Tunable anti-plane wave bandgaps in 2D periodic hard-magnetic soft composites

In this paper, we present a theoretical model for the analysis of large magneto-deformation and the anti-plane shear wave bandgaps in 2D periodic two-phase hard magnetic soft composite structures 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 media are utilized. Using the developed framework, we numerically study the dependency of the bandgap width and their location on the direction and magnitude of the 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. The crucial inferences from the present investigation can find their potential use in the design and manufacturing of futuristic smart soft wave devices with tunable band structures.