Kavli Affiliate: L. Mahadevan
| First 5 Authors: Gaurav Chaudhary, Lauren Niu, Marta Lewicka, Qing Han, L Mahadevan
| Summary:
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.
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