Topology optimization of hard-magnetic soft laminates for wide tunable SH wave bandgaps

Abstract

The periodic laminates made of hard-magnetic soft materials (HMSMs) have recently received increasing attention due to their tunable phononic bandgap characteristics—ranges of frequencies at which sound and vibrations cannot propagate, which can be controlled remotely through magnetically induced finite deformations. In this work, we present a gradient-based topology optimization framework for determining the optimum distribution of laminate phases to optimize the anti-plane shear wave (SH wave) bandgap characteristics. In particular, by employing the method of moving asymptotes (MMA), we maximize the bandgap width when the laminate is subjected to external magnetic fields. The Gent material model of hyperelasticity, in conjunction with the ideal HMSMs model, is used to describe the constitutive response of the laminate phases. To extract the band structure of the hard-magnetic soft laminate, we employ an in-house finite element model. To demonstrate the capability of the developed numerical framework, a parametric study exploring the effect of the applied external magnetic field on the optimized bandgap characteristics and the design of the periodic laminated composite unit cell is presented. The optimization framework presented in this study will be helpful in the design and development of futuristic tunable wave manipulators.