Year: 2021
Type: preprint
Abstract: The presence of cuts in a thin planar sheet can dramatically alter its mechanical and geometrical response to loading, as the cuts allow the sheet to deform strongly in the third dimension. We use numerical experiments to characterize the geometric mechanics of kirigamized sheets as a function of the number, size and orientation of cuts. We show that the geometry of mechanically loaded sheets can be approximated as a composition of simple developable units: flats, cylinders, cones and compressed Elasticae. This geometric construction yields simple scaling laws for the mechanical response of the sheet in both the weak and strongly deformed limit. In the ultimately stretched limit, this further leads to a theorem on the nature and form of geodesics in an arbitrary kirigami pattern, consistent with observations and simulations. By varying the shape and size of the geodesic in a kirigamized sheet, we show that we can control the deployment trajectory of the sheet, and thence its functional properties as a robotic gripper or a soft light window. Overall our study of random kirigami sets the stage for controlling the shape and shielding the stresses in thin sheets using cuts.
Source: arXiv (Cornell University)
Authors: Chaudhary, Gaurav, Niu, Lauren, Lewicka, Marta, Han, Qing, Mahadevan, L
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G2143730391, G2345624000, G2692471796, G3274770636, G3684603985, Dimension Reduction and Singular Limits of Prestrained Structures, DMREF: Hydrogel-actuated cellular soft robotic materials with programmable mechanical properties, G7982268849, EFRI C3 SoRo: Soft, Strong, and Safe Configurable Robots for Diverse Manipulation Tasks, Materials Research Science and Engineering Center
OpenAlex ID: W4226514347