Magnetically tunable anti-plane wave bandgaps in 2D periodic two-phase hard-magnetic soft composites

Abstract

The active manipulation of phononic bandgaps has been a topic of great interest in the recent past. Phononic crystals, or periodic composite structures built from soft elastomers, offer the potential for reversible manipulation of their phononic bandgaps through finite deformation of the periodic composite. By using hard-magnetic soft materials, which undergo reversible, finite deformations when subjected to an applied magnetic flux density, it is possible to tune the frequency ranges of elastic wave bandgaps or generate new bandgaps through magnetic stimuli. Here, we present a theoretical model for the analysis of large magneto-deformation and the anti-plane shear wave bandgaps in an infinite 2D periodic two-phase hard magnetic soft composite structure subjected to magnetic stimuli. The constitutive behavior of the phases in the hard-magnetic soft composite is described using the incompressible Gent model. To solve the incremental anti-plane wave equations, the finite element method and the Floquet-Bloch theorem for periodic medium are utilized. Using the developed framework, we numerically study the dependency of the bandgap width and their location on the direction and magnitude of applied magnetic flux density vector, material parameter contrasts, and geometry and volume fraction of the inclusion phase. The numerical results reveal that significant tunability of the bandgap is achieved when the applied magnetic flux density direction is along the residual magnetic flux density direction. Also, it is seen that the geometry of the inclusion has significant effect on the bandgap width.