DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Eliot Fried, McGill University

**Title: ***
Wrinkling of a stretched thin sheet
*

**Abstract:**
When a thin rectangular sheet is clamped along two opposing edges and stretched,
its inability to accommodate the Poisson contraction near the clamps may lead to
the formation of wrinkles with crests and troughs parallel to the axis of stretch.
A variational model for this phenomenon is proposed. The underlying energy functional
includes bending and membranal contributions. Motivated by work of Cerda, Ravi-Chandar,
and Mahadevan, the functional is minimized subject to a
global constraint on the area of the mid-surface of the sheet.
Analysis of a boundary-value problem for the ensuing Euler-Lagrange equation
shows that wrinkled solutions exist only above a threshold of the applied stretch.
A sequence of critical values of the applied stretch, each element of which corresponds
to a discrete number of wrinkles, is determined. Whenever the applied stretch is
sufficiently large to induce more than one wrinkle, previously proposed scaling relations
for the wrinkle wavelength and root-mean-square amplitude are confirmed. Comparisons with
experimental measurements and numerical results indicate that the analytical results are
remarkably robust.

**Time:** Thursday, Jan. 20, 2010, 1:00-2:00 p.m. (NOTE SPECIAL TIME AND DATE)

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491