Designing Elastic Metamaterials with Roton-like and Plateau Dispersion via Topology Optimization

The design of elastic metamaterials with prescribed dispersion curves, which define the relationship between wave frequency and wavenumber, poses significant challenges due to its nonlinear and non-convex nature. This study introduces a novel optimization framework to tailor 2D elastic metamaterials dispersion relations utilizing a genetic algorithm. The proposed method encodes beam configurations in a binary vector and employs topology optimization to evolve structures toward desired dispersion characteristics. By representing dispersion curves with polynomial functions, constraints are applied to ensure the desired properties of monotonic and non-monotonic dispersion bands, such as roton-like and plateau-shaped behaviors. The approach demonstrates its robustness and versatility in achieving diverse dispersion profiles, validated through numerical simulations. Results reveal the ability to create unique wave phenomena by nonlocal interaction, paving the way for on-demand wave manipulation in advanced engineering applications.