Séminaires MSC
"Matière et Systèmes Complexes"


Lundi 19 mai 2008 à 11h30
Bâtiment Condorcet, 6ème étage, salle 646 A.

Tom Witten
(Physical Sciences Collegiate, Chicago)

Induced singularities in smoothly deformed elastic sheets

When a thin sheet is gradually confined in a smaller and smaller volume, it deforms to make sharp ``vertices". This talk considers {\it induced} singularities that arise from the interaction of these ``vertex" singularities with their environment. For example, if two vertices are present, the curvature on the line joining them also diverges, forming the familar ridge singularity [1]. Other induced singularities are coming to light. Here we consider two such singularities. The first is the induced vertex at the boundary [2] of a disk that has been compressed until it contains two interior vertices. Asymptotically, the triangular region bounded by the two interior vertices and the induced one becomes arbitrarily flat as the sheet thickness goes to zero, while the curvature outside approaches a nonzero limit. The second singularity appears when a vertex is formed by forcing a flat sheet into a circular ring so that the sheet buckles. Then the ring force induces a singular radial curvature in the sheet. Remarkably this curvature just sufficient to make the mean curvature vanish where the the ring contacts the sheet [3]. We explore the generality of the phenomenon of induced elastic singularities.