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