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Toward a Nonlinear Asymptotic Model for Thin Magnetoelastic Plates

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Part of the book series: Advanced Structured Materials ((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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References

  • Brown WF (1966) Magnetoelastic Interactions. Springer, Berlin

    Google Scholar 

  • DeSimone A, Podio-Guidugli P (1996) On the continuum theory of deformable ferromagnetic solids. Arch Rational Mech Anal 136:201–233

    Google Scholar 

  • Dorfmann L, Ogden RW (2014) Nonlinear Theory of Electroelastic and Magnetoelastic Interactions. Springer, New York

    Google Scholar 

  • Giaquinta M, Hildebrandt S (1996) Calculus of Variations, vol I. Springer, Berlin

    Google Scholar 

  • James RD (2002) Configurational forces in magnetism with application to the dynamics of a small-scale ferromagnetic shape memory cantilever. Continuum Mech Thermodyn 14:55–86

    Google Scholar 

  • Kankanala SV, Triantafyllidis N (2004) On finitely strained magnetorheological elastomers. J Mech Phys Solids 52:2869–2908

    Google Scholar 

  • Kovetz A (2000) Electromagnetic Theory. Oxford University Press, Oxford

    Google Scholar 

  • Maugin GA (1988) Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam

    Google Scholar 

  • Steigmann DJ (2004) Equilibrium theory for magnetic elastomers and magnetoelastic membranes. Int J Non-linear Mech 39:1193–1216

    Google Scholar 

  • Steigmann DJ (2013) A well-posed finite-strain model for thin elastic sheets with bending stiffness. Math Mech Solids 13:103–112

    Google Scholar 

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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.

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Correspondence to Sushma Santapuri .

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Santapuri, S., Steigmann, D.J. (2018). Toward a Nonlinear Asymptotic Model for Thin Magnetoelastic Plates. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 1. Advanced Structured Materials, vol 89. Springer, Cham. https://doi.org/10.1007/978-3-319-72440-9_38

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  • DOI: https://doi.org/10.1007/978-3-319-72440-9_38

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72439-3

  • Online ISBN: 978-3-319-72440-9

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