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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
82/2005

On the passage from atomic to continuum theory for thin films

Bernd Schmidt

Abstract

We give a rigorous derivation of continuum theory from atomic models for thin films as proposed by Friesecke and James in [JMPS 48 (2000)]. The resulting continuum energy expression is obtained by integrating a stored energy density which not only depends on the deformation gradient but also on $\nu-1$ director fields when $\nu$ is the (fixed) number of atomic film layers.

Received:
Sep 13, 2005
Published:
Sep 13, 2005

Related publications

inJournal
2008 Journal Open Access
Bernd Schmidt

On the passage from atomic to continuum theory for thin films

In: Archive for rational mechanics and analysis, 190 (2008) 1, pp. 1-55