Incremental magnetoelastic deformations, with application to surface instability

Ottenio, M., Destrade, M. and Ogden, R.W. (2008) Incremental magnetoelastic deformations, with application to surface instability. Journal of Elasticity, 90(1), pp. 19-42. (doi:10.1007/s10659-007-9120-6)

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Abstract

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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Ogden, Professor Raymond
Authors: Ottenio, M., Destrade, M., and Ogden, R.W.
Subjects:Q Science > QA Mathematics
Q Science > QC Physics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Elasticity
ISSN:0374-3535
ISSN (Online):1573-2681
Published Online:13 September 2007

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