Skip to main content
SpringerLink
Log in

Asymptotic fields in the finite element analysis of electrically permeable interface cracks in piezoelectric bimaterials

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

Summary

The interface crack problem for a piezoelectric bimaterial based on permeable conditions is studied numerically. To find the singular electromechanical field at the crack tip, an asymptotic solution is derived in connection with the conventional finite element method. For mechanical and electrical loads, the complex stress intensity factor for an interface crack is obtained. The influence of the applied loads on the electromechanical fields near the crack tip is also studied. For a particular case of a short crack with respect to the bimaterial size, the numerical results are compared with the exact analytical solutions, obtained for a piezoelectric bimaterial plane with an interface crack.

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

Similar content being viewed by others

References

  1. Parton, V.Z.: Fracture mechanics of piezoelectric materials. Acta Astronaut 3 (1976) 671–683

    Article  MATH  Google Scholar 

  2. Pak, Y.E.: Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fracture 54 (1992) 79–100.

    Article  Google Scholar 

  3. Sosa, H.: On the fracture mechanics of piezoelectric solids. Int J Solids Struct 29 (1992) 2613–2622

    Article  MATH  Google Scholar 

  4. Suo, Z.;Kuo, C.M.;Barnet, D.M.;Willis, J.R.: Fracture mechanics for piezoelectric ceramics. J Mech Phys Solids 40 (1992) 739–765

    Article  MATH  MathSciNet  Google Scholar 

  5. Govorukha, V.B.;Munz, D.;Kamlah, M.: On the singular integral equations approach to the interface crack problem for piezoelectric materials. Arch Mech 52 (2000) 247–273

    MATH  Google Scholar 

  6. Kuna, M.: Finite element analyses of crack problems in piezoelectric structures. Compu Mat Sci 13 (1998) 67–80.

    Article  Google Scholar 

  7. Wu, C.C.;Sze, K.Y.;Huang, Y.Q.: Numerical solutions on fracture of piezoelectric materials by hybrid element. Int J Solids Struct 38 (2001) 4315–4329

    Article  MATH  Google Scholar 

  8. Gruebner, O.;Kamlah, M.;Munz D.: Finite element analysis of cracks in piezoelectric materials taking into account the permittivity of the crack medium. Eng Fracture Mech 70 (2003) 1399–1413

    Article  Google Scholar 

  9. Kemmer, G.: Berechnung von elektromechanischen Intensitätsparametern bei Rissen in Piezokeramiken. PhD-thesis, Technische Universität Dresden. VDI-Verlag; Düsseldorf: (2000)

    Google Scholar 

  10. Scherzer, M.;Kuna, M.: Asymptotic analysis of interface problems in piezoelectric composite materials. In: Hoffmann, K.H., ed., Smart Materials Springer, Berlin Heidelberg New york (2001) pp. 137–148.

    Google Scholar 

  11. Parton, V.Z.;Kudryavtsev, B.A.: Electromagnetoelasticity. Gordon and Breach; New York (1998)

    Google Scholar 

  12. Kuo, C.M.; Barnett, D.M.: Stress singularities of interfacial cracks in bounded piezoelectric half-spaces. In: (Wu, J.J., Ting, T.C.T., Barnet, D.M. eds.) Modern theory of anisotropic elasticity and applications SIAM Proc Series, Philadelphia, (1991) pp. 33–50

  13. Ting, T.C.T.: Explicit solution and invariance of the singularities at an interface crack in anisotropic composites. Int J Solids Struct 22 (1986) 965–983

    Article  MATH  MathSciNet  Google Scholar 

  14. ABAQUS/Standard: Version 6.1. Karlsson & Sorensen Inc., Hibbith (2000)

  15. Park, S.B.;Sun, C.T.: Effect of electric field on fracture of piezoelectric ceramics. Int J Fracture 70 (1995) 203–216

    Article  Google Scholar 

  16. Herrmann, K.P.;Loboda, V.V.: Fracture-mechanical assessment of electrically permeable interface cracks in piezoelectric bimaterials by consideration of various contact zone models. Arch Appl Mech 70 (2000) 127–143

    Article  MATH  Google Scholar 

  17. Rice, J.R.: Elastic fracture mechanics concepts for interfacial cracks. J Appl Mech 55 (1988) 98–103

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Computational Mathematics, Dnepropetrovsk National University, 49050, Dnepropetrovsk, Ukraine Corresesponding author

    V. Govorukha

  2. Institut for Materials Research II, Forschungszentrum Karlsruhe, Postfach 3640, 76021, Karlsruhe, Germany

    M. Kamlah

Authors
  1. V. Govorukha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kamlah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Govorukha.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Govorukha, V., Kamlah, M. Asymptotic fields in the finite element analysis of electrically permeable interface cracks in piezoelectric bimaterials. Arch. Appl. Mech. 74, 92–101 (2004). https://doi.org/10.1007/BF02637211

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02637211

Keywords

Search

Navigation