Multi-material topology optimization of phononic crystal considering isotropic/anisotropic materials

Multi-material phononic crystals hold promise for manipulating elastic wave propagation, enhancing the rigidity of the host structure, and realizing multifunctionality, including electric conduction, sound insulation, and heat diffusion. This paper presents a multi-material topology optimization pipeline for phononic crystal design, incorporating both isotropic and anisotropic materials. First, the dispersion theory for elastic wave propagation in periodic structures is presented. Then a novel interpolation function is proposed for multi-material topology optimization by using a variant of the projection operator. Finally, both isotropic and anisotropic materials are utilized to demonstrate the effectiveness of the proposed method for multi-material phononic crystal design when compared with SIMP-based structures. The numerical analysis indicates that the proposed method performs well in optimizing the phononic structure with metal composite materials.