Eur. Phys. J. B 48, 379-383 (2005)
https://doi.org/10.1140/epjb/e2005-00415-9

Buckling of a compressed elastic membrane: a simple model

Laboratoire de Spectrométrie Physique, UJF - CNRS, 38402 Saint-Martin d'Hères, Cedex, France

Corresponding author: ^a philippe.peyla@ujf-grenoble.fr

Received: 12 August 2005
Published online: 23 December 2005

Abstract

The buckling of a folded membrane submitted to a bi-axial compression is studied in the framework of the continuum non-linear elasticity theory. We show that the formation of the fold patterning can be quantitatively well described with a simple non-linear model. As a matter of fact, with this model, we recover the experimental phase diagram of a secondary buckling instability with a very good precision. In addition, depending on the anisotropy of the applied compressive stress, we find that the buckling coarsening dynamics can be described as a 1D spinodal decomposition (for a uni-axial stress) or as a 2D XY model (for an isotropic bi-axial stress) with an irrotational non-scalar order parameter. For an isotropic bi-axial stress, we indeed recover the famous coarsening exponent: n=1/4. This exponent has to be confirmed experimentally.