Computational design and additive manufacturing of conformal metasurfaces by combining topology optimization with Riemann mapping theorem

In this paper, we present a computational framework for computational design and additive manufacturing of spatial free-form periodic metasurfaces. The proposed scheme rests on the level-set based topology approach and the conformal mapping theory. A 2D unit cell of metamaterial with tailored effective properties is created using the 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 when mapping the 2D design to a 3D surface. 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 with no need of CAD reconstructions. The proposed computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces in different fields of interest. The performance of the proposed scheme is illustrated through a benchmark example where a negative-Poisson's-ratio unit cell pattern is mapped to a 3D human face and fabricated through additive manufacturing.