Transverse isotropy in magnetoactive elastomers

Magnetoactive elastomers (MAEs) are field-controllable materials with magnetically switchable properties. The presence of an external magnetic field results in the change in the macroscopic shape of the MAE. The magnetic field also introduces a mechanical anisotropy with an axis of symmetry along the magnetic field. We aim to derive an effective material model which considers the initial shape of the MAE from the free energy of an isotropic MAE in the dipole approximation. Primarily, we consider uniaxial deformations parallel and perpendicular to the applied field direction. The stress-strain behaviour of the MAE yields diretion-dependent tensile modulus. It indicates that the MAE behaves as a transversely isotropic material in the presence of an external magnetic field. Finally, we compare our predictions with the conventional transversely isotropic material model and find a good agreement. This comparison allows us to extract the dimensionless scaling parameter of a transversely isotropic MAE which characterizes the influence of the magnitude of a magnetic field as well as the initial shape of an MAE sample.