Séminaires
MSC
"Matière et Systèmes Complexes"
Lundi
19 mai 2008 à 11h
Bâtiment Condorcet, 6ème
étage, salle 646 A.
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.