Harvard University Division of Engineering and Applied Sciences Kavli Institute School of Engineering and Applied Sciences Department of Organismic and Evolutionary Biology Harvard University
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Mathematical Drapery

The couturier drapes the three-dimensional human body with a two-dimensional fabric, working hard to subvert the relentless force of gravity to her cause using a combination of cuts, folds and tucks to transform a featureless textile into a piece of art. Indeed the depiction of drapery, in the form of a carelessly thrown shawl on one's knee is an important theme in renaissance art, both in sculpture and in sketching. Modern art has found another expression for the aesthetics of drapery in the carefully orchestrated wrapping of an entire building. Inspired by these observations, we consider the gravity-induced draping of a three-dimensional object with a naturally flat, isotropic elastic sheet. As the size of the sheet increases, we observe the appearance of new folded structures of increasing complexity which arise due to the competition between elasticity and gravity. We analyze some of the simpler 3-dimensional structures by determining their shape, and analyzing their response and stability, and show that these structures can easily switch between a number of metastable configurations. For more complex draperies, we derive scaling laws for the appearance and disappearance of new length scales.

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   Last Updated: January 31, 2018

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