A principal axis formulation for nonlinear magnetoelastic deformations: Isotropic bodies

•A new set of invariants are proposed to be used in the modelling of magneto-active elastomers.•The new set of invariants has clearer physical meanings than the standard set of Rivlin and Spencer.•Some simple boundary value problems are solved considering the new formulation.•A general form for the total energy function has been proposed.

In this work a new set of principal axis invariants is proposed in order to study the problem of considering large magneto-elastic deformations, for bodies that are isotropic in the un-deformed configuration when no external magnetic induction is applied. The new set of invariants has clear physical meanings and may have an experimental advantage over the standard invariants used in many previous works in this area. The principal axis invariant formulation is also shown to be more general. Some simple boundary value problems are solved, such as the simple shear, and the biaxial extension of a slab, where with the use of these new invariants, it is possible to study in a much simpler manner the effect of different types of deformations on the response of the material. An illustrated simple specific constitutive equation is proposed which compares well with experiment.