Antrittsvorlesung: On wrinkling of thin elastic sheets

Date

Nov 11, 2015

Time

5:00 PM - 6:00 PM

Speaker

Prof. Dr. Oliver Sander

Affiliation

TU Dresden, Institut für Numerische Mathematik

Series

TUD Dresdner Mathematisches Seminar

Language

de

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. R. Schilling / Prof. Dr. A. Fischer

Description

Thin sheets show typical wrinkling patterns when loaded in shear. The simulation of such patterns is challenging, because they are highly nonlinear phenomena. One contender for a mathematical model for such wrinkling is a Cosserat-type model recently proposed by Neff. It describes configurations of the sheet as the deformation of the midsurface, together with a field of microrotations, that is, a function mapping the domain into the special orthogonal group SO(3). The numerical treatment of this model is difficult, because the set of admissible configurations of Sobolev smoothness does not form a vector space. In the talk, we present generalizations of standard finite element methods to function spaces with a nonlinear codomain. These generalized FE spaces are H^1 conforming, and we show optimal a priori discretization error bounds. When used to simulate wrinkling patterns of a Cosserat sheet model, we obtain good quantitative agreement with experimental results from the literature.

Links

• Dresdner Mathematisches Seminar

Last modified: Oct 20, 2015, 4:07:50 PM