Elastic wave propagation in isotropic magneto-active polymers

Magnetoactive polymers (MAPs) exhibit tunable mechanical properties under external magnetic fields, making them promising candidates for advanced functional materials. This study explores the influence of magnetic fields on the propagation of longitudinal (P-wave) and transverse (S-wave) elastic waves in isotropic MAPs. An enriched magnetoelastic energy function was formulated, from which explicit expressions for P- and S-wave speeds were derived as functions of deformation, magnetic field, and magneto-mechanical coupling parameters. Analytical results showed that, in the absence of deformation, only the in-plane S-wave (polarized along the magnetic field) speed depends directly on the magnetic field and the coupling parameter. Experimental results confirmed the theoretical prediction: exclusively the in-plane S-wave exhibited a measurable increase in speed with increasing magnetic field. This sensitivity is attributed to magnetic-field-induced variations in the material's elastic response in the direction of the magnetic field. In contrast, the P-wave and out-of-plane S-wave (polarized perpendicular to the field) remained unaffected. These findings shed light on the anisotropy of elastic waves induced by magnetic fields in MAPs.