Shape instability of a magnetic elastomer membrane

Shape instability occurring in a thin plate (membrane) made of a soft magnetoelastic material under a uniform magnetic field is predicted and analysed. The instability onset is shown to be similar to the second-order transition; the dependence of the threshold field on the magnetic and geometric parameters of the membrane is derived analytically; the membrane shapes (domes) are evaluated with the aid of numerical simulation. The theory proposed is in general agreement with experiments performed on a siloxane rubber/iron carbonyl composite.