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Surface stability of a layered magnetoelastic half-space

We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic equations in Eulerian and Lagrangian forms, we derive the constitutive relations from a total energy function dependent on the deformation gradient and Lagrangian magnetic induction. Energy principles yield the equilibrium equations, magnetic field equations, and boundary conditions. The second variation of the energy functional provides the incremental equations and conditions for stability analysis. Surface instability is studied by linearizing increments of deformation and magnetic induction about a finitely deformed state under a magnetic field normal to the surface. Four illustrative cases are considered: (i) a layered non-magnetizable half-space with varying stiffness contrast; (ii) the critical stretch of a magnetoelastic half-space as a function of magnetic induction; (iii) surface stability of a magneto-sensitive layer atop a non-magnetizable substrate; and (iv) bifurcation conditions in a two-layered magnetoelastic solid with different stiffness ratios. Graphical results are provided throughout.