Bandgap design of 3D single-phase phononic crystals by geometric-constrained topology optimization

Phononic crystals (PnCs) possessing desired bandgaps find many potential applications for elastic wave manipulation. Considering the propagating essence of three-dimensional (3D) elastic waves and the interface influence of multiphase material, the bandgap design of 3D single-phase PnCs is crucial and appealing. Currently, the main approaches for designing 3D single-phase PnCs rely on less efficient trial-and-error approaches, which are heavily dependent on researchers' empirical knowledge. In comparison, topology optimization offers a dominant advantage by transcending the restriction of predefined microstructures and obtaining topologies with desired performance. This work targeted the exploration of various novel microstructures with exceptional performance by geometric-constrained topology optimization. To deal with high-dimensional design variables in topology optimization, the unit cell structure of a PnC was confined by pyramid symmetry to maximumly deduct the variable number of the unit cell. More importantly, to alleviate mesh dependence inherent in conventional topology optimization, node-to-node and edge-to-edge connection strategies were adopted, supplemented by the insertion of cylinders to ensure the stability of these connections. Finally, unstable PnC structures were filtered out using extra geometric constraints. Leveraging the proposed framework for the optimization of 3D single-phase PnCs, various novel structures were obtained. Particularly, our results demonstrate that PnC structures with only one type of mass lump exhibit significant potential to possess outstanding performance, and geometric configurations of the ultimately optimized structures are intricately linked to the particular sequence of the bandgaps.