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 email@example.com
Published online: 23 December 2005
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.
PACS: 46.32.+x – Static buckling and instability / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005