Theoretical models for magneto-sensitive elastomers: A comparison between continuum and dipole approaches

Abstract

In the literature, different theoretical models have been proposed to describe the properties of systems which consist of magnetizable particles that are embedded into an elastomer matrix. It is well known that such magneto-sensitive elastomers display a strong magneto-mechanical coupling when subjected to an external magnetic field. Nevertheless, the predictions of available models often vary significantly since they are based on different assumptions and approximations. Up to now the actual accuracy and the limits of applicability are widely unknown. In the present work, we compare the results of a microscale continuum and a dipolar mean field approach with regard to their predictions for the magnetostrictive response of magneto-sensitive elastomers and reveal some fundamental relations between the relevant quantities in both theories. It turns out that there is a very good agreement between both modeling strategies, especially for entirely random microstructures. In contrast, a comparison of the finite-element results with a modified approach, which-similar to the continuum model-is based on calculations with discrete particle distributions, reveals clear deviations. Our systematic analysis of the differences shows to what extent the dipolar mean field approach is superior to other dipole models.

Analytical estimation of non-local deformation-mediated magneto-electric coupling in soft composites

“…Moreover, this study deliberately did not consider the micro-heterogeneous nature of classical magnetic elastomers, e.g. MREs [19,22,28,35,[63][64][65] for which one can expect even richer coupling characteristics. Hence, multiscale investigations parallel to the works [44,45,61,66] are a natural extension of this work.…”

Magnetization-induced shape transformations in flexible ferromagnetic rings

“…Such elastomers include nanoparticle based flexible magnetic chains (wires) [9,10] and ribbons [11,12]. The magnetic properties of elastomers are well described by the long range dipoledipole interaction [13].…”

Importance of matrix inelastic deformations in the initial response of magnetic elastomers

“…Computer simulations have been one of the main tools used to support the theoretical modelling of magnetic gels and elastomers, together with mean-field and continuum analytical theories, 30 , 42 – 46 for more than one decade already. Despite the appearance of promising experimental observation techniques, 33 the understanding of the field-induced local rearrangements of the embedded particles and their impact on the macroscopic response of these materials can still largely benefit from simulations.…”