

Preprint 3/2004
Self-similar folding patterns and energy scaling in compressed elastic sheets
Sergio Conti, Antonio DeSimone, and Stefan Müller
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Submission date: 22. Jan. 2004
Pages: 25
published in: Computer methods in applied mechanics and engineering, 194 (2005) 21/24, p. 2534-2549
DOI number (of the published article): 10.1016/j.cma.2004.07.044
Bibtex
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Abstract:
Thin elastic sheets under isotropic compression,
such as for example blisters formed by thin films which debonded from
the substrate, can exhibit remarkably complex folding patterns.
We discuss the scaling of the elastic energy with respect to the film
thickness, and show that in certain regimes the optimal energy scaling
can be reached by self-similar folding patterns that refine towards
the boundary, in agreement with experimental observations.
We then extend the analysis to anisotropic compression, and discuss
a simplified scalar model which suggests the presence of a
transition between a regime where the deformation is governed by
global properties of the domain and another one where
the direction of maximal compression dominates and the scale of the
folds is mainly determined by the distance to the boundary in the
direction of the folds themselves.