Incremental Magnetoelastic Deformations, with Application to Surface Instability

TL;DR

This paper develops equations for incremental deformations in magnetoelastic materials, analyzing surface stability under magnetic fields, and demonstrates how magnetic effects can either stabilize or destabilize the material surface.

Contribution

It derives the incremental magnetoelastic equations and boundary conditions, and applies them to surface stability analysis of a magnetoelastic Mooney-Rivlin solid.

Findings

Magnetic fields can influence surface stability of magnetoelastic materials.

The derived equations account for complex coupling between magnetic and elastic effects.

Magnetoelastic coupling parameters determine whether magnetic fields stabilize or destabilize the surface.

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 7x7 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.