Method for flat-foldable curved Miura-ori tessellations

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Abstract

Miniaturizing mechanical tessellations with rigid origami behavior is difficult since rigid origami can only be approached in real mechanical systems. Rigid-origami means that the fold-lines have zero stiffness, and the facets have infinite stiffnes. However, zero stiffness and infinite stiffness can physically not be obtained. To approach the rigid-origami behavior in mechanical tessellation, the stiness of the fold-lines must be reduced. To acquire this low stiness on a micron scale, it is chosen to explore a manufacturing method that uses
at material. These at foldable curved tessellations could be used to compensate for the naturally occurring out-of-plane bending of the free edges when at foldable Miura-ori is bend into a cylindrical shell or tube. To compensate for this behavior a legitimate design variation on the Miura-ori pattern has been defined to create a curvature in the folded Miura-ori tessellation. Simulations are used to explore the behavior of the curvature for different parameters of the design variation. Additionally, simulations are performed to explore the behavior of the bend sheet when bend into a Miura-ori tube tessellation. From this simulation the variation indeed showed a curvature for the sheet tessellation and a reduction in curvature of the tube tessellation. To validate if a real mechanical tessellation would show similar curvature in a folded state. A titanium tessellation has been chemically etched and mechanically folded using special
made mold-stamps. The mechanical titanium sheet tessellations shows a curvature in the folded state, but the curvature is smaller, which is an expected result due to rigid-origami assumptions in the iso-geometric-analysis(IGA) model.