Deformation of a sphere made of magnetoactive elastomer under a strong uniform magnetic field

Magnetostriction effect of a spherical sample of a magnetoactive elastomer (MAE) is analyzed. In comparison with the preceding study, the consideration is done on a more realistic basis: taking into account saturation of the MAE magnetization in contrast to the former model where the magnetization was supposed to be linear whatever the field strength. This more thorough investigation has revealed that the striction-induced elongation effect, depending on the material parameters, may occur in two forms. One scenario manifests itself as tapering of the polar zones of the former sphere, where 'beaks' are formed, so that the shape of the object drastically deviates from a spheroidal one. The mechanism the underlies the occurrence of beaks is the surface instability of a magnetizable elastic continuum, and the beak nucleation follows the second-order transition pattern; the resulting overall elongation of the body does not display any hysteresis. Another scenario—it is related to MAEs with higher magnetic properties and softer matrices—implies that the beak formation happens simultaneously with a jump-like overall elongation of the former sphere, and this transformation resembles the first-order transition pattern. Upon assessing the chances to observe the predicted effects on the samples of now existing MAEs, one comes to a conclusion that the second scenario is hardly possible, whereas the first one, i.e., beak formation without hysteretic stretching, is much more realizable. (paper)