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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 distinction between “reinforcement” and “cloaking” has been overlooked in optimization-based design of devices intended to conceal a defect in an elastic medium. In the former, a so-called “cloak” is severely biased toward one or a few specific elastic disturbances, whereas in the latter, an “unbiased cloak” is effective under any elastic disturbance. We propose a two-stage approach for optimization-based design of elastostatic cloaks that targets true, unbiased cloaks. First, we perform load-case optimization to find a finite set of worst-case design loads. Then we perform topology optimization of the cloak microstructure under these worst-case loads using a judicious choice of the objective function, formulated in terms of energy mismatch. Although a small subset of the infinite load cases that the cloak must handle, these highly nonintuitive, worst-case loads lead to designs that approach perfect and unbiased elastostatic cloaking. In demonstration, we consider elastic media composed of spinodal architected materials, which provides an ideal testbed for exploring elastostatic cloaks in media with varying anisotropy and porosity, without sacrificing manufacturability. To numerically verify the universal nature of our cloaks, we compare the elastic response of the medium containing the cloaked defect to that of the undisturbed medium under many random load cases not considered during design. By using digital light processing additive manufacturing to realize the elastic media containing cloaked defects and analyzing their response experimentally using compression testing with digital image correlation, this study provides a physical demonstration of elastostatic cloaking of a three-dimensional defect in a three-dimensional medium. 

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.