Finite Curved Creases in Infinite Isometric Sheets*

Geometric stress focusing, e.g. in a crumpled sheet, creates point-like vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of elastic thin sheets. We address this question by modeling the observed crescent with a more geometric approach: we treat the crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the crescent in a crumpled sheet has features not previously addressed. These features together with the general constraints of isometry lead to constraints linking the surface profile to the crease-line geometry. We construct several examples obeying these constraints, showing finite curved creases are fully realizable. This approach gives new information about the asymptotic shape of the crease, and provides a new viewpoint for explaining the scaling of the crescent size.