Fri September 2nd 2016
11:00 – 12:00
Seminar Imposing curvature on solid sheets: From instability to isometry
Benny Davidovitch


Imposing a curved shape on a solid sheet, generates in it elastic stress. This familiar motif is a consequence of Gauss’ theorema Egregium, which posits that there exists no isometric map between two surfaces of different Gaussian curvatures. This coupling between geometry (curvature) and mechanics (stress) underlies the morphological richness observed in solid sheets, and their nontrivial response to exerted forces. In this talk I will attempt to provide a unifying framework for this geometry-mechanics interplay, using the concept of “asymptotic isometry” that characterizes the state of a very thin sheet under very weak loads. Focusing on two problems – twisting a ribbon and poking a floating sheet – I will demonstrate how specific parameter regimes are characterized by distinct mechanisms through which the Gaussian curvature is accommodated or repelled by the solid sheet. Novel morphological transitions between wrinkled, folded, and crumpled configurations are predicted to emerge at the borderlines between distinct parameter regimes.

Different types of configurations exhibited by a twisted ribbon (adapted from Chopin & Kudroli, Phys. Rev. Lett. 2013)
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing