11/28/2022 0 Comments Tessellation in nature#Tessellation in nature full#Nature is full of several types of patterns that are naturally occurring, non-random organized sequences. Altogether, our approach, combining geometry, topology and optimization, highlights the potential for generalized kirigami tessellations as building blocks for shape-morphing mechanical metamaterials. She has taught college level Physical Science and Biology. Finally, we fabricate physical models that deploy in two and three dimensions to validate this inverse design approach. A simple mechanical analysis of the resulting structure allows us to determine and control the stability of the deployed state and control the deployment path. We then encode these conditions into a flexible constrained optimization framework to obtain generalized kirigami patterns derived from various periodic tesselations of the plane that can be deployed into a wide variety of prescribed shapes. We first identify the constraints on the lengths and angles of generalized kirigami tessellations that guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a compact, non-overlapping planar cut pattern. Here we pose and solve the inverse problem of determining the number, size and orientation of cuts that enables the deployment of a closed, compact regular kirigami tessellation to conform approximately to any prescribed target shape in two or three dimensions. However, geometric and topological constraints make the design of such structures challenging. A regular hexagon has 6 sides of equal length, and this shape is seen again and again in the world around us. Abstract:Kirigami tessellations, regular planar patterns formed by partially cutting flat, thin sheets, allow compact shapes to morph into open structures with rich geometries and unusual material properties. Hexagons in Nature: Another of nature’s geometric wonders is the hexagon.
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