Article  Google Scholar 

  4. H.D. Espinosa, A.L. Juster, F.J. Latourte, O.Y. Loh, D. Gregoire, and P.D. Zavattieri, Nat. Comm. 2 (2011).

  5. 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).

    Article  Google Scholar 

  6. H.D. Espinosa, T. Filleter, and M. Naraghi, Adv. Mater. 24, 2805 (2012).

    Google Scholar 

  7. 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).

    Google Scholar 

  8. L.P. Canal, C. González, J. Segurado, and J. Llorca, Comp. Sci. Technol. 72, 1223 (2012).

    Article  Google Scholar 

  9. C. González and J. Llorca, Comp. Sci. Technol. 67, 2795 (2007).

    Article  Google Scholar 

  10. B. Budiansky and N.A. Fleck, Appl. Mech. Rev. 47, S246 (1994).

    Article  Google Scholar 

  11. F. Sket, R. Seltzer, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 72, 350 (2012).

    Article  Google Scholar 

  12. B. Cox and Q. Yang, Science 314, 1102 (2006).

    Article  Google Scholar 

  13. MIL-HDBK-17-1F, Composite Materials Handbook, Vol. 1—Polymer Matrix Composites, Guidelines for Characterization of Structural Materials, 2002.

  14. M. Rodríguez, J.M. Molina-Aldareguía, C. González, and J. Llorca, Acta Mater. 60, 3953 (2012).

    Article  Google Scholar 

  15. J.M. Molina-Aldareguía, M. Rodríguez, C. González, and J. Llorca, Philos. Mag. 91, 1293 (2011).

    Article  Google Scholar 

  16. M. Rodriguez, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 72, 1924 (2012).

    Article  Google Scholar 

  17. T.J. Vogler, S.-Y. Hsu, and S. Kyriakides, Int. J. Solids Struct. 37, 1765 (2000).

    MATH  Article  Google Scholar 

  18. E. Totry, C. González, and J. Llorca, Comp. Sci. Technol. 68, 3128 (2008).

    Article  Google Scholar 

  19. E. Totry, C. González, and J. Llorca, Comp. Sci. Technol. 68, 829 (2008).

    Article  Google Scholar 

  20. L.P. Canal, J. Segurado, and J. Llorca, Int. J. Solids Struct. 46, 2265 (2009).

    MATH  Article  Google Scholar 

  21. E. Totry, J.M. Molina-Aldareguía, C. González, and J. Llorca, Comp. Sci. Technol. 70, 970 (2010).

    Article  Google Scholar 

  22. E. Totry, C. González, J. Llorca, and J. Molina-Aldareguía, Int. J. Fract. 158, 197 (2009).

    MATH  Article  Google Scholar 

  23. T.J. Vaughan and C.T. McCarthy, Comp. Sci. Technol. 71, 388 (2011).

    Article  Google Scholar 

  24. M. Romanowicz, Comput. Mater. Sci. 51, 7 (2012).

    Article  Google Scholar 

  25. V. Smilauer, C.G. Hoover, Z.P. Bazant, F.C. Caner, A.M. Waas, and K.W. Shahwan, Eng. Fract. Mech. 78, 901 (2011).

    Article  Google Scholar 

  26. 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.

