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Buckling of a compressed elastic membrane: a simple model

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  • P. Peyla

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. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Suggested Citation

  • P. Peyla, 2005. "Buckling of a compressed elastic membrane: a simple model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 48(3), pages 379-383, December.
    • Handle: RePEc:spr:eurphb:v:48:y:2005:i:3:p:379-383
    DOI: 10.1140/epjb/e2005-00415-9
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