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Acta Mechanica

, Volume 230, Issue 3, pp 1061–1076 | Cite as

First-order perturbation-based stochastic homogenization method applied to microscopic damage prediction for composite materials

  • Tien-Dat HoangEmail author
  • Naoki Takano
Original Paper
  • 74 Downloads

Abstract

In this paper, a first-order perturbation-based stochastic homogenization method was developed to predict the probabilities of not only macroscopic properties but also microscopic strain damage in multiphase composite materials, considering many random physical parameters. From the stochastic solution of microscopic strains, damage propagation was analyzed to predict where progressive damage would occur in the microstructures of composites subject to a given macroscopic strain. As an example, a short fiber-reinforced plastic, consisting of short fibers, matrix, and interphase, was used to show the influence of random physical parameters for each constituent material on the variability of the homogenized properties and microscopic strain. In another example, a coated particle-embedded composite material was stochastically analyzed to consider even slight influences of uncertainty in the mechanical properties of the coating material and show damage propagation in this coating layer. Characteristic displacements representing material heterogeneity were thoroughly investigated and extensively used with the aim of reducing the computational cost of finding them in a nonlinear analysis of the microscopic damage propagation.

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Notes

Acknowledgements

This work was supported by a Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (B) (KAKENHI Grant No. 16H04239). The first author thanks the Ministry of Education, Culture, Sports, Science, and Technology of Japan for support in the form of a full scholarship to study and research at Keio University.

