Journal of Elasticity

, Volume 90, Issue 1, pp 19–42 | Cite as

Incremental Magnetoelastic Deformations, with Application to Surface Instability



In this paper the equations governing the deformations of infinitesimal (incremental) disturbances superimposed on finite static deformation fields involving magnetic and elastic interactions are presented. The coupling between the equations of mechanical equilibrium and Maxwell’s equations complicates the incremental formulation and particular attention is therefore paid to the derivation of the incremental equations, of the tensors of magnetoelastic moduli and of the incremental boundary conditions at a magnetoelastic/vacuum interface. The problem of surface stability for a solid half-space under plane strain with a magnetic field normal to its surface is used to illustrate the general results. The analysis involved leads to the simultaneous resolution of a bicubic and vanishing of a 7×7 determinant. In order to provide specific demonstration of the effect of the magnetic field, the material model is specialized to that of a “magnetoelastic Mooney–Rivlin solid”. Depending on the magnitudes of the magnetic field and the magnetoelastic coupling parameters, this shows that the half-space may become either more stable or less stable than in the absence of a magnetic field.


Magnetoelasticity Surface instability Finite deformations 

Mathematics Subject Classifications (2000)

74B20 74F15 74G60 


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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Laboratoire de Mécanique Physique, CNRS (UMR 5469)Université Bordeaux 1Talence CedexFrance
  2. 2.Institut Jean le Rond d’Alembert, CNRS (UMR7190)Université Pierre et Marie CurieParis Cedex 05France
  3. 3.Department of MathematicsUniversity of GlasgowGlasgowUK

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