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Talk

Energy scaling law for the regular cone

  • Heiner Olbermann (Rheinische Friedrich-Wilhelms-Universität Bonn, Hausdorff Center for Mathematics)
A3 01 (Sophus-Lie room)

Abstract

When one removes a sector from a circular sheet of paper and glues the edges back together, the resulting shape is approximately conical. Despite the simplicity of the setup, a proof of this 'fact' starting from basic models for thin elastic sheets has not been found yet. In this talk we investigate the scaling of the elastic energy with the sheet thickness $h$ for this setting. Our main innovation is the identification of a suitable technical assumption to work with. Namely, we think of the deformed sheet as an immersed 2-dimensional Riemannian manifold in Euclidean 3-space and assume that the exponential map at the origin (the center of the sheet) supplies a diffeomorphism of some subset of the tangent space at 0 with the whole manifold. Under this assumption, we will show that the elastic energy per unit thickness scales with $h^2|\log h|$, which is the scaling of a (regularized) cone.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss