Computational design and additive manufacturing of periodic conformal metasurfaces by synthesizing topology optimization with conformal mapping

In this paper, we present a computational framework for computational design and additive manufacturing of free-form periodic metasurfaces. The proposed scheme rests on the level-set-based topology approach and the conformal mapping theory. A metamaterial with pre-specified performance is created using a level-set-based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle during the mapping. With embedded geometric information, the proposed level-set-based optimization methods not only can act as a motivator for design synthesis, but also can be seamlessly hooked with additive manufacturing without the need of CAD reconstructions. The current computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces for different fields of interests. The performance of the proposed scheme is illustrated through two benchmark examples where a negative-Poisson's-ratio unit cell pattern, and a stiff and light inner structure are mapped to 3D free-form surfaces and fabricated through additive manufacturing.