PHYSICAL MATHEMATICS SEMINAR


TOPIC:		SINGULARITIES IN THE DEFORMATIONS OF ELASTIC PLATES


SPEAKER:	AREZKI BOUDAOUD
		Department of Mechanical Engineering
		Massachusetts Institute of Technology

ABSTRACT:

Elastic plates were shown to exhibit singularities when deformed.  These
singularities are due to the concentration of energy into ridges (linear
singularities) or developable cones (point-like singularities).  In the
small thickness limit, the ridge energy is dominant. We show that in
practice, this limit is usually not reached so that the d-cones are
dominant.  We study experimentally, numerically and theoretically two
generic model situations.  In the first, a clamped plate is pushed down.  
Two then four d-cones are observed.  The four d-cones form a diamond,
which rotates and is transformed into a trapezoid. The numerics show good
agreement with the force vs. displacement curve. The energy of the plate
is estimated using geometrical arguments.  In the second situation, a
ridge is compressed longitudinally. It becomes unstable by branching or by
bending.  A theoretical analysis accounts for the instability and the
energy of the plate.  The consequences to the cascade to small scales in
crumpled paper are discussed.

DATE:		TUESDAY, MAY 9, 2000

TIME:		2:30 PM

LOCATION:	Building 2, Room 338

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


					Massachusetts Institute of Technology
					Department of Mathematics
					Cambridge, MA  02139