Magneto-induced remodelling of fibre-reinforced elastomers

Fibre-reinforced elastomers are a class of elastomeric materials with peculiar mechanical properties. If the fibres are metallic or metallic-coated their orientation can be controlled by applying a magnetic field during the curing phase of the elastomer so to tailor the material anisotropy. Once the elastomer is cured, the application of a magnetic field may be used to control the deformation of the solid. In this paper, we aim at modelling both the pre-curing and post-curing phases within a unifying framework compatible with nonlinear elasticity and growth theory. The coupling between elasticity and magnetic field is obtained by considering a proper form of the free energy density which accounts for the mutual orientation between the magnetic field and the fibres. By considering some asymptotic limits, it is shown that the proposed approach incorporates both the usual magneto-elastic model of solids as well as those models used to study the magnetic reorientation of fibres in viscous solutions.