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

Being able to predict and understand the behaviour of soft magnetic materials paves the way to their technological applications. In this study we analyse the magnetic response of soft magnetic elastomers (SMEs) with magnetically hard particles. We present experimental evidence of a difference between the first and next magnetisation loops exhibited by these SMEs, which depends non-monotonically on the interplay between the rigidity of the polymer matrix, its mechanical coupling with the particles, and the magnetic interactions in the system. In order to explain the microstructural mechanism behind this behaviour, we used a minimal computer simulation model whose results evidence the importance of irreversible matrix deformations due to both translations and rotations of the particles. To confirm the simulation findings, computed tomography (CT) was used. We conclude that the initial exposure to the field triggers the inelastic matrix relaxation in the SMEs, as particles attempt to reorient. However, once the necessary degree of freedom is achieved, both the rotations and the magnetisation behaviour become stationary. We expect this scenario not only to be limited to the materials studied here, but also to apply to a broader class of hybrid SMEs.

Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling.

Ferrogels and magnetorheological elastomers are composite materials obtained by embedding magnetic particles of mesoscopic size in a crosslinked polymeric matrix. They combine the reversible elastic deformability of polymeric materials with the high responsivity of ferrofluids to external magnetic fields. These materials stand out, for example, for significant magnetostriction as well as a pronounced increase of the elastic moduli in the presence of external magnetic fields. By means of x-ray micro-computed tomography, the position and size of each magnetic particle can be measured with a high degree of accuracy. We here use data extracted from real magnetoelastic samples as input for coarse-grained dipole-spring modeling and calculations to investigate internal restructuring, stiffening, and changes in the normal modes spectrum. More precisely, we assign to each particle a dipole moment proportional to its volume and set a randomized network of springs between them that mimics the behavior of the polymeric elastic matrix. Extending our previously developed methods, we compute the resulting structural changes in the systems as well as the frequency-dependent elastic moduli when magnetic interactions are turned on. Particularly, with increasing magnetization, we observe the formation of chain-like aggregates. Interestingly, the static elastic moduli can first show a slight decrease with growing amplitude of the magnetic interactions, before a pronounced increase appears upon the chain formation. The change of the dynamic moduli with increasing magnetization depends on the frequency and can even feature nonmonotonic behavior. Overall, we demonstrate how theory and experiments can complement each other to learn more about the dynamic behavior of this interesting class of materials.