Skip to main content
Log in

Asymptotic Derivation of a Linear Plate Model for Soft Ferromagnetic Materials

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

The authors use the asymptotic expansion method by P. G. Ciarlet to obtain a Kirchhoff-Love-type plate model for a linear soft ferromagnetic material. They also give a mathematical justification of the obtained model by means of a strong convergence result.

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

Access this article

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. Brown, W. F. Jr, Magnetoelastic Interactions, Springer-Verlag, Berlin, Heidelberg, New York, 1966.

    Book  Google Scholar 

  2. Ciarlet, P. G., Mathematical Elasticity, II, Theory of Plates, North-Holland, Amsterdam, 1997.

    MATH  Google Scholar 

  3. Danas, K. and Triantafyllidis, N., Instability of a magnetoelastic layer resting on a non-magnetic substrate, J. Mech. Phys. Solids, 69, 2014, 67–83.

    Article  MathSciNet  MATH  Google Scholar 

  4. Dorfmann, A. and Ogden, R. W., Nonlinear magnetoelastic deformations of elastomers, Acta Mechanica, 167, 2004, 13–28.

    Article  MATH  Google Scholar 

  5. Kankanala, S. V. and Triantafyllidis, N., Magnetoelastic buckling of a rectangular block in plane strain, J. Mech. Phys. Solids, 56, 2008, 1147–1169.

    Article  MathSciNet  MATH  Google Scholar 

  6. Maugin, G. A., Continuum Mechanics of Electromagnetic Solids, North-Holland, Amsterdam, 1988.

    MATH  Google Scholar 

  7. Maugin, G. A. and Eringen, A. C., Deformable magnetically saturated media I, Field equations, J. Math. Phys., 13, 1972, 143–155.

    Google Scholar 

  8. Maugin, G. A. and Goudjo, C., The equations of soft ferro-magnetic elastic plates, Int. J. Solid Struct., 8, 1982, 889–912.

    Article  MATH  Google Scholar 

  9. Miya, K., Hara, K. and Someya, K., Experimental and theoretical study on magnetoelastic buckling of a ferromagnetic cantilevered beam-plate, J. Appl. Mech., 45, 1978, 355–360.

    Article  Google Scholar 

  10. Moon, E. C., Magneto-Solid Mechanics, Wiley, New York, 1984.

    Google Scholar 

  11. Nečas, J., Direct Methods in the Theory of Elliptic Equations, Springer-Verlag, Berlin, Heidelberg, 2012.

    MATH  Google Scholar 

  12. Pao, Y. H. and Yeh, C. S., A linear theory for soft ferromagnetic elastic solids, Int. J. Engng., 11, 1973, 415–436.

    Article  MATH  Google Scholar 

  13. Tiersten, H. F., Coupled magnetomechanical equations for magnetically saturated insulators, J. Math. Phys., 5, 1964, 1298–1318.

    Article  MathSciNet  MATH  Google Scholar 

  14. Truesdell, C. and Toupin, R., The Classical Field Theories, Handbuch der Physik, III/I, Principles of Classical Mechanics and Field Theories, Flügge, S. (ed.), Springer-Verlag, Berlin, 1960, 226–790.

  15. Zhou, Y. H. and Zheng, X. J., A theoretical model of magnetoelastic buckling for soft ferromagnetic thin plates, Acta Mechanica Sinica (English edition), 12, 1996, 213–224.

    Article  MATH  Google Scholar 

  16. Zhou, Y. H. and Zheng, X., General expression of magnetic force for soft ferromagnetic plates in complex magnetic fields, Int. J. Engng., 35, 1997, 1405–1417.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhou, Y. H., Zheng, X. and Miya K., Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic fields, Fusion Engng. design, 30, 1995, 325–337.

    Article  Google Scholar 

Download references

Acknowledgements

We thank K. Danas and N. Triantafyllidis for many useful discussions on magnetoelastic materials.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Giuseppe Geymonat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Geymonat, G., Krasucki, F. & Serpilli, M. Asymptotic Derivation of a Linear Plate Model for Soft Ferromagnetic Materials. Chin. Ann. Math. Ser. B 39, 451–460 (2018). https://doi.org/10.1007/s11401-018-0077-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-018-0077-5

Keywords

2000 MR Subject Classification

Navigation