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Toward a Nonlinear Asymptotic Model for Thin Magnetoelastic Plates

  • Sushma Santapuri
  • David J. Steigmann
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 89)

Abstract

An asymptotic two-dimensional formulation for the potential energy of a thin magnetoelastic plate is obtained from that for a three-dimensional magnetoelastic body subjected to conservative tractions and an applied magnetic field.

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Notes

Acknowledgements

SS thanks the Institute of Functional Nanomaterials at the University of Puerto Rico and the US National Science Foundation, through grant number EPS-1002410, for their support of her Visiting Professorship at UC Berkeley. DJS gratefully acknowledges support provided by the US National Science Foundation through grant number CMMI-1538228.

References

  1. Brown WF (1966) Magnetoelastic Interactions. Springer, BerlinGoogle Scholar
  2. DeSimone A, Podio-Guidugli P (1996) On the continuum theory of deformable ferromagnetic solids. Arch Rational Mech Anal 136:201–233Google Scholar
  3. Dorfmann L, Ogden RW (2014) Nonlinear Theory of Electroelastic and Magnetoelastic Interactions. Springer, New YorkGoogle Scholar
  4. Giaquinta M, Hildebrandt S (1996) Calculus of Variations, vol I. Springer, BerlinGoogle Scholar
  5. James RD (2002) Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape memory cantilever. Continuum Mech Thermodyn 14:55–86Google Scholar
  6. Kankanala SV, Triantafyllidis N (2004) On finitely strained magnetorheological elastomers. J Mech Phys Solids 52:2869–2908Google Scholar
  7. Kovetz A (2000) Electromagnetic Theory. Oxford University Press, OxfordGoogle Scholar
  8. Maugin GA (1988) Continuum Mechanics of Electromagnetic Solids. North-Holland, AmsterdamGoogle Scholar
  9. Steigmann DJ (2004) Equilibrium theory for magnetic elastomers and magnetoelastic membranes. Int J Non-linear Mech 39:1193–1216Google Scholar
  10. Steigmann DJ (2013) A well-posed finite-strain model for thin elastic sheets with bending stiffness. Math Mech Solids 13:103–112Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Applied MechanicsIndian Institute of Technology DelhiNew DelhiIndia
  2. 2.Department of Mechanical EngineeringUniversity of California BerkeleyBerkeleyUSA

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