Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.
Properties of translation operator and the solution of the eigenvalue and boundary value problems of arbitrary space–time periodic metamaterials
