# Science at the triple point between mathematics, mechanics and materials science

## Publication 22

### Energy scaling laws for conically constrained thin elastic sheets

##### Authors:

Jeremy Brandman
Corporate Strategic Research Laboratory
ExxonMobil Research and Engineering Company

Robert V Kohn
Courant Institute of Mathematical Sciences
New York University

Hoai-Minh Nguyen
Department of Mathematics
University of Minnesota

##### Abstract:
We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet's center is of order$h| \log h|$, where $h << 1$ is the thickness of the sheet, we establish matching upper and lower bounds of order $h2| \log h|$ for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.
##### Get the paper in its entirety
EnergyscalingKohn.pdf

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