On Magnetoacoustic Waves in Finitely Deformed Elastic Solids

TL;DR

This paper investigates magnetoacoustic wave propagation in finitely deformed magnetoelastic solids, deriving explicit formulas for wave conditions and providing a basis for experimental parameter determination in magneto-sensitive elastomers.

Contribution

It introduces explicit expressions for magnetoacoustic tensors in finitely deformed magnetoelastic materials and analyzes wave propagation under various conditions, advancing understanding of magnetoelastic wave behavior.

Findings

Explicit formulas for magnetoacoustic tensors in incompressible isotropic magnetoelastic materials.

Derived propagation conditions for incremental plane waves in deformed magnetoelastic solids.

Provided a framework for experimental determination of material parameters from wave speed measurements.

Abstract

In this paper, in the context of the quasi-magnetostatic approximation, we examine incremental motions superimposed on a static finite deformation of a magnetoelastic material in the presence of an applied magnetic field. Explicit expressions are obtained for the associated magnetoacoustic (or magnetoelastic moduli) tensors in the case of an incompressible isotropic magnetoelastic 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 magnetoelastic 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.