PHYSICAL MATHEMATICS SEMINAR


TOPIC:		CRESCENTS, CONES AND STRESS FOCUSING 
		IN A CRUMPLED SHEET


SPEAKER:	DR. SAHRAOUI CHAIEB
		Department of Mechanical Engineering
		Massachusetts Institute of Technology

ABSTRACT:

A crumpled piece of paper is made up of cylindrically curved or nearly
planar regions folded along line-like ridges, which themselves pivot about
point-like peaks; the deformation is focused into these localized objects.  
The localization of deformation in a thin sheet is a consequence that
bending a sheet is energetically cheaper than stretching it.

I will talk about the topology of these objects that we call
developable cones; they consist of a stretched core in which some of the
energy resides and a peripheral region dominated by bending.  Our results
show that the early stages of crumpling are dominated by bending only.

We will show that contrary to zero thickness sheets, the core of such
objects for finite thickness sheets is a crescent shaped line.  The
response of the sheet to buckling is investigated through the measure of
the core size versus the deformation and the measure of the force during
the deformation.  The force was measured directly with force sensors and
indirectly from the sheet profile from which we retrieved information on
the stress focusing in the core region.By studying the interactions
between to conical singularities we show the relevance of this study to
crumpled paper.


DATE:			TUESDAY, OCTOBER 12, 1999

TIME:			2:30 PM

LOCATION:		Building 2, Room 338


Refreshments will be served at 3:30 PM in Building 2, Room 349


					Massachusetts Institute of Technology
					Department of Mathematics
					Cambridge, MA  02139