Addressing a physics problem that dates back to Galileo, three University of Massachusetts Amherst researchers this week propose a new approach to the theory of how thin sheets can be forced to conform to “geometrically incompatible” shapes – think gift-wrapping a basketball – that relies on weaving together two fundamental ideas of geometry and mechanics that were long thought to be irreconcilable.
Theoretical physicist Benny Davidovitch, polymer scientist Greg Grason and doctoral student Yiwei Sun, writing in Proceedings of the National Academy of Sciences, suggest and demonstrate via numerical simulations that naturally flat sheets forced to change their curvature can accommodate geometrically-required strain by developing microscopic wrinkles that bend the sheet instead of stretching it to the breaking point, a solution that costs less energy, as well.
This advance is important as biotechnologists increasingly attempt to control the level of strain encountered in thin films conforming to complex, curving and 3D shapes of the human body, for example, in flexible and wearable sensors for personalized health monitoring, they explain. Many of these devices rely on electrical properties of the film which is shown to be highly vulnerable to stretching, but which can tolerate some bending.
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