To lower costs and improve efficiency, most additively manufactured parts are printed as thin shells filled with a lightweight cellular material, which reacts to secondary stresses and provides distributed support to the load-carrying outer casing. This paper proposes a two-step method to design filling metamaterials that are intrinsically strong, stiff and lightweight. First, the space is divided into repetitive volumes according to available three-dimensional tessellation schemes. The tessellation is then transformed into a trabecular wireframe by converting each unit volume into a kinematically-rigid open cell with edge beams and bracings. Dimensional analysis allows the lattice structures to be characterized mechanically and elastically with a finite number of simple computational analyses. The paper shows that the properties of metamaterials with triangular, square and hexagonal prismatic cells compare favourably with state-of-the art porous materials like foams and honeycombs.
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