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Harnessing instabilities of multicomponent multistable structural assemblies can potentially lead to scalable and reversible functionalities, which can be enhanced by exploring frustration. For instance, standard Kresling origami cells exhibit nontunable intrinsic energy landscapes determined by their geometry and material properties, limiting their adaptability after fabrication. To overcome this limitation, we introduce frustration to enable fine-tuning of the energy landscape and resulting deformation states. By prestressing the Kresling cell by means of special springs with individual control, we induce either global or localized (i.e., crease level) frustration, which allows changing the energy barrier (cell or assembly). We investigate the mechanical behavior of frustrated Kresling assemblies, both theoretically and experimentally, under various loading and boundary conditions. Our findings reveal that changing the frustration state leads to precise control of folding sequences, enabling previously inaccessible folding paths. The proposed concept paves the way for applications in mechanical metamaterials and other fields requiring highly programmable and reconfigurable systems – e.g., prosthetic limbs. 

The concepts of origami and kirigami have often been presented separately. Here, we put forth a synergistic approach—the folded kirigami—in which kirigami assemblies are complemented by means of folding, typical of origami patterns. Besides the emerging patterns themselves, the synergistic approach also leads to topological mechanical metamaterials. While kirigami metamaterials have been fabricated by various methods, such as 3D printing, cutting, casting, and assemblage of building blocks, the “folded kirigami” claim their distinctive properties from the universal folding protocols. For a target kirigami pattern, we design an extended high-genus pattern with appropriate sets of creases and cuts, and proceed to fold it sequentially to yield the cellular structure of a 2D lattice endowed with finite out-of-plane thickness. The strategy combines two features that are generally mutually exclusive in canonical methods: fabrication involving a single piece of material and realization of nearly ideal intercell hinges. We test the approach against a diverse portfolio of triangular and quadrilateral kirigami configurations. We demonstrate a plethora of emerging metamaterial functionalities, including topological phase-switching reconfigurability between polarized and nonpolarized states in kagome kirigami, and availability of nonreciprocal mechanical response in square-rhombus kirigami.