Magnetostriction effect in soft magnetic elastomers

We discuss the magnetostriction effect in soft magnetic elastomers: stretching/shrinking of a sample under the action of uniform magnetic field in the absence of mechanical loads. Qualitative analysis shows that the field has a twofold effect on the medium; one of those mechanisms works at the macroscopic scale whereas the other one stems from the mesoscopic processes. Essentially, the latter one is defined by the architecture of short-range spatial order existing in the ferromagnet particle assembly. This conclusion is illustrated with the aid of numerical modeling. First, it is done on a 2D elastic array filled with linearly magnetizable particles. It is shown that it is indeed the presence of clusters that controls both the sign and magnitude of magnetostriction in the composite. In other words, two composites with the same matrix/filler content may behave very differently depending on their mesoscale structure. Further on, to get a more realistic description, the modeling is extended to a 3D array of spherical particles randomly distributed in an elastic matrix. Although the general conclusions hold, the quantitative results differ substantially.