Aerospace Engineering and Mechanics

University of Chicago

**In this talk we explore the crushing of an thin elastic membrane into a
small sphere. Such crushing occurs when macroscopic sheets are crumpled or when
microscopic membranes are distorted by osmotic or hydrodynamic forces. Crushing
produces singular points of high curvature. We study the interaction between
these singular vertices by energy-balance arguments and by numerical
simulations. We find that two vertices are connected by a characteristic ridge,
whose width and radius of curvature scale as the two-thirds power of the
distance between the vertices. The associated deformation energy scales as the
one-third power of this distance. Thus large, thin sheets have their
deformation energy concentrated in an arbitrarily small fraction of the sheet.
Still, the deformation is weak enough that the sheet may be accurately described
by linear elasticity. With these features in mind we discuss the energy of
confinement for a crushed sheet. The generalization of this crushing to higher
spatial dimensions yields a surprise: the crushing can break symmetry to produce
preferred directions in the membrane.**

**See** **http://arnold.uchicago.edu:80/MRSEC/Nuggets/Crumpling/**

209 Akerman Hall

2:30 p.m. - 3:30 p.m.

Disability accommodations provided upon request.

Contact the Department of Aerospace Engineering and Mechanics , (612) 625-8000.