Applied Maths Seminar: Macaskill -- Wrinkles in thin sheets

When a thin sheet of elastic material is stretched, it can wrinkle, with the wrinkles
aligning with the direction of stretching.  As the applied tension is increased, the
amplitude and number of wrinkles increases.  These general observations can be explained
using the weakly nonlinear Von Karman equations that describe the bending of elastic
plates.  A related problem was discussed this year at the Mathematics in Industry Study
Group (MISG 2007).  When thin steel sheet is cold-pressed between rollers, it sometimes
happens that a small ridge appears near the centre of the sheet.  The ridge may be only
a few centimetres wide, and some millimetres in amplitude, but can extend for tens of
metres or more in the direction of transport of the sheet, rendering the product
useless.  In this talk I will discuss how wrinkles arise in thin elastic sheets and
therefore provide an initiating mechanism for the observed ridge formation in
steel-sheet pressing.