Tunable Bandgap Design of Soft Phononic Crystals Using Topology Optimization

Soft phononic crystals (PnCs) have significant advantages for tuning bandgaps and undergoing reversible large deformations. However, the difficulty of the design arises from the presence of material and geometrical nonlinearities coupled with the energy band performance. This study presents an effective topological optimization method to realize tunable bandgap designs of mechanism-driven soft PnCs composed of two hyperelastic materials. Based on the material-field series-expansion method, the topology optimization model with a small number of topological design variables is defined as maximizing the bandgaps of PnCs before and/or after stretching. The optimization problem is then solved by a gradient-free algorithm, which eliminates the need for the complex sensitivity analysis. Numerical examples show that using tensile deformation to switch between different acoustic functions can achieve the maintenance, opening, and closing of arbitrary order bandgaps, and the proposed method provides an effective way to design soft PnCs with rapid tunability of bandgaps.