PERIODIC FOLDING OF THIN SHEETS

When a thin sheet of a flexible material such as paper is fed from a h orizontal spool towards a rough horizontal plane below it, the sheet f olds on itself in a regular manner. We model this phenomenon as a free boundary problem for a nonlinearly elastic sheet, taking into account the stiffness and weight of the sheet, and the height of the spool ab ove the plane. By using a continuation scheme we solve the problem num erically and follow the evolution of one period of the fold for variou s values of the parameters. The results are found to agree well with o bservations of the folding of paper sheets.