Field-induced upward bending of a magnetoelastomer cantilever residing on a horizontal plane: An unconventional cilium

Abstract

The mechanical response of a cantilever made of a magnetoactive elastomer (MAE) of magnetically soft type positioned on a solid plane and subjected to a uniform magnetic field is studied. Under a field normal to the plane, the cantilever may lose its straight configuration either by lifting its free end or by forming an arc. Under cyclic variation of the field, both deformation modes exhibit a substantial magnetomechanical hysteresis when evolving from/to straight configuration under the field strength sweep. Theoretical analysis shows that these deformation scenarios are similar to that of the first-order transition, that is, a jump-like change of the characteristic parameter followed by hysteresis. However, unlike the customary case, hereby the initial state remains stable under arbitrary strong fields, the onset of instability requires a perturbation of finite strength. The effect is essentially different from the known behaviour of MAE cantilevers under an in-plane field where the transition to the curved configuration is of the second-order (reversible) kind. If to consider a horizontal plane-supported MAE cantilever as an element of a magnetic cilia assembly, it behaves in the way opposite to that of conventional systems where in the initial state the MAE cilia stand normally to the surface.