  27. J. Segurado and J. Llorca, Int. J. Solids Struct. 41, 2977 (2004).

    MATH  Article  Google Scholar 

  28. ASTM, Test Method D6671-01 (West Conshohocken, PA: American Society for Testing and Materials, 2002).

  29. A. Puck and H. Schürmann, Comp. Sci. Technol. 62, 1633 (2002).

    Article  Google Scholar 

  30. C.G. Dávila, P.P. Camanho, and C.A. Rose, J. Comp. Mater. 39, 323 (2005).

    Article  Google Scholar 

  31. S.T. Pinho, L. Iannucci, and P. Robinson, Composites A 37, 63 (2006).

    Article  Google Scholar 

  32. A.S. Kaddour, M.J. Hinton, and P.D. Soden, Comp. Sci. Technol. 64, 449 (2004).

    Article  Google Scholar 

  33. P.P. Camanho, P. Maimí, and C.G. Dávila, Comp. Sci. Technol. 67, 2715 (2007).

    Article  Google Scholar 

  34. S.T. Pinho, P. Robinson, and L. Iannucci, Comp. Sci. Technol. 66, 2069 (2006).

    Article  Google Scholar 

  35. S.R. Hallet and M.R. Wisnom, J. Comp. Mater. 40, 1229 (2006).

    Article  Google Scholar 

  36. W.G. Jiang, S.R. Hallet, and M.R. Wisnom, Int. J. Numer. Methods Eng. 69, 1982 (2007).

    MATH  Article  Google Scholar 

  37. S.R. Hallet, W.G. Jiang, B. Khan, and M.R. Wisnom, Comp. Sci. Technol. 68, 80 (2008).

    Article  Google Scholar 

  38. C. Bouver, B. Castanié, M. Bizeul, and J.-J. Barrau, Int. J. Solids Struct. 46, 2809 (2009).

    Article  Google Scholar 

  39. E.V. Iarve, M.R. Gurvich, D.H. Mollenhauer, C.A. Rose, and C.G. Dávila, Int. J. Numer. Methods Eng. 88, 749 (2011).

    MATH  Article  Google Scholar 

  40. X.J. Fang, Q.D. Yang, B.N. Cox, and Z.Q. Zhou, Int. J. Numer. Methods Eng. 88, 841 (2011).

    MathSciNet  MATH  Article  Google Scholar 

  41. P. Ladevèze and G. Lubineau, Comp. Sci. Technol. 61, 2149 (2001).

    Article  Google Scholar 

  42. P. Maimí, P.P. Camanho, J.A. Mayugo, and C.G. Dávila, Mech. Mater. 39, 897 (2007).

    Article  Google Scholar 

  43. P. Maimí, P.P. Camanho, J.A. Mayugo, and C.G. Dávila, Mech. Mater. 39, 909 (2007).

    Article  Google Scholar 

  44. C.S. Lopes, P.P. Camanho, Z. Gürdal, and B.F. Tatting, Int. J. Solids Struct. 44, 8493 (2007).

    MATH  Article  Google Scholar 

  45. 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.

  46. C.S. Lopes, P.P. Camanho, Z. Gürdal, P. Maimí, and E.V. González, Comp. Sci. Technol. 69, 937 (2009).

    Article  Google Scholar 

  47. E.V. González, P. Maimí, P.P. Camanho, C.S. Lopes, and N. Blanco, Comp. Sci. Technol. 71, 805 (2011).

    Article  Google Scholar 

  48. C.S. Lopes, O. Seresta, Z. Gürdal, P.P. Camanho, and B. Thuis, Comp. Sci. Technol. 69, 926 (2009).

    Article  Google Scholar 

  49. T.A. Sebaey, E.V. González, C.S. Lopes, N. Blanco, and J. Costa, Comp. Struct. 95, 569 (2013).

    Google Scholar 

  50. National Research Council of the U.S. National Academies, Integrated Computational Materials Engineering (Washington, DC: The National Academy Press, 2008).

  51. National Science and Technology Council, Materials Genome Initiative for Global Competitiveness (Washington, DC: The National Academy Press, 2011).

    Google Scholar 

  52. J. LLorca and C. González, 1st World Congress on Integrated Computational Materials Engineering (Warrendale, PA: TMS, 2011), pp. 121–127.

  53. Q.H. Zeng, A.B. Yu, and G.Q. Lu, Prog. Pol. Sci. 33, 191 (2008).

    Article  Google Scholar 

  54. S. Lopatnikov, P. Simacek, J. Gillespie Jr., and S.G. Advani, Model. Simul. Mater. Sci. Eng. 12, S191 (2004).

    Article  Google Scholar 

  55. F. Trochu, E. Ruiz, V. Achim, and S. Soukane, Composites A 37, 890 (2006).

    Article  Google Scholar 

  56. S.G. Advani, Int. J. Mater. Form. 2, 39 (2009).

    Article  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. LLorca.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11837-012-0509-8

Keywords

  • Representative Volume Element
  • Multiscale Modeling
  • Interface Element
  • Cohesive Crack
  • Continuum Damage Mechanic