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تسجيل مستخدم جديدA Theorem on the Compatibility of Spherical Kirigami Tessellations
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We present a theorem on the compatibility upon deployment of kirigami tessellations restricted on a spherical surface with patterned cuts forming freeform quadrilateral meshes. We show that the spherical kirigami tessellations have either one or two compatible states, i.e., there are at most two isolated strain-free configurations along the deployment path. The proof of the theorem is based on analyzing the number of roots of the compatibility condition, under which the kirigami pattern allows a piecewise isometric transformation between the undeployed and deployed configurations. As a degenerate case, the theorem further reveals that neutral equilibrium arises for planar quadrilateral kirigami tessellations if and only if the cuts form parallelogram voids. Our study provides new insights into the rational design of morphable structures based on Euclidean and non-Euclidean geometries.
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The concept of kirigami has been extensively utilized to design deployable structures and reconfigurable metamaterials. Despite heuristic utilization of classical kirigami patterns, the gap between complex kirigami tessellations and systematic design
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The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $dgeq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting tessellation are studi
ed using tools from spherical integral geometry. Also the spherical pair-correlation function of the $(d-1)$-dimensional Hausdorff measure is computed explicitly and compared to its analogue for Poisson great hypersphere tessellations. Finally, the typical cell distribution and the distribution of the typical spherical maximal face of any dimension $kin{1,ldots,d-1}$ are expressed as mixtures of the related distributions of Poisson great hypersphere tessellations. This in turn is used to determine the expected length and the precise birth time distribution of the typical maximal spherical segment of a splitting tessellation.
Kirigami involves cutting a flat, thin sheet that allows it to morph from a closed, compact configuration into an open deployed structure via coordinated rotations of the internal tiles. By recognizing and generalizing the geometric constraints that
enable this art form, we propose a design framework for compact reconfigurable kirigami patterns, which can morph from a closed and compact configuration into a deployed state conforming to any prescribed target shape, and subsequently be contracted into a different closed and compact configuration. We further establish a condition for producing kirigami patterns which are reconfigurable and rigid deployable allowing us to connect the compact states via a zero-energy family of deployed states. All together, our inverse design framework lays out a new path for the creation of shape-morphing material structures.
Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simpl
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