Finite deformation theory for soft ferromagnetic elastic solids

A general theory of finite deformation of soft ferromagnetic elastic solids is formulated following the linear theory developed earlier by Pao and Yeh. The constitutive equations, field equations, and the boundary conditions of this theory are applied to analyse the buckling of a plate under the action of a uniform magnetic field. A nontrivial equilibrium configuration for the deformed plate is shown to exist, and the critical value of the externally applied magnetic induction at which the plate buckles is determined. It is demonstrated that the non-linear deformation affects the critical magnetic induction considerably.