Skip to main content
SpringerLink
Log in

The singularity problem of the magneto-electro-elastic wedge-junction structure with consideration of the air effect

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

Abstract

The analytical compound model of a magneto-electro-elastic wedge-junction structure simultaneously combines a bimaterial magneto-electro-elastic wedge and a three-material electromagnetic junction. This model gives special consideration to the electrostatic and magnetostatic fields in air. Based on the author’s previous study, new results of antiplane singularity orders at the apex of this wedge-junction structure have been obtained in this paper. The characteristic equation and numerical results are obtained for discussions. As a result, the existence of the air plays an important role to reduce the singularity when the permittivity or permeability of the solid approaches that of the air. This wedge-junction compound model is more realistic and shows the important roles of the electrostatic and magnetostatic fields in the air.

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. Van Suchtelen J. (1972). Product properties: a new application of composite materials. Philips Res. Repts. 27: 28–37

    Google Scholar 

  2. Van Den Boomgaard J., Terrell D.R., Born R.A.J. and Giller H.F.J.I. (1974). An in situ grown eutectic magnetoelectric composite material. Part I: Composition and unidirectional solidification. J. Mater. Sci. 9: 1705–1709

    Article  Google Scholar 

  3. Van Run A.M.J.G., Terrell D.R. and Scholing J.H. (1974). An in situ grown eutectic magnetoelectric composite material. Part II: Physical properties.. J. Mater. Sci. 9: 1710–1714

    Article  Google Scholar 

  4. Echigoya J., Hayashi S. and Obi Y. (2000). Directional solidification and interface structure of BaTiO3–CoFe2 O4 eutectic. J. Mater. Sci. 35: 5587–5591

    Article  Google Scholar 

  5. Zheng H. (2004). Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303: 661–663

    Article  Google Scholar 

  6. Nan C.W. (1994). Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rew. B 50(9): 6082–6088

    Article  Google Scholar 

  7. Song Z.F. and Sih G.C. (2003). Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation. Theor. Appl. Fract. Mech. 39: 189–207

    Article  Google Scholar 

  8. Spyropoulos C.P., Sih G.C. and Song Z.F. (2003). Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation. Theor. Appl. Fract. Mech. 39: 281–289

    Article  Google Scholar 

  9. Chue C.H. and Liu T.J.C. (2005). Magneto-electro-elastic antiplane analysis of a bimaterial BaTiO3–CoFe2O4 composite wedge with an interface crack. Theor. Appl. Fract. Mech. 44: 275–296

    Article  Google Scholar 

  10. Wang B.L., Zhang H.Y. and Han J.C. (2007). A periodic array of cracks in a transversely isotropic magnetoelectroelastic material. Arch. Appl. Mech. 77: 541–558

    Article  MATH  Google Scholar 

  11. Gao C.F., Tong P. and Zhang T.Y. (2003). Interfacial crack problems in magnetoelectroelastic solids. Int. J. Eng. Sci. 41: 2105–2121

    Article  Google Scholar 

  12. Zhao M.H., Yang F. and Liu T. (2006). Analysis of a penny-shaped crack in a magneto-electro-elastic medium. Philos. Mag. 86: 4397–4416

    Article  Google Scholar 

  13. Wang B.L. and Mai Y.W. (2003). Crack tip field in piezoelectric/piezomagnetic media. Eur. J. Mech. A 22: 591–602

    Article  MATH  Google Scholar 

  14. Liu T.J.C. and Chue C.H. (2006). On the singularities in a bimaterial magneto-electro-elastic composite wedge under antiplane deformation. Compos. Struct. 72: 254–265

    Article  Google Scholar 

  15. Sue W.C., Liou J.Y. and Sung J.C. (2007). Investigation of the stress singularity of a magnetoelectroelastic bonded antiplane wedge. Appl. Math. Model. 31: 2313–2331

    Article  MATH  Google Scholar 

  16. Williams M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in tension. J. Appl. Mech. ASME 19: 526–528

    Google Scholar 

  17. Bogy D.B. (1968). Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading. J. Appl. Mech. ASME 35: 460–466

    MATH  Google Scholar 

  18. Hein V.L. and Erdogan F. (1971). Stress singularities in a two-material wedge. Int. J. Fract. Mech. 7: 317–330

    Google Scholar 

  19. Ma C.C. and Hour B.L. (1989). Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation. Int. J. Solids Struct. 25: 1295–1309

    Article  MATH  Google Scholar 

  20. Chue C.H. and Chen C.D. (2003). Antiplane stress singularities in a bonded bimaterial piezoelectric wedge. Arch. Appl. Mech. 72: 673–685

    Article  MATH  Google Scholar 

  21. Chen C.D. and Chue C.H. (2003). Singular electro-mechanical fields near the apex of a piezoelectric bonded wedge under antiplane shear. Int. J. Solids Struct. 40: 6513–6526

    Article  MATH  Google Scholar 

  22. Liu T.J.C., Chen C.D. and Chue C.H. (2006). Discussion of antiplane singularities of piezoelectric–dielectric and piezoelectric–conductor wedges. Arch. Appl. Mech. 76: 245–248

    Article  MATH  Google Scholar 

  23. Pageau S.S., Joseph P.F. and Biggers S.B. (1994). The order of stress singularities for bonded and disbonded three-material junctions. Int. J. Solids Struct. 31: 2979–2997

    Article  MATH  Google Scholar 

  24. Chen H.P. (1998). Stress singularities in anisotropic multi-material wedges and junctions. Int. J. Solids Struct. 35: 1057–1073

    Article  MATH  Google Scholar 

  25. Chen M.C., Zhu J.J. and Sze K.Y. (2006). Electroelastic singularities in piezoelectric–elastic wedges and junctions. Eng. Fract. Mech. 73: 855–868

    Article  Google Scholar 

  26. Wigger H.M. and Becker W. (2005). Inplane stress singularities at the interface corner of a bimaterial junction. Compos. Struct. 69: 193–199

    Article  Google Scholar 

  27. Uchino K. (1997). Piezoelectric Actuators and Ultrasonic Motors. Kluwer, Boston

    Google Scholar 

  28. Ikeda T. (1990). Fundamentals of Piezoelectricity. Oxford University Press, New York

    Google Scholar 

  29. Sneddon I.N. (1972). The Use of Integral Transforms. McGraw-Hill, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Vehicle Engineering, Mingchi University of Technology, 84 Gungjuan Road, Taishan, Taipei, 243, Taiwan

    Thomas Jin-Chee Liu

  2. Graduate Institute of Electro-Mechanical Engineering, Mingchi University of Technology, 84 Gungjuan Road, Taishan, Taipei, 243, Taiwan

    Thomas Jin-Chee Liu

Authors
  1. Thomas Jin-Chee Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Jin-Chee Liu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, T.JC. The singularity problem of the magneto-electro-elastic wedge-junction structure with consideration of the air effect. Arch Appl Mech 79, 377–393 (2009). https://doi.org/10.1007/s00419-008-0240-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-008-0240-7

Keywords

Search

Navigation