Skip to main content
SpringerLink
Log in

Evaluation of the effective elastic properties of periodic nanofiber composites with surface effect using eigenfunction expansion-variational method

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The effective elastic properties of composites with double periodic nanofibers are studied theoretically. Based on the Gurtin–Murdoch surface elasticity theory, the elastic field in the nanocomposite can be expanded by applying a functional variational method to a unit cell. The analytical solution of the effective anti-plane shear modulus of the periodic nanocomposites is presented. The convergence of the analytical results is discussed. The comparisons of the obtained macroscopic and nanoscale solutions with the existing results show the effectiveness and accuracy of the proposed method. Based on the analytical solution obtained, the size effect of the effective properties of the periodic nanocomposites is discussed. The effects of the period ratio of microstructure, the fiber/matrix stiffness matching and the nanoporous volume fraction on the effective shear modulus of the nanocomposites are discussed in detail.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Nemat-Nasser, S., Taya, M.: On effective of moduli of an elastic body containing periodically distributed voids. Q. Appl. Math. 39(1), 43–60 (1981)

    Article  MATH  Google Scholar 

  2. Nemat-Nasser, S., Taya, M.: On effective moduli of an elastic body containing periodically distributed voids: comments and corrections. Q. Appl. Math. 43(2), 187–188 (1985)

    Article  MATH  Google Scholar 

  3. Aboudi, J.: Mechanics of composite materials: a unified micromechanical approach. Elsevier Science Publisher, Amsterdam (1991)

    MATH  Google Scholar 

  4. Nemat-Nasser, S., Hori, M.: Micromechanics: overall properties of heterogeneous materials. Elsevier, Amsterdam (1999)

    MATH  Google Scholar 

  5. Saito, M., Imanishi, Y.: Host-guest composites containing ultrasonically arranged particles. J. Mater. Sci. 35, 2373–2377 (2000)

    Article  Google Scholar 

  6. Hashemi, R., Weng, G.J., Kargarnovin, M.H., Shodja, H.M.: Piezoelectric composites with periodic multi-coated inhomogeneities. Int. J. Solids Struct. 47(21), 2893–2904 (2010)

    Article  MATH  Google Scholar 

  7. Rodriguez-Ramos, R., Berger, H., Guinovart-Diaz, R., Lopez-Realpozo, J.C., Wurkner, M., Gabbert, U., Bravo-Castillero, J.: Two approaches for the evaluation of the effective properties of elastic composite with parallelogram periodic cells. Int. J. Eng. Sci. 58, 2–10 (2012)

    Article  MATH  Google Scholar 

  8. Du, D.X.: Theoretical studies on the effective properties of multiphase materials. Tsinghua University, Beijing (2000)

    Google Scholar 

  9. Xia, Z.H., Zhang, Y.F., Ellyin, F.: A unified periodical boundary conditions for representative volume elements of composites and applications. Int. J. Solids Struct. 40(8), 1907–1921 (2003)

    Article  MATH  Google Scholar 

  10. Dong, C.Y.: Effective elastic properties of doubly periodic array of inclusions of various shapes by the boundary element method. Int. J. Solids Struct. 43(25–26), 7919–7938 (2006)

    Article  MATH  Google Scholar 

  11. Yan, P., Jiang, C.P., Song, F., Xu, X.H.: Estimation of transverse thermal conductivity of doubly-periodic fiber reinforced composites. Chin. J. Aeronaut. 23, 54–60 (2010)

    Article  Google Scholar 

  12. Ping, X.C., Chen, M.C., Xie, J.H.: Studies on stress interactions within periodic polygonal. Chin. J. Comput. Mech. 27(6), 1117–1122 (2010)

    Google Scholar 

  13. Xing, Y.F., Yang, Y.: An eigenelement method of periodical composite structures. Compos. Struct. 93(2), 502–512 (2011)

    Article  Google Scholar 

  14. Li, X.: Application of doubly quasi-periodic boundary value problems in elasticity theory. Berlin University, Berlin (1999)

    Google Scholar 

  15. Duan, H.L., Wang, J., Huang, Z.P., Karihaloo, B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53(7), 1574–1596 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Mogilevskaya, S.G., Crouch, S.L., Stolarski, H.K.: Multiple interacting circular nano-inhomogeneities with surface/interface effects. J. Mech. Phys. Solids 56, 2298–2327 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gazit, O., Cohen, Y., Tannenbaum, R.: Periodic nanocomposites: a simple path for the preferential self-assembly of nanoparticles in block-copolymers. Polymer 51, 2185–2190 (2010)

