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In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface can be designed. We then present a more general method that specifies a fixed lattice of kirigami cuts to be performed on a flat sheet. This single pluripotent lattice of cuts permits a wide variety of target surfaces to be programmed into the sheet by varying the folding directions. Significance How can flat surfaces be transformed into useful three-dimensional structures? Recent research on origami techniques has led to algorithmic solutions to the inverse design problem of prescribing a set of folds to form a desired target surface. The fold patterns generated are often very complex and so require a convoluted series of deformations from the flat to the folded state, making it difficult to implement these designs in self-assembling systems. We propose a design paradigm that employs lattice-based kirigami elements, combining the folding of origami with cutting and regluing techniques. We demonstrate that this leads to a pluripotent design in which a single kirigami pattern can be robustly manipulated into a variety of three-dimensional shapes.

Light-emitting diodes (LEDs) become an attractive alternative to conventional light sources due to high efficiency and long lifetime. However, different material properties between GaN and sapphire cause several problems such as high defect density in GaN, serious wafer bowing, particularly in large-area wafers and poor light extraction of GaN-based LEDs. Here, we suggest a new growth strategy for high efficiency LEDs by incorporating silica hollow nanospheres (S-HNS). In this strategy, S-HNSs were introduced as a monolayer on a sapphire substrate and the subsequent growth of GaN by metalorganic chemical vapor deposition results in improved crystal quality due to nano-scale lateral epitaxial overgrowth. Moreover, well-defined voids embedded at the GaN/sapphire interface help scatter lights effectively for improved light extraction and reduce wafer bowing due to partial alleviation of compressive stress in GaN. The incorporation of S-HNS into LEDs is thus quite advantageous in achieving high efficiency LEDs for solid-state lighting.

In this paper we discuss the transformation of a sheet of material into a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. Each choice of hierarchical cut motif and cut level allows the material to expand into a unique structure with a unique set of properties. We can reverse-engineer the desired expanded geometries to find the requisite cut pattern to produce it without changing the physical properties of the initial material. The concept was experimentally realized and applied to create an electrode that expands to >800% the original area with only very minor stretching of the underlying material. The generality of our approach greatly expands the design space for materials so that they can be tuned for diverse applications.

We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface can be designed. We then present a more general method that specifies a fixed lattice of kirigami cuts to be performed on a flat sheet. This single \"pluripotent\" lattice of cuts permits a wide variety of target surfaces to be programmed into the sheet by changing the folding directions.

In this paper we explore and develop a simple set of rules that apply to cutting, pasting, and folding honeycomb lattices. We consider origami-like structures that are extinsically flat away from zero-dimensional sources of Gaussian curvature and one-dimensional sources of mean curvature, and our cutting and pasting rules maintain the intrinsic bond lengths on both the lattice and its dual lattice. We find that a small set of rules is allowed providing a framework for exploring and building kirigami -- folding, cutting, and pasting the edges of paper.