Skip to main content
Browse by:
GROUP

Until further notice, in-person public events have been canceled. This includes recruitment events, tours, student programs, reunions, performances, conferences and social events.
Event listings include how to access online content. Contact event sponsor with questions.
Please note that all visitors to campus must comply with Duke’s community safety measures, which include wearing a mask,
check https://returnto.duke.edu/campus-visitors/ before coming to campus, and follow direction provided by campus personnel.

A Variational Perspective on Wrinkling Patterns in Thin Elastic Sheets: What sets the local length scale of tensile wrinkling?

Robert V. Kohn, NYU, Gergen Lecture
Icon calendar
Wednesday, March 20, 2019
Icon time
12:00 pm - 1:00 pm
Icon speaker
Robert V. Kohn (New York University, Courant Institute)
Icon series
Math Department presents Gergen Lectures Seminar

The wrinkling of thin elastic sheets is very familiar: our skin wrinkles, drapes have coarsening folds, and a sheet stretched over a round surface must wrinkle or fold.

What kind of mathematics is relevant? The stable configurations of a sheet are local minima of a variational problem with a rather special structure, involving a nonconvex membrane term (which favors isometry) and a higher-order bending term (which penalizes curvature). The bending term is a singular perturbation; its small coefficient is the sheet thickness squared. The patterns seen in thin sheets arise from energy minimization -- but not in the same way that minimal surfaces arise from area minimization. Rather, the analysis of wrinkling is an example of "energy-driven pattern formation," in which our goal is to understand the asymptotic character of the minimizers in a suitable limit (as the nondimensionalized sheet thickness tends to zero).

What kind of understanding is feasible? Read the complete abstract at https://math.duke.edu/events/82667-variational-perspective-wrinkling-patterns-thin-elastic-sheets-what-sets-local-length