Aaron Mowitz PhD Thesis Defense
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. This size depends on the outer dimension of the sheet, but intuition and rudimentary energy balance indicate it should only depend on the sheet thickness. We address this discrepancy by modeling the d-cone tip with a more geometric approach, where we treat the observed core crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the core crescent has its own unique features: the material crescent terminates within the material, and the material extent is much larger than the extent of the crescent. 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 has some particular advantages over previous analyses, as we are able to describe the entire material around the crescent, without having to resort to excluding the core region, as there are no energetic divergences. Finally, we deduce testable relations between the crease and the surrounding sheet, and discuss some of the implications of our approach with regards to the scaling of the crescent size.
Tom Witten (chair)
Aaron is currently searching for postdoctoral positions in physics and science education research.