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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
47/2014

Transition between planar and wrinkled regions in uniaxially stretched thin elastic film

Peter Bella

Abstract

We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal energy can be written as a minimum of the underlying (convex) relaxed problem plus a term, which grows linearly in the thickness of the film. We show that in the limit of vanishing thickness the prefactor in the scaling law for the original problem can be obtained by minimization of simpler {\it scalar} constrained variational problems.

Received:
Apr 11, 2014
Published:
Apr 22, 2014

Related publications

inJournal
2015 Repository Open Access
Peter Bella

The transition between planar and wrinkled regions in a uniaxially stretched thin elastic film

In: Archive for rational mechanics and analysis, 216 (2015) 2, pp. 623-672