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- W3100706341 abstract "We consider a thin elastic sheet in the shape of a disk whose reference metric is that of a singular cone. That is, the reference metric is flat away from the center and has a defect there. We define a geometrically fully nonlinear free elastic energy and investigate the scaling behavior of this energy as the thickness h tends to 0. We work with two simplifying assumptions: Firstly, we think of the deformed sheet as an immersed 2-dimensional Riemannian manifold in Euclidean 3-space and assume that the exponential map at the origin (the center of the sheet) supplies a coordinate chart for the whole manifold. Secondly, the energy functional penalizes the difference between the induced metric and the reference metric in $$L^infty $$ (instead of, as is usual, in $$L^2$$ ). Under these assumptions, we show that the elastic energy per unit thickness of the regular cone in the leading order of h is given by $$C^*h^2|log h|$$ , where the value of $$C^*$$ is given explicitly." @default.
- W3100706341 created "2020-11-23" @default.
- W3100706341 creator A5004156369 @default.
- W3100706341 date "2015-10-07" @default.
- W3100706341 modified "2023-09-26" @default.
- W3100706341 title "Energy Scaling Law for the Regular Cone" @default.
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- W3100706341 doi "https://doi.org/10.1007/s00332-015-9275-4" @default.
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