Skip to main content
SpringerLink
Log in

A spheroidal inclusion within a 1D hexagonal piezoelectric quasicrystal

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

In this study, we investigate the induction field and the phonon and phason stress fields of a spheroidal inclusion embedded within an infinite matrix of a one-dimensional (1D) hexagonal piezoelectric quasicrystal subjected to the following three prescribed uniform traction boundary conditions: axisymmetric loading, out-of-plane and in-plane shear. The explicit expressions are derived in the surrounding matrix and the inclusions by setting the correct potential function. The reduced results show that the stresses exhibit a singularity on the crack faces. The obtained results can also serve as a reference for exploring other 1D piezoelectric quasicrystals reinforced by spheroidal inclusions.

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

Similar content being viewed by others

References

  1. Ronchetti, M.: Quasicrystals an introduction overview. Philos. Mag. 56, 237–249 (1987)

    Article  Google Scholar 

  2. Wang, R.H., Yang, W.G., Hu, C.Z., et al.: Point and space groups and elastic behaviours of one-dimensional quasicrystals. J. Phys. Condens. Matter 9, 2411–2422 (1997)

    Article  Google Scholar 

  3. Liu, G.T., Guo, R.P., Fan, T.Y.: On the interaction between dislocation and cracks in one dimensional hexagonal quasicrystals. Chin. Phys. 12(22), 1149–1155 (2003)

    Google Scholar 

  4. Liu, G.T., Guo, R.P., Fan, T.Y.: Plane elasticity and dislocation of one dimensional hexagonal quasicrystal with point group 6. J. Beijing Inst. Technol. 14(1), 87–91 (2005)

    MathSciNet  MATH  Google Scholar 

  5. Hu, Y.Q., Xia, P., Wei, K.X.: The interaction between a dislocation and circular inhomogeneity in 1D hexagonal quasicrystals. Appl. Mech. Mater. 429, 34–35 (2010)

    Google Scholar 

  6. Zhao, M.H., Dang, H.Y., Fan, C.Y., et al.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 1: theoretical solution. Eng. Fract. Mech. 179, 59–78 (2017)

    Article  Google Scholar 

  7. Dang, H.Y., Zhao, M.H., Fan, C.Y., et al.: Analysis of a three-dimensional arbitrarily shaped interface crack in a one-dimensional hexagonal thermo-electro-elastic quasicrystal bi-material. Part 2: numerical method. Eng. Fract. Mech. 180, 268–281 (2017)

    Article  Google Scholar 

  8. Fabrikant, V.I.: Green’s functions for the magneto-electro-elastic anisotropic half-space and their applications to contact and crack problems. Arch. Appl. Mech. 87, 1859–1869 (2017)

    Article  Google Scholar 

  9. Li, X.Y., Li, P.D., Wu, T.H., et al.: Three-dimensional fundamental solutions for one-dimensional hexagonal quasicrystal with piezoelectric effect. Phys. Lett. A 378, 826–834 (2014)

    Article  MathSciNet  Google Scholar 

  10. Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. A 241, 376–396 (1957)

    MathSciNet  MATH  Google Scholar 

  11. Kogan, L., Hui, C.Y., Molkov, V.: Stress and induction field of a spheroidal inclusion or a penny-shaped crack in a transversely isotropic piezo-electric material. Int. J. Solids Struct. 33(19), 2719–2737 (1996)

    Article  Google Scholar 

  12. Wang, X., Pan, E.Y.: Interaction between an edge dislocation and a circular inclusion with interface slip and diffusion. Acta Mater. 59, 797–804 (2011)

    Article  Google Scholar 

  13. Wang, X.: Eshelby’s inclusion and dislocation problems for an isotropic circular domain bonded to an anisotropic medium. Acta Mech. 226, 103–121 (2015)

    Article  MathSciNet  Google Scholar 

  14. Wang, X., Schiavone, P.: Decagonal quasicrystalline elliptical inclusions under thermomechanical loading. Acta Mech. Solida Sin. 27, 518–530 (2014)

    Article  Google Scholar 

  15. Lou, F., Cao, T., Qin, T.Y., et al.: Plane analysis for an inclusion in 1D hexagonal quasicrystal using the hypersingular integral equation method. Acta Mech. Solida Sin. 32, 249–260 (2019)

    Article  Google Scholar 

  16. Altay, G., Dokmeci, M.C.: On the fundamental equations of piezoelasticity of quasicrystal media. Int. J. Solids Struct. 49, 3255–3262 (2012)

    Article  Google Scholar 

  17. Yu, J., Guo, J.H., PAN, E.N., et al.: General solutions of plane problem in one-dimensional quasicrystal piezoelectric materials and its application on fracture mechanics. Appl. Math. Mech. (Engl. Ed.) 36, 793–814 (2015)

    Article  MathSciNet  Google Scholar 

  18. Wang, B.: Three-dimensional analysis of a flat elliptical crack in a piezoelectric material. Int. J. Eng. Sci. 30(12), 781–791 (1992)

    Article  Google Scholar 

  19. Wang, B.L., Noda, N., Han, J.C., et al.: A penny-shaped crack in a transversely isotropic piezoelectric layer. Eur. J. Mech. A Solid Mech. 20, 997–1005 (2001)

    Article  Google Scholar 

  20. Chen, W.Q., Shioya, T.: Complete and exact solutions of a penny-shaped crack in a piezoelectric solid. Int. J. Solids Struct. 37, 2603–2619 (2000)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11762016 and 11762017) and Major Innovation Projects for Building First-class Universities in China’s Western Region (Grant No. ZKZD2017009).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China

    Zhiguo Zhang, Shenghu Ding & Xing Li

Authors
  1. Zhiguo Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shenghu Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shenghu Ding or Xing Li.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, Z., Ding, S. & Li, X. A spheroidal inclusion within a 1D hexagonal piezoelectric quasicrystal. Arch Appl Mech 90, 1039–1058 (2020). https://doi.org/10.1007/s00419-020-01657-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-020-01657-8

Keywords

Search

Navigation