Magneto-deformation and transverse elastic waves in hard-magnetic soft laminates

We study the magneto-mechanical behavior of periodic laminates made of hard-magnetic active elastomers (HMAEs). We formulate the amended free-energy function for HMAEs, and derive an explicit expression for the induced deformation of the HMAE laminate as a function of the applied magnetic field. Next, we employ the “small-on-large” framework and examine the small-amplitude shear waves propagating in the finitely deformed HMAE laminate in a magnetic field. We find that the remanent magnetization of HMAE phases can result in compressive deformations (in the direction of the applied magnetic field), as opposed to the induced tensile deformation in previously considered soft-magnetic active laminates. Further, we derive the dispersion relations for the transverse elastic waves propagating in the direction perpendicular to the layers. We use the analytical results to illustrate the tunability of the shear wave band gaps with varying remanent magnetizations of the phases; moreover, the shear wave band gaps can be actively controlled by a remotely applied magnetic field.