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Propagating transition fronts, in which local interactions sequentially trigger state changes, are widely observed across natural, biological, and engineered systems. While such propagation has been engineered using energy-driven…
Manipulation of thin sheets by folding and cutting offers opportunity to engineer structures with novel mechanical properties, and to prescribe complex force-displacement relationships via material elasticity in combination with the…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
The Miura ori is a very classical origami pattern used in numerous applications in Engineering. A study of the shapes that surfaces using this pattern can assume is still lacking. A constrained nonlinear partial differential equation (PDE)…
We combine large-scale atomistic modelling with continuum elastic theory to study the shapes of graphene sheets embedding nanoscale kirigami. Lattice segments are selectively removed from a flat graphene sheet and the structure is allowed…
Kirigami metamaterial sheets and tubes, owing to their capacity to undergo large elastic deformations while developing three-dimensional surface textures, have enormous potential as skins for soft robots. Here, we propose to use kirigami…
Consider an oriented curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$. Thinking of $D$ as a piece of paper, one can make a curved folding in the Euclidean space $\boldsymbol R^3$. This can be expressed as the image of an…
Traditional origami starts from flat surfaces, leading to crease patterns consisting of Euclidean vertices. However, Euclidean vertices are limited in their folding motions, are degenerate, and suffer from misfolding. Here we show how…
Flat electronic bands with tunable structures offer opportunities for the exploitation and manipulation of exotic interacting quantum states. Here, we present a controllable route to construct easily tunable flat bands in folded graphene,…
Miniature robots provide unprecedented access to confined environments and show promising potential for novel applications such as search-and-rescue and high-value asset inspection. The capability of body deformation further enhances the…
Transitions of multistability in structures have been exploited for various functions and applications, such as spectral gap tuning, impact energy trapping, and wave steering. However, a fundamental and comprehensive understanding of the…
For origami structures, perforating or cutting slits along creases is an effective method to define fold lines and alleviate stress concentrations at vertices. In this letter we show numerically and experimentally that for…
The art and science of folding intricate three-dimensional structures out of paper has occupied artists, designers, engineers, and mathematicians for decades, culminating in the design of deployable structures and mechanical metamaterials.…
Kirigami, the Japanese art of paper cutting, has recently enabled the design of stretchable mechanical metamaterials that can be easily realized by embedding arrays of periodic cuts into an elastic sheet. Here, we exploit kirigami…
We study, experimentally and theoretically, the mechanical response of sheet materials on which line cracks or cuts are arranged in a simple pattern. Such sheet materials, often called kirigami (the Japanese words, kiri and gami, stand for…
Rigid origami is a branch of origami with great potential in engineering applications to deal with rigid-panel folding. One of the challenges is to compactly fold the polyhedra made from rigid facets with a single degree of freedom. In this…
Kirigami tessellations, regular planar patterns formed by cutting flat, thin sheets, have attracted recent scientific interest for their rich geometries, surprising material properties and promise for technologies. Here we pose and solve…
Bistable mechanical systems exhibit two stable configurations where the elastic energy is locally minimized. To realize such systems, origami techniques have been proposed as a versatile platform to design deployable structures with both…
Origami-inspired self-deployable structures offer lightweight, compact, and autonomous deployment capabilities, making them highly attractive for aerospace and defence applications, such as solar panels, antennas, and reflector systems.…
We present a theorem on the compatibility upon deployment of kirigami tessellations restricted on a spherical surface with patterned slits forming freeform quadrilateral meshes. We show that the spherical kirigami tessellations have either…