Comptes Rendus
New nonlinear multi-scale models for wrinkled membranes
Comptes Rendus. Mécanique, Volume 341 (2013) no. 8, pp. 616-624.

A new macroscopic approach to the modelling of membrane wrinkling is presented. Most of the studies of the literature about membrane behaviour are macroscopic and phenomenological, the influence of wrinkles being accounted for by nonlinear constitutive laws without compressive stiffness. The present method is multi-scale and it permits to predict the wavelength and the spatial distribution of wrinkling amplitude. It belongs to the family of Landau–Ginzburg bifurcation equations and especially relies on the technique of Fourier series with slowly varying coefficients. The result is a new family of macroscopic membrane models that are deduced from Föppl–von Kármán plate equations. Numerical solutions are presented, giving the size of the wrinkles as a function of the applied compressive and tensile stresses.

Published online:
DOI: 10.1016/j.crme.2013.06.001
Keywords: Wrinkling, Membrane, Slowly variable Fourier coefficients, Multi-scale

Noureddine Damil 1; Michel Potier-Ferry 2, 3; Heng Hu 4

1 Laboratoire dʼingénierie et matériaux, LIMAT, faculté des sciences Ben MʼSik, université Hassan II Mohammedia Casablanca, Sidi Othman, Casablanca, Morocco
2 Laboratoire dʼétudes des microstructures et de mécanique des matériaux, LEM3, UMR CNRS 7239, université de Lorraine, île du Saulcy, 57045 Metz cedex 01, France
3 Laboratory of Excellence on Design of Alloy Metals for Low-Mass Structures (DAMAS), université de Lorraine, France
4 School of Civil Engineering, Wuhan University, 8 South Road of East Lake, 430072 Wuhan, PR China
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     title = {New nonlinear multi-scale models for wrinkled membranes},
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Noureddine Damil; Michel Potier-Ferry; Heng Hu. New nonlinear multi-scale models for wrinkled membranes. Comptes Rendus. Mécanique, Volume 341 (2013) no. 8, pp. 616-624. doi : 10.1016/j.crme.2013.06.001.

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