References

  1. 1.
    Carneiro-Molina, A.J., Curiel-Sosa, J.L.: A multiscale finite element technique for nonlinear multi-phase materials. Finite Elem. Anal. Des. 94, 64–80 (2015)CrossRefGoogle Scholar
  2. 2.
    Yang, D.S., Zhang, H.W., Zhang, S., Lu, M.K.: A multiscale strategy for thermo-elastic plastic stress analysis of heterogeneous multiphase materials. Acta Mech. 226, 1549–1569 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Wen, P., Takano, N., Kurita, D.: Probabilistic multiscale analysis of three-phase composite material considering uncertainties in both physical and geometrical parameters at microscale. Acta Mech. 227, 2735–2747 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Wu, L., Noels, L., Adam, L., Doghri, I.: A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models. Comput. Methods Appl. Mech. Eng. 236, 164–179 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Zhang, D., Waas, A.M.: A micromechanics based multiscale model for nonlinear composites. Acta Mech. 225, 1391–1417 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ziegler, T., Neubrand, A., Piat, R.: Multiscale homogenization models for the elastic behaviour of metal/ceramic composites with lamellar domains. Compos. Sci. Technol. 70, 664–670 (2014)CrossRefGoogle Scholar
  7. 7.
    Takano, N., Uetsuji, Y., Kashiwagi, Y., Zako, M.: Hierarchical modelling of textile composite materials and structures by the homogenization method. Model. Simul. Mater. Sci. Eng. 7, 207–231 (1999)CrossRefGoogle Scholar
  8. 8.
    Dixit, A., Harlal, S.: Modeling techniques for predicting the mechanical properties of woven-fabric textile composites: a review. Mech. Compos. Mater. 49, 1–20 (2013)CrossRefGoogle Scholar
  9. 9.
    Lin, P.J., Ju, J.W.: Effective elastic moduli of three-phase composites with randomly located and interacting spherical particles of distinct properties. Acta Mech. 208, 11–26 (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Yang, B.J., Kim, B.R., Lee, H.K.: Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites. Acta Mech. 223, 1307–1321 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ramírez-Torres, A., Penta, R., Rodríguez-Ramos, R., José, M., Federico, J.S., Julián, B.C., Raúl, G.D., Luigi, P., Alfio, G.: Three scales asymptotic homogenization and its application to layered hierarchical hard tissues. Int. J. Solids Struct. 131, 190–198 (2018)CrossRefGoogle Scholar
  12. 12.
    Arabnejad, S., Pasini, D.: Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods. Int. J. Mech. Sci. 77, 249–262 (2013)CrossRefGoogle Scholar
  13. 13.
    Fantoni, F., Bacigalupo, A., Paggi, M.: Multi-field asymptotic homogenization of thermo-piezoelectric materials with periodic microstructure. Int. J. Solids Struct. 120, 31–56 (2017)CrossRefGoogle Scholar
  14. 14.
    Fish, J., Yu, Q.: Multiscale damage modelling for composite materials: theory and computational framework. Int. J. Numer. Methods Eng. 52, 161–191 (2001)CrossRefGoogle Scholar
  15. 15.
    Xu, X.F.: A multiscale stochastic finite element method on elliptic problems involving uncertainties. Comput. Methods Appl. Mech. Eng. 196, 2723–2736 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Savvas, D., Stefanou, G.: Assessment of the effect of microstructural uncertainty on the macroscopic properties of random composite materials. J. Compos. Mater. 51, 2707–2725 (2017)CrossRefGoogle Scholar
  17. 17.
    Zhou, X.Y., Gosling, P.D., Pearce, C.J., Ullah, Z., Kaczmarczyk, L.: Perturbation-based stochastic multi-scale computational homogenization method for woven textile composites. Int. J. Solids Struct. 80, 368–380 (2016)CrossRefGoogle Scholar
  18. 18.
    Wen, P., Takano, N., Akimoto, S.: General formulation of the first-order perturbation based stochastic homogenization method using many random physical parameters for multi-phase composite materials. Acta Mech. (2018).  https://doi.org/10.1007/s00707-017-2096-9
  19. 19.
    Sakata, S., Ashida, F., Enya, K.: A microscopic failure probability analysis of a unidirectional fiber reinforced composite material via a multiscale stochastic stress analysis for a microscopic random variation of an elastic property. Comput. Mater. Sci. 62, 35–46 (2012)CrossRefGoogle Scholar
  20. 20.
    Ma, J., Sahraee, S., Wriggers, P., De Lorenzis, L.: Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure. Comput. Mech. 55, 819–835 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Ju, J.W., Wu, Y.: Stochastic micromechanical damage modeling of progressive fiber breakage for longitudinal fiber-reinforced composites. Int. J. Damage Mech. 25, 203–227 (2016)CrossRefGoogle Scholar
  22. 22.
    Alzebdeh, K., Al-Ostaz, A., Jasiuk, I., Ostoja-Starzewski, M.: Fracture of random matrix-inclusion composites: scale effects and statistics. Int. J. Solids Struct. 35, 2537–2566 (1998)CrossRefzbMATHGoogle Scholar
  23. 23.
    Ostoja-Starzewski, M.: Microstructural randomness and scaling in mechanics of materials. CRC Press, Boca Raton (2008)zbMATHGoogle Scholar
  24. 24.
    Yoshimura, A., Waas, A.M., Hirano, Y.: Multiscale homogenization for nearly periodic structures. Compos. Struct. 153, 345–355 (2016)CrossRefGoogle Scholar
  25. 25.
    Hollister, S.J., Riemer, B.A.: Digital-image-based finite element analysis for bone microstructure using conjugate gradient and Gaussian filter techniques. SPIE Proc. Math. Methods Med. Imag. 2035, 95–106 (1993)Google Scholar
  26. 26.
    Takano, N., Zako, M., Kubo, F., Kimura, K.: Microstructure-based stress analysis and evaluation for porous ceramics by homogenization method with digital image-based modeling. Int. J. Solids Struct. 40, 1225–1242 (2003)CrossRefzbMATHGoogle Scholar
  27. 27.
    Takano, N., Ohnishi, Y., Zako, M., Nishiyabu, K.: The formulation of homogenization method applied to large deformation problem for composite materials. Int. J. Solids Struct. 37, 6517–6535 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Lions, J.L.: Some Methods in the Mathematical Analysis of Systems and Their Control. Science Press, Beijing (1981)zbMATHGoogle Scholar
  29. 29.
    Guedes, J.M., Kikuchi, N.: Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput. Methods Appl. Mech. Eng. 83, 143–198 (1990)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Science and TechnologyKeio UniversityYokohamaJapan
  2. 2.Faculty of International TrainingThai Nguyen University of TechnologyTich Luong DistrictVietnam
  3. 3.Department of Mechanical EngineeringKeio UniversityYokohamaJapan

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