Topology optimization of multifunctional porous phononic crystals and customized in-plane mechanical performance

• An effective optimization framework for designing multifunctional porous phononic crystals is proposed. • Floating projection constraints to avoid weak elements in optimization and obtain a smooth 0/1 design. • Optimization methods have achieved customization of mechanical performance (static stiffness and negative Poisson’s ratio). • Lower symmetry is used to increase bandwidth under the constraint of negative Poisson’s ratio. • The mechanical performance and wave propagation are investigated to validate the effectiveness of the method. Incorporating the porous characteristics inspired by bio-materials into the phononic crystal (PnC) structure may lead to a more extensive range of properties or new functional spaces. On the contrary, the mechanical deficiencies in PnCs, apart from the band gap (BG) characteristics, pose challenges for engineering applications. Therefore, a floating projection topology optimization (FPTO) framework is proposed here to design new porous PnCs for wider BGs and in-plane mechanical performance. With the aim of PnCs with smooth structural boundaries in the course of the optimization, the floating projection constraints with linear interpolation model are adopted to attain smooth design. The elastic tensor of the structure is solved using homogenization methods, and in-plane mechanical properties are characterized by relevant components, including the bulk modulus and shear modulus reflecting static stiffness , alongside a negative Poisson’s ratio. Some cases are presented, and the effects of BG order, mechanical properties, volume fraction, and symmetry on bandwidth are discussed, which demonstrates that this method flexibly and precisely achieves inverse and customized multifunctional PnCs design. The effectiveness of the method was further validated by simulation and experiment of mechanical performance. An effective optimization framework for designing multifunctional porous PnCs is proposed, facilitating the integration of different function requirements for practical applications.