MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

Invertibility and noninvertibility in thin elastic structures

Peter Hornung


The nonlinear elastic energy of a thin film of thickness $h$ is given by a functional $E^h$. Recently, Friesecke, James and Müller derived the $\Gamma$-limits, as $h\to 0$, of the functionals $h^{-\alpha} E^h$ for $\alpha\geq 3$. We study the local invertibility of almost minimizers of these functionals and prove an upper bound for the diameter of preimages. We also prove that almost minimizers are in fact invertible almost everywhere on subdomains which have positive distance from the boundary, and we provide an upper bound for this distance. Then we give two examples which show that the bounds derived in the positive results are optimal. In particular, for all $\alpha\geq 3$ there exist almost minimizers which are two to one on a connected set of nonzero volume.

Jul 11, 2006
Jul 11, 2006
MSC Codes:
thin films, nonlinear elasticity

Related publications

2011 Repository Open Access
Peter Hornung

Invertibility and non-invertibility in thin elastic structures

In: Archive for rational mechanics and analysis, 199 (2011) 2, pp. 353-368