On magneto-acoustic waves in finitely deformed elastic solids

In this paper, in the context of the quasi-magnetostatic approximation, we examine incremental motions superimposed on a static finite deformation of a magneto-elastic material in the presence of an applied magnetic field. Explicit expressions are obtained for the associated magneto-acoustic (or magneto-elastic moduli) tensors in the case of an incompressible isotropic magneto-elastic material, and these are then used to study the propagation of incremental plane waves. The propagation condition is derived in terms of a generalized acoustic tensor and the results are illustrated by obtaining explicit formulas in two special cases: first, when the material is undeformed but subject to a uniform bias field and, second for a prototype model of magneto-elastic interactions in the finite deformation regime. The results provide a basis for the experimental determination of the material parameters of a magneto-sensitive elastomer from measurements of the speed of incremental waves for different pre-strains, bias magnetic fields, and directions of propagation.