Qualitative properties of a continuum theory for thin films

Bernd Schmidt

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Submission date: 13. Sep. 2005
Pages: 42
published in: Annales de l'Institut Henri Poincaré / C, 25 (2008) 1, p. 43-75 
DOI number (of the published article): 10.1016/j.anihpc.2006.09.001
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Abstract:
We discuss qualitative aspects of a continuum theory for thin films. The stored energy density is examined for convexity properties and limiting behavior under large and small strains. A study of the dependence of the theory on relaxation parameters leads to the result that the scale of convergence used to derive the theory from atomic models is the only scale for which a limiting theory that also accounts for atomic relaxation effects is non-trivial.