Optimization design of all-angle negative refraction phononic crystals at a specified frequency

All-angle negative refraction (AANR) is an effective way to achieve negative refraction in phononic crystals (PnCs). It is difficult to achieve AANR using a traditional heuristic design. In this work, we propose a novel topology optimization framework for optimizing the material distribution of air/solid PnCs to achieve AANR at a specified frequency. The optimization goal is to minimize the curvature at a specific point of the equal-frequency contours (EFCs), and the Kriging-based material-field series expansion (KG-MFSE) algorithm is adopted to solve the complicated optimization problem. To ensure the connectivity of the air domain inside the unit cell, the virtual temperature technique is employed, and the filtering and threshold projection are used to control the minimum length scale of the air domain. Numerical examples show that the proposed optimization framework is effective for the material design of AANR PnCs, and several optimized design samples were fabricated with additive manufacturing. The corresponding negative refraction is verified through numerical simulation and experiment.