Supplementary material from "Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites"

For a long time, the search for magneto-electric materials concentrated on multi-ferroics and hard-matter composites. By contrast, rather recently the exploitation of strain-mediated magneto-electric (ME) coupling in soft composites was proposed. The basic idea behind this approach is to combine the magneto- and electro-mechanical responses of composites consisting of a soft matrix carrying magnetic inclusions. Despite that such composites are straightforward to manufacture and have cheap constituents, they did not gain much attention up to now. In this contribution, we demonstrate that ME coupling induced by finite deformations could be of significant magnitude. Our approach relies on shape effects as a special non-local phenomenon in magneto- and electro-elasticity. Based on that we characterize an up to now overlooked ME coupling mechanism which purely relies on these shape effects in soft-matter-based magnetic and electric media. While soft magnetic media are commonly realized as composites, the coupling effect to be highlighted exists independently of the origin of a body's magnetic and electric properties. We show that the magnitude of the effect is indeed significant and, among ellipsoidal bodies, most pronounced for those of spherical to moderately prolate shape. Finite-element simulations are performed to assess the quality of the analytical predictions.