Design of hard-magnetic soft laminated composites for wide longitudinal wave band gaps using topology optimization

Abstract

As a class of soft active materials, hard-magnetic soft materials (HMSMs) exhibit rapid, reversible deformations, high remanence, and the ability to alter their instantaneous moduli in response to applied magnetic fields. These properties make periodic laminated composites of HMSMs promising candidates for phononic crystals (PnCs), which can exhibit tunable band gaps – frequency ranges in which elastic or acoustic waves are prohibited – by manipulating magnetic fields. PnCs with broad and adjustable band gaps are highly desirable for applications such as elastic/acoustic filters, waveguides, noise reduction, sensors, and acoustic cloaking devices. To improve the performance of magnetically actuated laminated PnCs composed of HMSMs, a gradient-based topology optimization framework is proposed to maximize the longitudinal elastic wave band gap width. The optimization employs a nonlinear, hyperelastic, compressible Gent material model to describe the constitutive behavior of the composite phases. For band gap extraction, an in-house finite element model is used, where the properties of each finite element are treated as design variables in the topology optimization process. An analytical sensitivity calculation is performed to compute the gradient of the band gap maximization function. A parametric study demonstrates the effectiveness of the model by examining the influence of the external magnetic field on the optimized band gap characteristics and unit cell design of the periodic laminated composite. This optimization framework provides valuable insights for the design of advanced, remotely controlled wave manipulation devices.