Magnetic-field-induced stress in confined magnetoactive elastomers.

We present a theoretical approach for calculating the state of stress induced by a uniform magnetic field in confined magnetoactive elastomers of arbitrary shape. The theory explicitly includes the magnetic field generated by magnetizable spherical inclusions in the sample interior assuming a non-linear magnetization behavior. The initial spatial distribution of particles and its change in an external magnetic field are considered. This is achieved by the introduction of an effective demagnetizing factor where both the sample shape and the material microstructure are taken into account. Theoretical predictions are fitted to the stress data measured using a specifically designed experimental setup. It is shown that the theory enables the quantification of the effect of material microstructure upon introducing a specific microstructural factor and its derivative with respect to the extensional strain in the undeformed state. The experimentally observed differences between isotropic and anisotropic samples, compliant and stiff elastomer matrices are explained.