Hierarchical combinatorial design and optimization of non-periodic metamaterial structures

Abstract As advanced manufacturing techniques like additive manufacturing have enabled the fabrication of complex geometries, it is worthwhile to explore potential techniques that can be used to design metamaterial structures to achieve desired behaviors or physical properties. Designing the fine-scale geometry of a metamaterial structure to perform a specific behavior defines an inverse problem that is often intractable. To make this inverse problem tractable, most researchers represent metamaterial structures relying on a single-type periodic unit cell that is repeated in regular grids. Such a representation simplifies modeling and simulation tasks but at the cost of conceivably limiting the spectrum of physical properties that can be achieved by using more than one type of unit cells. This paper defines a non-periodic representation via implicit functions that generate two types of unit cells in pairs, which cope with the geometric frustration of interface connection in non-periodic metamaterial design. To solve the inverse problem of non-periodic metamaterial design, we propose a genetic algorithm-based combinatorial optimization scheme to design light-weight and high-strength functional parts by optimizing relevant parameters in the generating functions of non-periodic unit cells.