    Article  Google Scholar 

  18. Cricri, G., Garofalo, E., Naddeo, F., Incarnato, L.: Stiffness constants prediction of nanocomposites using a periodic 3D-FEM model. J. Polym. Sci. Part B-Polym. Phys. 50, 207–220 (2012)

    Article  Google Scholar 

  19. Yang, H.B., Wang, S.: Interface tension-induced stress field around periodic nano-inclusions of arbitrary shape. Math. Mech. Solids 24, 2844–2857 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  20. Xu, Y.L., Tian, Q., Xiao, J.H.: Doubly periodic array of coated cylindrical inclusions model and applications for nanocomposites. Acta Mech. 231, 661–681 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Alemi, B., Shodja, H.M.: Effective moduli and characteristic lengths of micropolar media with dense periodic distribution of ellipsoidal nano-/micro-inhomogeneities. Eur. J. Mech. A-Solids 85, 104103 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  22. Korchagin, S., Pleshakova, E., Alexandrova, I., Dolgov, V., Dogadina, E., Serdechnyy, D., Bublikov, K.: Mathematical modeling of electrical conductivity of anisotropic nanocomposite with periodic structure. Mathematics 9, 2948 (2021)

    Article  Google Scholar 

  23. Davis, M.E.: Ordered porous materials for emerging applications. Nature 417(6891), 813–821 (2002)

    Article  Google Scholar 

  24. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  25. Gurtin, M.E., Murdoch, A.I.: Surface stress in solids. Int. J. Solids Struct. 14, 431–440 (1978)

    Article  MATH  Google Scholar 

  26. Gurtin, M.E., Weissmuller, J., Larche, F.: A general theory of curved deformable interfaces in solids at equilibrium. Philos. Mag. A 78, 1093–1109 (1998)

    Article  Google Scholar 

  27. Xiao, J.H., Xu, Y.L.: Micromechanics prediction of the effective elastic property of composites reinforced with cylindrically orthotropic nano fiber under antiplane shear. Arch. Appl. Mech. 92, 2237–2246 (2022)

    Article  Google Scholar 

  28. Xiao, J.H., Xu, B.X., Xu, Y.L., Zhang, F.C.: The generalized self-consistent micromechanics prediction of the magnetoelectroelastic properties of multi-coated nanocomposites with surface effect. Smart Mater. Struct. 28, 055004 (2019)

    Article  Google Scholar 

  29. Xiao, J.H., Xu, Y.L., Zhang, F.C.: A generalized self-consistent method for nano composites accounting for fiber section shape under antiplane shear. Mech. Mater. 81, 94–100 (2015)

    Article  Google Scholar 

  30. Luo, J., Wang, X.: On the anti-plane shear of an elliptic nano inhomogeneity. Eur. J. Mech. A/Solids 28(5), 926–934 (2009)

    Article  MATH  Google Scholar 

  31. Jiang, C.P., Xu, Y.L., Cheung, Y.K., Lo, S.H.: A rigorous analytical method for doubly periodic cylindrical inclusions under longitudinal shear and its application. Mech. Mater. 36(3), 225–237 (2004)

    Article  Google Scholar 

  32. Chen, C.H.: Fiber-reinforced composites under longitudinal shear loading. J. Appl. Mech. 37, 198–201 (1970)

    Article  Google Scholar 

  33. Adams, D.F., Doner, D.R.: Longitudinal shear loading of a unidirectional composite. J. Compos. Mater. 1, 4–17 (1967)

    Article  Google Scholar 

  34. Xiao, J.H., Xu, Y.L., Zhang, F.C.: Size-dependent effective electroelastic moduli of piezoelectric nanocomposites with interface effect. Acta Mech. 222(1–2), 59–67 (2011)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by the Natural Science Foundation of Hebei Province (A2022203025) and the Science and Technology Project of Hebei Education Department (ZD2021104).

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Yanshan University, Qinhuangdao, 066004, China

    Xin Zheng, Junhua Xiao & Yaoling Xu

  2. Hebei Key Laboratory of Mechanical Reliability for Heavy Equipments and Large Structures, Yanshan University, Qinhuangdao, 066004, China

    Xin Zheng, Junhua Xiao & Yaoling Xu

  3. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China

    Peng Yan

Authors
  1. Xin Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junhua Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yaoling Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junhua Xiao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, X., Xiao, J., Yan, P. et al. Evaluation of the effective elastic properties of periodic nanofiber composites with surface effect using eigenfunction expansion-variational method. Acta Mech 234, 3459–3468 (2023). https://doi.org/10.1007/s00707-023-03567-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-023-03567-6

Search

Navigation